&EPA
           United States
           Environmental Protection
           Agency
           Environmental Research
           Laboratory
           Athens, GA 30613
EPA 600-3-90/012
Feb 1990
           Research and Development
Expert System for
Hydrodynamic Mixing
Zone Analysis of
Conventional and Toxic
Submerged Single Port
Discharges (CORM1X1)

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                                 EPA/600/3-90/012
                                 February 1990
  EXPERT SYSTEM FOR HYDRODYNAMIC MIXING ZONE
 ANALYSIS OF CONVENTIONAL AND TOXIC SUBMERGED
       SINGLE PORT DISCHARGES (CORMIX1)

                      by

    Robert L. Doneker and Gerhard H. Jirka

        DeFrees Hydraulics Laboratory
School of Civil and Environmental Engineering
              Cornell University
           Ithaca, New York  14853
      Cooperative Agreement No. CR813093
               Project Officer:
           Thomas 0. Barnwell, Jr.
              Assessment Branch
      Environmental Research Laboratory
               Athens, Georgia
      ENVIRONMENTAL RESEARCH LABORATORY
      OFFICE OF RESEARCH AND DEVELOPMENT
     U.S. ENVIRONMENTAL PROTECTION AGENCY
            ATHENS, GEORGIA  30613

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                           DISCLAIMER

     The information in this document has been funded wholly or
in part by the United States Environmental Protection Agency
under Cooperative Agreement Number CR813093 to Cornell University.
•It has been subjected to the Agency's peer and administrative
review, and it has been approved for publication as an EPA
document.
                               11

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                            FOREWORD


      As environmental controls become more costly to implement
and the penalties of judgment errors become more severe, en-
vironmental quality management requires more efficient manage-
ment tools based on greater knowledge of the environmental
phenomena to be managed.  As part of this Laboratory's research
on the occurrence, movement, transformation, impact, and control
of environmental contaminants, the Assessment Branch develops
state-of-the-art mathematical models for use in water quality
evaluation and management.

     Special water quality regulations have been proposed to
limit lethal acute concentrations of toxic pollutants to a
spatiallly restricted toxic dilution zone.  Predictive mathe-
matical models are used to establish the initial dilution of a
given discharge and the characteristics of its mixing zone.  To
assist the analyst in choosing the appropriate models, deter-
mining the limits of applicability, and establishing data needs,
an expert system has been developed.  The structured computer
program uses knowledge and inference procedures that would be
used by water quality experts.  Operated on a personal computer,
the program appears to be a highly flexible tool for regulatory
analysis that is adaptable to the evaluation of alternatives
in engineering design.


                                Rosemarie C. Russo, Ph.D.
                                Director
                                Environmental Research Laboratory
                                Athens, Georgia
                               111

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                              ABSTRACT


      U.S. water quality policy includes the concept of a mixing
zone, a limited area or volume of water where the initial dilution
of a discharge occurs.  Water quality standards apply at the edge
and outside the mixing zone.   The implementation of this policy
in the permitting process places the burden of prediction of ini-
tial dilution on both regulators and dischargers.  Dischargers of
aqueous toxic substances are subject to additional mixing zone
requirements.  Give a myriad of possible discharge configurations,
ambient environments, and mixing zone definitions, the analyst
needs considerable training and expertise to conduct accurate and
reliable mixing zone analysis.

     The Cornell Mixing Zone Expert System (CORMIX1) was developed
to predict the dilution and trajectory of a submerged single port
discharge of arbitrary density  (positive, neutral, or negative)
into a stratified or uniform density ambient environment with or
without crossflow.  CORMIX1 uses knowledge and inference rules
based on hydrodynamic expertise to classify and predict buoyant
jet mixing.  CORMIX1 gathers the necessary data, checks for data
consistency, assembles and executes the appropriate hydrodynamic
models, interprets the results of the simulation in terms of the
legal requirements including toxic discharge criteria, and sug-
gests design alternatives to improve dilution characteristics.

     CORMIXl, with its emmpasis on rapid intitial mixing, assumes
a conservative pollutant discharge neglecting any physical, chem-
ical, or biological reaction or decay process.  The predictive
results can be readily converted, however, to adjust for first-
order reaction processes.

     The results of the hydrodymanic simulations are in good to
excellent agreement with field and laboratory data.  In particular,
CORMIXl correctly predicts highly complex discharge situations
involving boundary interactions, dynamic bottom attachments, in-
ternal layer formation, and buoyant intrusions--all features that
are beyond the predictive capabilities of other currently avail-
able initial mixing models.

    This report was submitted in partial fulfillment of Coopera-
tive Agreement No. CR813093 with Cornell University under the
sponsorship of the U.S. Environmental Protection Agency.  This
report covers a period from July 1986 to July 1989, and work was
completed as of July 1989.
                                IV

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                         CONTENTS

Abstract	   iv

Acknowledgments 	     xv

                         Chapter  I

INTRODUCTION AND LEGAL BACKGROUND 	    1

1.1 Introduction  	    1
1.2 Overview of U.S. Water Quality Policy 	    2
1.2.1 The Federal Water Pollution Control Act of
    1972	    4
1.2.2 The Clean Water Act of 1977	    6
1.3 The Concept of Mixing Zones	9
1.3.1 Mixing Zones: Development and Regulations ....  9
1.3.2 Special Mixing Zone Requirements for
    Toxic Substances	   13
1.4 Regulatory Assessment of Discharges and the
    Permitting Process  	   14
1.4.1 The NPDES Permit System	   14
1.4.2 Need for Regulatory Assessment Tools	14
1.4.3 Motivation for Expert Systems Approach  ....   15
1.5 CORMIX1: An Expert System for Mixing Zone
    Analysis of Submerged Single Port Aquatic
    Discharges	   18
1.5.1 Scope and Objective	   18
1.5.2 Results of an Earlier Feasibility Study ....   19
1.5.3 Summary of Present Study	   19


                        Chapter II

HYDRODYNAMIC ELEMENTS OF MIXING PROCESSES 	   21

2.1. Buoyant Jet Mixing Processes 	   23
2.1.1 Description of Turbulent Jets and Plumes  ...   23
2.1.2 Dimensional Analysis of Buoyant Jets  	   24
2.1.2.1 Simple Jet in Stagnant Uniform
    Environment	   25
2.1.2.2 Simple Plume in Stagnant Uniform
    Environment	27
2.1.2.3 Generalizations: Jet/Plume Interactions,
    Crossflow Effects, and Stratification Effects  .  .   29
2.1.3 Length Scales	32
2.1.3.1 Discharge Length Scale   	   32
2.1.3.2 Jet/Crossflow Length Scale  	   32
2.1.3.3 Plume/Crossflow Length Scale  	   33

                            v

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2.1.3.4 Jet/Plume Length Scale  	   33
2.1.3.5 Jet/Stratification Length Scale 	   33
2.1.3.6 Plume/Stratification Length Scale 	   34
2.1.4 Typical Flow Regimes of Unconfined Buoyant
    Jets	   34
2.1.4.1 Weakly Deflected Jet In Crossflow 	   35
2.1.4.2 Strongly Deflected Jet In Crossflow 	   36
2.1.4.3 Weakly Deflected Plume in Crossflow 	   37
2.1.4.4 Strongly Deflected Plume in Crossflow ....   37
2.1.4.5 Horizontal Jet with Vertical Buoyant
    Deflection	   38
2.1.4.6 Vertical Plume with Horizontal Momentum
    Deflection	   39
2.2.4.7 Vertical Jet in Linear Stratification ....   40
2.2 Buoyant Spreading Processes 	   41
2.2.1 Buoyant Surface Spreading 	   41
2.2.2 Buoyant Bottom Spreading  	   44
2.2.3 Buoyant Spreading at Pycnocline 	   44
2.2.4 Buoyant Spreading at Terminal Level 	   44
2.3 Passive Ambient Diffusion Processes 	   46
2.3.1 Diffusion in Unbounded Channel Flow	   46
2.3.2 Horizontal Diffusion in Unbounded Channel
    Flow	   48
2.3.3 Vertical Diffusion in Stratified Shear Flow .  .   49
2.4 Interaction Processes: Surface or Bottom
    Boundaries, and Internal Layer Formation  ....   49
2.4.1 Near-Horizontal Surface Approach  	   50
2.4.2 Near-Vertical Surface Impingement with
    Buoyant Upstream Spreading  	   54
2.4.3 Near-Vertical Surface Impingement with
    Full Vertical Mixing	   57
2.4.4 Bottom Interaction Processes  	 57
2.4.4.1 Wake Attachment 	   58
2.4.4.2 Coanda Attachment 	   60
                        Chapter III

HYDRODYNAMIC FLOW CLASSIFICATION  	   61

3.1 Ambient and Discharge Data: Geometry and Flow
    Variables	   61
3.1.1 Ambient Geometry and Flow Conditions	   61
3.1.2 Ambient Density Stratification  	   62
3.1.3 Discharge Parameters  	   64
3.2 Near-field Flow Classification  	   66
3.2.1 General Procedure 	   68
3.2.2 Flow Classes S for Linear Ambient
    Stratification  	   75
3.2.3 Flow Classes V or H for Buoyant Discharges
    into Uniform Ambient Layers 	   76
3.2.4 Flow Classes NV or NH for Negatively
    Buoyant Discharges in Uniform Ambient Layers   .  .   77
3.2.5 Flow Classes (..)A for Bottom Attached

                            vi

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    Flows	   78
3.3 Far-Field Flow Behavior	   79
                        Chapter IV

EXPERT SYSTEM CORMIX1: GENERAL FRAMEWORK  	   81

4.1 Background on Expert Systems and Logic
    Programming	   82
4.2 Structure of CORMIX1	   85
4.2.1 Data Input Element: DATIN	   85
4.2.2 Parameter Computation Element: PARAM  	   89
4.2.3 Flow Classification Element: CLASS  	   89
4.2.4 Hydrodynamic Simulation Element: HYDRO  ....   91
4.2.5 Hydrodynamic Simulation Summary Element: SUM   .   91


                         Chapter V

CORMIX1: FLOW PROTOCOLS AND SIMULATION MODULES  ...   93

5.1 Flow Protocols	   93
5.1.1 Flow Protocols for Buoyant Discharges into
    Uniform Ambient Layers (Flow Classes V and H)  .  .   96
5.1.2 Flow Protocols for Negatively Buoyant
    Discharges into Uniform Ambient Layers (Flow
    Classes NV and NH)  	101
5.1.3 Flow Protocols for Discharges Trapped in
    Linearly Stratified Ambients  (Flow Class S)  .  .  .  101
5.1.4 Flow Protocols for Bottom Attached Flows
    (Flow Classes (..)A)  	107
5.2 Hydrodynamic Simulation Modules 	  107
5.2.1 Simulation Modules for Buoyant Jet Near-Field
    Flows	110
5.2.1.1 Introductory Comments 	  110
5.2.1.1 Discharge Module (MOD01)   	  Ill
5.2.1.2 Weakly Deflected Jet In Crossflow (MOD11,
    mdnf)	112
5.2.1.3 Weakly Deflected Wall Jet in Crossflow
    (MOD12, mdnf-wj)  	  113
5.2.1.4 Near-Vertical Jet in Linear Stratification
    (MOD13, mdls-v)  	  113
5.2.1.5 Near-Horizontal Jet in Linear Stratification
    (MOD14, mdls-h)  	  114
5.2.1.6 Strongly Deflected Jet In Crossflow
    MOD16, mdff)   	  114
5.2.1.8 Strongly Deflected Wall Jet in Crossflow
    (MOD17, mdff-wj)  	  115
5.2.1.4 Weakly Deflected Plume in Crossflow (MOD21,
    bdnf)	115
5.2.1.9 Strongly Deflected Plume in Crossflow
    (MOD22,bdff)   	  115
5.2.2 Simulation Modules for Boundary Interaction
                           vii

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    Processes	116
5.2.2.1 Near-Horizontal Surface/Bottom/Pycnocline
    Approach (MOD31)   	  116
5.2.2.2 Near-Vertical Surface/Bottom/Pycnocline
    Impingement with Buoyant Upstream Spreading
    (MOD32)	117
5.2.2.3 Near-Vertical Surface/Bottom/Pycnocline
    Impingement with Full Vertical Mixing (MOD33) .   .  118
5.2.2.4 Near-Vertical Surface/Bottom/Pycnocline
    Impingement with Unstable Recirculation, Buoyant
    Restratification, and Upstream Spreading
    (MOD34)	118
5.2.2.5 Stratified Terminal Layer Impingement with
    Buoyant Upstream Spreading (MOD36)  	  118
5.2.2.6 Stratified Near-Vertical Surface Injection
    with Upstream Spreading (MOD37)  	  119
5.2.3 Simulation Modules for Buoyant Spreading
    Processes	119
5.2.3.1 Buoyant Surface/Bottom Spreading (MOD41)  .   .  119
5.2.3.2 Buoyant Terminal Layer Spreading (MOD42)  .   .  120
5.2.4 Simulation Modules for Attachment/Detachment
    Processes	120
5.2.4.1 Wake Recirculation (MOD51)  	  120
5.2.4.1 Lift-Off/Fall-Down (MOD52)  	  120
5.2.5 Simulation Modules for Ambient Diffusion
    Processes	120
5.2.5.1 Passive Diffusion in Uniform Ambient
    (MOD61)	121
5.3.5.4 Passive Diffusion in Stratified Ambient
    (MOD62)	121
5.3 Transition Rules, Flow Criteria and Coefficient
    Values	121
5.3.1 Transition Rules  	  122
5.3.2 Flow Classification Criteria  	  122
5.3.3 Terminal Layer Expressions  	  128
5.3.4 Model Coefficient Values  	  128
                        Chapter VI

SYSTEM EVALUATION AND VERIFICATION   	   133

6.1 Buoyant Jets in Unconfined Ambient	134
6.1.1 Comparison With Experimental Data	134
6.1.1.1 Stagnant Ambient   	   134
6.1.1.2 Flowing Unstratified Ambient   	   137
6.1.1.2.1 Pure Jets In Crossflow	137
6.1.1.2.2 Buoyant Jets in  Crossflow  	   141
6.1.1.2.3 Negatively Buoyant Jets in Crossflow   .  .  .   141
6.1.1.2.4 Buoyant Jets with Three-Dimensional
    Trajectories  	   141
6.1.1.3 Buoyant Jet in Stratified Stagnant Ambient   .   147
6.1.2 Comparison of Predictions With Jet Integral
    Models	150

                           viii

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6.1.2.1 Buoyant Jet in Uniform Crossflow  	  150
6.1.2.2 Buoyant Jet in Stratified Crossflow  	  150
6.2 Complex Flows With Boundary Interaction  	  153
6.2.1 Jet Flows in Shallow Receiving Waters  	  153
6.2.2 Strongly Buoyant Jets in Shallow Receiving
    Waters	153
6.2.3 Flows with Wake Interaction	156
6.2.4 Negatively Buoyant Flows With Upstream
    Spreading Along Bottom  	  158
6.3 Summary and Appraisal	158
                        Chapter  VII

APPLICATIONS OF CORMIX1 .	161

7.1 AB Chemical Corporation	161
7.1.1 The Problem Statement	161
7.1.2 CORMIX1 Analysis  	  162
7.2 MN Municipal Treatment Plant  	  169
7.2.1 The Problem Statement	169
7.2.2 CORMIX1 Analysis  	  169
7.3 PQ Power Company	174
7.2.1 The Problem Statement	174
7.3.2 CORMIX1 Analysis  	  176
7.4 Comments on the Application of CORMIX1	179
7.4.1  Limitations of CORMIX1	179
7.4.2  Hints for CORMIX1 Use in Extreme
    Conditions	181
7.4.2.1  (Near-)Surface Discharges  	  181
7.4.2.2  Elevated Discharges  	  182
7.4.3  Application to Non-Dimensional Coordinate
    Systems	182
7.4.4 Adaptation to First-Order Reaction
    Processes	  183

                        Chapter  VIII

CONCLUSIONS AND RECOMMENDATIONS 	  184

REFERENCES	186


                        Appendix A

STABILITY OF STRATIFIED AMBIENT SHEAR
    FLOWS	192


                        Appendix B

ON-LINE USER ADVICE FOR DATA INPUT (DATIN)  	194

B.I Introductory Advice 	  194

                            ix

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B.2 Ambient Advice	196
B.3 Density Profile Advice  	  199
B.4 Discharge Advice  	  199
B.5 Mixing Zone Advice	200
B.6 Design Advice	  201
                        APPENDIX C

FLOW CLASSIFICATION DESCRIPTIONS  	  204

C.I V-Flow Classes	204
C.2 H-Flow Classes	210
C.3 S-Flow Classes	217
C.4 NV-Flow Classes	222
C.5 NH-Flow Classes	228
C.6 Attached Flow Classes	233
                        Appendix D

HYDRO OUTPUT FILE EXAMPLE	238


                        Appendix E

CASE SUMMARY AND DESIGN RECOMMENDATION
    EXAMPLE	244
                             x

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                      List of Tables
Table l.l Key Federal Water Pollution Control Laws

Table 1.2 Examples of Conventional, Nonconventional,
    and  Toxic Pollutants 	
Table 1.3 Examples of Technology-Based Effluent
    Limitations Under The Clean Water Act of 1977 .  .     8

Table 1.4 State Legal Mixing Zones  	    11

Table 3.1 Flow Classification Variables and Length
    Scales	    67

Table 3.2 Near-Field Flow Classification Procedure  .    73

Table 4.1 CORMIX1 Program File Directories	    87

Table 5.1 Flow Prediction Modules of CORMIX1  ....    94

Table 5.2 Flow Protocols for Buoyant Discharges into
    Uniform Ambient Layers  	    98

Table 5.3 Flow Protocols for Negatively Buoyant
    Discharges into Uniform Ambient Layers  	   102

Table 5.4 Flow Protocols for Discharges Trapped in
    Linearly Stratified Ambients  	   105

Table 5.5 Flow Protocols for Bottom Attached Flows  .   108

Table 5.6 Transition Rules	123

Table 5.7 Coefficients Used in Transition Rules . .  .   125

Table 5.8 Flow Classification Criteria	126

Table 5.9 Stratified Terminal Height Expressions  .  .   129

Table 5.10 Module Constants	130
                           XI

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                      List  of Figures
Figure 2.1  Illustrative Near-Field and Far-Field
    Regions of Submerged Positively Buoyant
    Discharge .	   22

Figure 2.2  Pure Jet in Stagnant Environment  ....   26

Figure 2.3  Simple Plume in Stagnant Environment  .  .   28

Figure 2.4  Examples of Combined Effects of Momentum
    Flux, Buoyancy Flux, Crossflow, and Density
    Stratification on Flow Behavior 	   30

Figure 2.5  Buoyant Surface Spreading Process ....   42

Figure 2.6  Density Perturbation of Ambient
    Stratification Leading to Buoyant Spreading
    Processes	   45

Figure 2.7  Passive Ambient Diffusion Process ....   47

Figure 2.8  Flow Interaction Process with Water
    Surface	   51

Figure 2.9  Near-Field Attachment Processes   ....   59

Figure 3.1  Definition Diagram for Single Port
    Discharge Geometry in Ambient Channel with
    rectangular Cross-Section 	 ...   63

Figure 3.2  Representative Stable Density Profiles
    (Four Stratification Types)  	   65

Figure 3.3  Sub-Classification:  Assessment of Ambient
    Density Stratification and Different Flow Classes
    for Internally Trapped Discharges 	   69

Figure 3.4  Sub-Classification:  Behavior of Positively
    Buoyant Discharges in Uniform Ambient Layer ...   70

Figure 3.5  Sub-Classification:  Behavior of Negatively
    Buoyant Discharges in Uniform Ambient Layer ...   71

Figure 3.6  Sub-Classification:  Dynamic Bottom
    Attachment of Discharge Due to Wake or Coanda
    Effects	   72

Figure 4.1  System Elements of CORMIX1  	   86

Figure 5.1  General Behavior for Buoyant Jet in
    Unconfined and Unstratified Crossflow 	   97

                           xii

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Figure 6.1  Horizontal Buoyant Jet Trajectory in
    Stagnant Ambient  	  135

Figure 6.2  Horizontal Buoyant Jet Trajectories in
    Stagnant Ambient Over a Range of Froude Numbers  .  136

Figure 6.3  Horizontal Buoyant Jet Dilution in
    Stagnant Ambient  	  138

Figure 6.4  Non-buoyant Jet Trajectory in Uniform
    Crossflow	139

Figure 6.5  Non-Buoyant Jets at Various Discharge
    Angles in Uniform' Crossflow	140

Figure 6.6  Buoyant Jet Discharging Vertically into
    Weak Crossflow	142

Figure 6.7  Buoyant Jet Discharging Vertically into
    Strong Crossflow  	  143

Figure 6.8  Buoyant Jet Discharged Vertically into
    Weak Crossflow (Logarithmic presentation)  ....  144

Figure 6.9  Negatively Buoyant Jet Discharging
    Obliquely Upward in Uniform Crossflow 	  145

Figure 6.10  Three-Dimensional Trajectory of
    Transverse Horizontal Buoyant Jet in Weak
    Crossflow   	146

Figure 6.11  Three-Dimensional Trajectory of
    Transverse Horizontal Buoyant Jet in Strong
    Crossflow   	148

Figure 6.12  Buoyant Jet Trajectories in Stratified
    Stagnant Ambient  	  149

Figure 6.13  Comparison of CORMIX1 Predictions with
    Integral Buoyant Jet Models in Uniform Crossflow   151

Figure 6.14  Comparison of CORMIX1 Predictions with
    Integral Buoyant Jet Models in Stratified
    Crossflow	152

Figure 6.16  Cooling Water Outfall from San Onofre
    Nuclear Power Plant (Unit 1)   	  154

Figure 6.17  Strongly Buoyant Plume in Crossflow  .   .  155

Figure 6.18  Interaction of Negatively Buoyant Jet
    with Bottom Boundary	159
                          Kill

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Figure 7.1    AB Chemical Company: Schematization of Cross-
              Section at the Discharge Site	163

Figure 7.2    AB Chemical Co. Design Case No. 1: Predictions
              (bottom attached jet)	165

Figure 7.3    AB Chemical Co. Design  Case  No.  2:  Close-up
              View   of   Unattached  Buoyant   Jet   Near
              Discharge	167

Figure 7.4    AB Chemical Co.  Design Case No.  2:  Overall
              Appearance of Discharge Plume 	  168

Figure 7.5    MN Treatment Plant: Typical Density Profiles
              for Summer and Winter Conditions  ...  170

Figure 7.6    MN  Treatment  Plant   Summer  Design  Case:
              Internal Flow Trapping  Caused  by Pycnocline
              Density Jump	172

Figure 7.7    MN Treatment Plant Summer Design Case: Far-
              Field Behavior of Internally Trapped Flow .
	173

Figure 7.8    MN Treatment Plant Winter Design Case: Plume
              Surface Interaction 	  175

Figure 7.9    PQ Cooling Water Outfall in Low Current Design
              ,Case: Near-Field Plume Behavior  ....  177

Figure 7.10   PQ Cooling Water Outfall High Current Design
              Case: Near-Field Plume Behavior  ....  178

Figure 7.11   Parameter Range of CORMIX1 Applicability
	180
                           xiv

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                      Acknowledgments

    This  study was  conducted at  the  DeFrees  Hydraulics
Laboratory,  Cornell  University,   in  cooperation  with the
United States Environmental Protection Agency, Environmental
Research Laboratory,  Athens, Georgia.  The authors want to
extend their appreciation to  Dr.  Thomas 0.  Barnwell, Jr.,
project officer, who provided the initial stimulus for the
project and further guidance throughout the study.

    The authors acknowledge  the assistance given by Dr. Anil
Nerode, Director of the Mathematical Sciences Institute at
Cornell University,  in the development of  expert  system
structure and logic elements.   Professor Douglas A.  Haith,
Department of Agricultural Engineering, Cornell University,
provided valuable  review and criticism.   Mr.  Paul  Akar,
Graduate  Research  Assistant  at  Cornell University,  was
instrumental  for  the timely  completion of the  project
through evaluation of the computer code and knowledge base
and the  execution of numerous  test  cases.    Mr.  Gilbert
Jones, Graduate Research Assistant, assisted  in final report
preparation and system evaluation.

    The work was carried out using the computer facilities
of the DeFrees Hydraulics Laboratory.  Mr. Cameron Willkens,
Electronics Technician, generously assisted with solutions
for computer hardware and software problems.

    This  report was  submitted  with essentially  similar
contents by Robert  L.  Doneker, Graduate Research Assistant,
to the Graduate School  of  Cornell University  in partial
fulfillment of the  requirements for the degree of Doctor of
Philosophy.  Dr. Gerhard H. Jirka, Professor of Civil and
Environmental Engineering,  was project supervisor.
                           xv

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                         Chapter  I

             Introduction and  Legal  Background
1.1 Introduction

    Consider the  numerous liquid waste  streams emanating
from  industrial,   municipal,  agricultural,  and  domestic
activities that are routinely discharged  into water bodies.
The size and flow  characteristics of receiving water bodies
vary widely  — they may  be small streams,  large rivers,
reservoirs, estuaries, or  coastal waters.   The water body
may be deep or  shallow, stagnant or flowing,  and may exhibit
ambient density stratification of various degree.  Also, the
discharge  type and configuration can be highly variable.
The flow may contain  pollutants ranging  from conventional
to toxic substances, vary  greatly in magnitude ranging from
low flowrates  for a small  sewage  treatment plant  to the
substantial cooling water  flows  for a large stream-electric
power plant, issue with high or low velocity, be denser or
lighter  than  the  ambient,  be   located near shore  or far
offshore, and exhibit various geometric details ranging from
single  port  submerged discharges  to multiport  submerged
diffusers to surface discharges.

    Given  this diversity  of  both  discharge and  ambient
environmental  conditions,   a large number of possible flow
patterns will  develop  as  the discharge waste stream mixes
in the  ambient water.  These flow patterns will determine
the  configuration,  size,   and  intensity   of  the  mixing
process, and any impact of the discharge on the water body
surface, bottom, shoreline, or other areas.

    All aqueous discharges located within the United States
are subject  to Federal and/or state regulation.    A key
aspect of these regulations is the concept of mixing zones.
The mixing zone is a legally defined spatial quantity that
allows  for the initial mixing of  the  discharge.   Legal
criteria  specify  the  mixing  zone  shape  and  effluent
concentrations  that must be maintained outside  and at the
edge of the mixing zone.   The  mixing  zone is an allocated
impact  zone  where  more  stringent  ambient water  quality
standards  may  be   exceeded  locally.   Current  mixing zone
regulations  are  a descendant  of  Federal  water  quality
legislation commencing in 1948.

    More recent regulations on discharges of aqueous toxic
substances define  additional  subregions within  the usual

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mixing zone.  The intent of these regulations is to require
rapid mixing of  toxic releases  to  limit  exposure of toxic
materials to aqueous flora and fauna.

    The mixing behavior of  the discharge  is  dependent on
the  depth  of  the ambient  water  body,  the momentum  and
buoyancy of the  discharge, the  spatial  orientation of the
discharge,  and the effects of many other factors.  Detailed
engineering analysis is necessary  to provide  estimates of
discharge dilution within the mixing zone.

    This work describes the development and implementation
of an engineering  tool — in  the  form of a micro-computer
based expert system —  for the analysis of submerged single
port discharges into water bodies with variable and complex
ambient conditions.  The purpose of the expert system is to
provide reliable and accurate  predictions of  the mixing
characteristics of such discharges within the framework of
the applicable legal requirements.
1.2 Overview of U.S. Water Quality Policy

    Prior to 1948, states, local, and regional agencies were
primarily  responsible  for  controlling  water  pollution.
After  the realization  in the  mid-1800s of  the  role  of
contaminated water  in the transmission  of  disease,  state
boards of health were formed to administer water pollution
control programs.   Most early  pollution control programs
focused on water-borne infectious diseases like typhoid and
cholera (Ortolano,1984).

    Table 1.1 outlines key federal water pollution control
legislation since 1948.   The  1948 Water Pollution Control
Act was designed to provide technical services to  the states
to strengthen their water pollution control programs.  The
1948 Act focused on the primacy of the state role in water
quality management.

    The Federal Water Pollution Control Act  (FWPCA) of 1956
expanded the federal  role  in  controlling water pollution.
The  Act  provided  a  program  of  subsidies for  municipal
treatment  plant  construction,   strengthened   powers  of
enforcement against polluters, increased funding for state
water  pollution control  efforts,  and provided  new support
for  research and teaching.   Each  of these programs was
included in the many amendments to the Act in the 1960s and
1970s.

    The Water Quality Act of 1965 set new requirements for
states  to establish  ambient  water quality standards and
increased the level of federal funding.    Water   quality

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Table 1.1
     Key  Federal  Water Pollution  Control  Laws
     Source: Ortolano, 1984
Year
Title
Selected   New  Elements   of
Federal Strategy8
1948
Water Pollution
Control Act
1956
1965
1972
Federal Water
Pollution Control
Act (FWPCA)
Water Quality
Act
FWPCA Amendments
1977
Clean Water Act
1981
Municipal Waste
Treatment
Construction
Grants Amendments
Funds for state water
  pollution control agencies
Technical Assistance to
  states
Limited provisions  for legal
  action against polluters

Funds for water pollution
  research and training
Construction grants to
  municipalities
Three stage enforcement
  process

States set water quality
  standards
States prepare implementation
  plans

Zero discharge of
  pollutants as a goal
BPT and BAT effluent
  limitations
NPDES permits
Enforcement based on  permit
  violations

BAT requirements for toxic
  substances
BCT requirements for
  conventional pollutants

Reduced federal share in
  construction grants program
aThe table  entries  include  only  significant new  changes
established by the law.

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standards were  designed  to protect designated  water uses
within a  stretch of river.   The Act required  that state
agencies set water quality criteria to meet these standards.
Criteria established the  suitability of water for different
activities.  If the uses of water within a stretch of river
and the criteria designed to protect those uses were known,
ambient water quality standards could be set.
1.2.1 The Federal Water Pollution Control Act of 1972

    Prior to the  1972  Federal  Water Pollution Control Act
(FWPCA) only the states had power to develop ambient water
quality  standards applicable  to  interstate  or  navigable
waters.  Water quality standards depended upon  intended use,
whether agricultural, industrial,  or recreational.

    Enforcement of water quality standards was  only possible
if  water quality  fell below  standards.   This  hampered
enforcement efforts because proof of causation  was difficult
in waters receiving wastes from various polluters.  A state
could lower its  water quality standards to attract industry
away  from states that had more  stringent water quality
standards.

    Congress decided to take rigorous  action  in 1972 with
the FWPCA amendments.  The Act  established a uniform system
of water quality standards, permits, and enforcement.  The
"goals"  of  the  legislation   were  to  produce  fishable,
swimmable water  by  1983  and a total elimination  of water
pollution by 1985 (Findley and Farber,  1983).

    Major changes in  the FWPCA  of 1972 included i)  national
water   quality   goals,   ii)   technology-based   effluent
limitations, iii) a  national discharge  permit system, and
iv) a provision for federal  court action against sources in
violation of permit conditions (Ortolano, 1984) .

    Congressional intent  in passing the  FWPCA was to rule
out arguments of assimilative capacity of receiving waters.
Congress  wanted  uniformity of standards  and  enforcement.
Ambient  water quality  standards were  intended to  be "more
stringent"  than  effluent  standards.  The aim of  the 1972
amendments  was   to   restore  and maintain  "the  chemical,
physical, and biological  integrity of the nation's waters"
(Weyerhauser Co. v.  Costle 590 F.2d 1001).

    The  1972  amendments  gave broad powers  to the federal
Environmental Protection  Agency (USEPA)  administrator to
define pollutants and to  determine and promulgate effluent
limitations.   Effluent limitations were  set  according to
industry   through   the   National   Pollution   Discharge
Elimination System (NPDES) permit system.  These discharge

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limits were  set  independent of the particular  context in
which  the pollution  discharge  occurs.    Dischargers  in
violation  of  NPDES  pollution  limits  were  subject  to
enforcement action.

    The Act contained ambient water quality standards that
supplemented federal discharge standards  for point sources.
Point sources were  defined  as "any discernable,  confined,
and discrete conveyance .... from which pollutants are, or
may be discharged."

    The 1972 FWPCA required that industry dischargers meet
"best practicable  control technology  currently available"
(BPT) standards  by 1977 and  " best  available  technology
economically achievable" (BAT) standards by 1983.

    The Act  required public  sources  of pollution  to use
secondary treatment by 1977  and use "best practicable waste
treatment over life of the works" by 1983.

    Specific sections of the Act include:

    Section 301 of the Act set standards for point sources
that were not  publicly owned treatment  works  (POTW).   It
requires  dischargers  to  reduce  emissions  using  "best
practicable control technology currently available" (BPT)
by   1977  and  "best   available   technology  economically
achievable" (BAT) by 1983.

    Section  302   of the  Act  set ambient  water  quality
standards.  Ambient water quality standards were to comply
with state or federal law,  whichever was more stringent to
achieve ambient water quality goals.

    Section 306  of  the  Act  pertains to new sources.  This
section   required   such  facilities   to  meet   standards
equivalent to 1983 BAT standards.

    Section 307 covers toxic water pollutants.  It requires
that standards be developed for toxic water pollutants based
on public health  and welfare and not technical feasibility.

    Section 402 of the Act empowers the federal government
to create a National Pollution Discharge Elimination System
(NPDES).  This pollution permit  system empowers the USEPA
to set national effluent standards and grants states, with
USEPA  approval,  the  responsibility  of  administering  the
program.   NPDES  applies to  any  discharge to  receiving
waters.    NPDES   permits  had to  incorporate  applicable
limitations under  sections  301,  302,   306,  and  307  of the
Act, including enforcement to  meet 1977 and 1983 deadlines.

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    Section  505  provides the  right of  citizen  suits  to
enforce provisions  of the Act.   States have  the primary
responsibility to enforce  the  provisions of the  Act,  but
the Federal government has the  right to step in and enforce
any provision of the Act.
1.2.2 The Clean Water Act of 1977

    In 1977 the FWPCA Act was amended by Congress.  These
amendments are known as the Clean Water Act (CWA).  The five
general categories of pollutants covered in the Act are; i)
conventional, ii) nonconventional,  iii)  toxics,  iv)  heat,
and v)  dredge and  fill spoil.  The Act distinguishes between
new and  existing sources for setting  effluent standards.
Table  1.2  lists  examples  of the  first three  pollutant
categories.

    Pollutants designated  as "conventional" would be "as
defined by the administrator in compliance with the Act as
amended,  generally  those  pollutants  that  are  naturally
occurring, biodegradable,  oxygen demanding materials and
solids.   In  addition, compounds which are not  toxic and
which are similar in characteristic  to naturally occurring,
biodegradable   substances   are   to   be  designated  as
conventional pollutants for the purposes of the provision"
(Congressional   Research   Service,   1977).     Pollutants
designated as "nonconventional"  would  be "those which are
not toxic or  conventional"  (Congressional Research Service,
1977).    Table  1.3  illustrates the   kinds  of  effluent
standards set by USEPA under the 1977 amendments.

    A  new   class   of  effluent  standards   called   "best
conventional  pollution  control  technology"  (BCT)   were
created  for  conventional  pollutants.   Cost consideration
could  be taken into  account by USEPA  in  determining BCT
effluent regulations  for  conventional  pollutants,  but not
for nonconventional pollutants or toxics.

    Congress modified BAT standards in the Clean Water Act
of 1977.  This action was  in response to criticism that the
original  BAT  effluent  limitations  required  too high  a
percentage removal of pollutants and the cost of reduction
in these residuals would be much greater than the benefits.
BAT standards apply to unconventional and toxic pollutants.
A variance provision  for BAT standards  for nonconventional
pollutants is contained in  section  301(g)  of  the Act.  It
allows  the  USEPA  along  with  state  approval  to  modify
effluent standards  for  nonconventional pollutants if this
did not  interfere with water quality  standards  or public
health.

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Table 1.2
Examples of Conventional, Nonconventional, and
Toxic Pollutants
    Source: Technical Guidance Manual  For The Regulations
    Promulgated Pursuant to Section 301(g) of the CWA 1977,
    USEPA, 1984.
    Conventional
     solids(TSS)

    fecal coliform
     bacteria
          Nonconventional
Toxic
biochemical
oxygen demand
(BOD)
pH
total suspended
chemical
oxygen demand
(COD)
fluoride
aluminum
chloroform
lead
f luorene
nickel
          sulfide
selenium
    oil and grease
          ammonia
benzidine

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Table 1.3     Examples   of    Technology-Based   Effluent
              Limitations Under The Clean Water Act of 1977

    Source: Ortolano, 1984.
    Publicly Owned Treatment Works:

    Requirements for 85% BOD  removal,  with possible case-
    by-case variances that allow lower removal percentages
    for marine discharges.
    Industrial Discharges (bases  for effluent limitations):
    Toxic pollutants - BAT

    Conventional pollutants - BCT; in determining required
    control technology, USEPA is directed to consider "the
    reasonableness of the relationship between the costs of
    attaining  a reduction  in effluent  and the  effluent
    reduction benefits derived."

    Nonconventional  pollutants  -  BAT,  but with  possible
    case-by-case variances that allow for lower degrees of
    treatment.

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percentage removal of pollutants and the cost of reduction
in these residuals would be much greater than the benefits.
BAT standards apply to unconventional and toxic pollutants.
A variance provision for BAT standards for nonconventional
pollutants is contained  in section  301(g)  of  the Act.   It
allows  the  USEPA along  with  state approval  to  modify
effluent standards  for  nonconventional  pollutants if this
did not  interfere with  water quality standards  or public
health.

    All river segments within states are  classified as water
quality limited or effluent limited  under section 303(e) of
the Act.   Effluent limited segments are defined as those
stream reaches for which ambient water quality standards can
be met in  1977  by application  of  best  practicable control
technology  currently  available  (BPT)   to  industry  and
secondary  treatment to publicly   owned  treatment  works
(POTW).  When ambient water quality  standards cannot be met
by BPT for industry and  secondary treatment for POTW, these
reaches are classified as water quality limited.
1.3 The Concept of Mixing Zones
1.3.1 Mixing Zones: Development and Regulations

    The mixing zone is defined as an "allocated impact zone"
where numeric water quality criteria can be exceeded as long
as acutely toxic conditions  are  prevented.   A mixing zone
can be thought of as a limited area or volume where the
initial  dilution  of  a  discharge  occurs  (Water  Quality
Standards Handbook, 1984).  Water quality  criteria apply at
the boundary of the mixing  zone,  not within the mixing zone
itself.  USEPA and its predecessor agencies have published
numerous documents  giving  guidance for determining mixing
zones such as the National  Academy of Science Water Quality
Criteria  1968  (Green  Book),  USEPA publications  Quality
Criteria for Water  1976 (Red Book) , and  Guidelines for State
and Area Wide  Water Quality  Management Program.   Guidance
published  by USEPA  in Water  Quality  Standards  Handbook
(1984) supersedes these sources.

    In setting requirements for mixing zones, USEPA (1984)
requires that "the area or volume of an individual zone or
group of zones be limited to an area or volume as small as
practicable that will not interfere with the designated uses
or with  the  established  community of  aquatic  life  in the
segment for which  the  uses are designated,"  and the shape
be "a  simple  configuration that is easy  to  locate  in the
body  of  water  and avoids  impingement  on  biologically
important  areas,"   and  "shore  hugging plumes  should  be
avoided."
    Within the mixing zone USEPA requires "any mixing zone
should be free of point or nonpoint source related:

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    (a)  Material  in  concentrations that will  cause acute
    toxicity to aquatic life;

    (b)  Materials  in concentrations  that  settle  to  form
    objectionable deposits;

    (c)  Floating debris,  oil scum  and other matter  in
    concentrations that form nuisances;

    (d)    Substances    in   concentrations   that   produce
    objectionable color,  odor, taste or turbidity; and

    (e)    Substances   in   concentrations  which   produce
    undesirable aquatic life or  result  in a  dominance  of
    nuisance  species."  (USEPA,  Water   Quality  Standards
    Handbook, 1984).

    The proposed rules for mixing zones recognize that the
state has the discretion to adopt or not to adopt a mixing
zone and to  specify  its dimensions.   USEPA allows the use
of a mixing zone in permit  applications except where one is
prohibited in state  regulations.   State  standards require
that water quality  criteria be met  at the  edge  of  the
regulatory mixing zone i)  to provide  a continuous zone  of
free passage  that  meets  water quality criteria  for free-
swimming  and   drifting  organisms  and  ii)   to  prevent
impairment of critical resource  areas  (USEPA,  Technical
Support Document  for Water  Quality-based  Toxics Control,
1985).   A  review of  individual state  mixing zone policies
shows that 48 out of  50 states make use of a mixing zone in
some form  (Table 1.4).

    The mixing zone dimensions vary from state to state as
shown in Table  1.4.   The mixing zone can  be  defined  as a
downstream distance,  cross-sectional  area,  or  volume  of
water.    Discharge  concentrations  of  pollutants  such  as
nitrogen,   phosphorus,  or  toluene,  are limited  to certain
numerical values at the edge of the mixing  zone.

    For discharges into streams, 17 of the 31 states that
propose a  mixing zone specify that the  mixing zone  shall not
exceed 1/4 of the cross-sectional area and/or volume of the
stream flow,  and the  remaining 3/4  of the  stream shall  be
maintained as a  zone  of passage  for swimming  and drifting
organisms.

    The remaining states have varying requirements allowing
dimensions of the mixing  zone to be as  low as  1/5 of the
cross-sectional area  (Ohio) to as much as 3/4 of the cross-
sectional  area  (South Dakota) .  West  Virginia is the only
state that specifies  a length dimension  for mixing zones.
                            10

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Table 1.4
State Legal Mixing Zones
    Source:  Draft  Technical   Guidance   Manual  for  the
    Regulations Promulgated Pursuant To Section 301(g)
    (USEPA 1984)
   State
     Water Body
Dimensions
  Alabama
  Alaska

  Arizona
  Arkansas
  California
  Colorado
  Connecticut
  Delaware

  D.C.
  Georgia
  Florida
  Hawaii
  Idaho
  Illinois

  Indiana
  Iowa
  Kansas
  Kentucky
  Louisiana
  Maine
  Maryland
  Massachusetts
  Michigan

  Minnesota
  Mississippi
  Missouri
  Montana
  Nebraska
  New Jersey
     river,streams
     lakes
     NR
     large streams
     0
     0
     streams
     streams
     lakes
     estuary
     0
     streams,rivers
                   lakes, estuaries
     0
     0
     all
     streams
     streams
     streams
     streams
     streams
     streams
     streams
     0
     0
     streams
     Lake Michigan
     streams
     0
     streams
     0
     0
     streams
  New Hampshire    streams<=l/4 CS
  New Mexico       streams
  New York streams <=l/2
<= 1/3 CS
<= 10% SA
NR
<=l/4 CS
0
0
<=l/4 CS
<=l/3 CS
<=10% SA
<=10% SA
0
<=800 meters
<=10%    total
length
<=125,600 m**2
(600'  radius)
<=10% SA
0
0
<=600' radius
<=l/4 CS
<=l/4 CS
<=l/4 CS
<=l/4 CS
<=l/3 CS
<=l/4 CS
<=l/4 CS
0
0
<=l/4 CS
<=1000' radius
<=l/4 CS
0
<= 1/4 CS
0
0
< = 1 / 4     C S
(thermal)

<=l/4 CS
CS (thermal)
                            11

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Table 1.4
(Continued)
State
Nevada
North Carolina
North Dakota
Ohio


Oklahoma
Oregon
Pennsylvania
Rhode Island

South Carolina
S . Dakota


Tennessee
Texas
Utah
Vermont
Virginia
Washington
W. Virginia







Wisconsin
Wyoming
Guam
Puerto Rico


Virgin Islands
Water Body
streams
0
streams
receiving
watercourse
mouth of receiving
streams
0
NR
streams

0
streams


0
streams
0
streams
0
0
warm water
fish streams

cold water
fish streams

lakes

streams
0
0
streams


streams
Dimensions
<=l/3 CS
0
<=l/4 CS

<=l/3 CS
<=l/5 CS
<=l/4 CS
0
NR
< = 1 / 4 C S
(thermal)
0
<=3/4 CS or 100
yds of stream's
width
0
<=l/4 CS
0
<=l/4 CS
0
0

<=33% CS, length
<=10*width

<=20% CS, length
<=5*width
<=300' any
direction
<=l/4 CS
0
0
<=l/4 CS
IMZ<= 400 '
FMZ<= 4000 '
<= 1/4 CS
     Where:

    CS = cross-sectional area
    NR = no reference
    IMZ =  initial mixing zone
                    SA = surface area
                    0 = not listed
                    FMZ = Final mixing zone
                             12

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The length of the mixing zone must be less than 10 times the
average width of the stream or less than 5 times the average
width of the stream for warm water and cold water streams,
respectively.

    In  states  that   specify a  mixing  zone  for  lakes,
dimensions for the mixing  zone vary  from 10% of the surface
area of the  lake to 300 to  1000  foot radial limits around
the discharge point.

    Pennsylvania and Arizona are  the two states that do not
make reference to a mixing zone.   Therefore the USEPA does
not recognize  any  mixing  zone for  these states  and water
quality criteria  must be  met at  the point of  discharge
unless the applicant and the state develop a mixing zone on
a case by case basis.

    Usually, the size of  the mixing zone  is determined on
a  case-by-case basis  taking  into  account the  critical
resource areas  that  need to be  protected.  Mixing zones
should be used  and evaluated in  cases where mixing is not
complete within a short distance of the outfall.
1.3.2 Special Mixing Zone Requirements for Toxic Substances

    For   toxic   discharges,   USEPA  recommends   careful
evaluation of mixing to prevent  zones  of chronic toxicity
that extend for  excessive distances because of poor mixing.
USEPA maintains  two water quality criteria for the allowable
magnitude  of   toxic  substances:  a   criterion  maximum
concentration  (CMC)  to protect  against  acute  or  lethal
effects; and a criterion continuous concentration (CCC) to
protect against chronic effects (USEPA,  1985) .

    The less restrictive criterion,  the  CCC, must be met at
the edge of  the  same regulatory  mixing  zone specified for
conventional and nonconventional discharges.

    To  prevent   lethal  concentrations  of  toxics  in  the
regulatory mixing zone,  the restrictive CMC criterion must
be met within a  short distance from the outfall or in the
pipe  itself.   If dilution  of  the toxic  discharge  in the
ambient environment  is allowed,  this requirement, which will
be defined  here as  a toxic dilution  zone  (TDZ) ,  is more
restrictive than the legal mixing  zone for conventional and
nonconventional pollutants.   The technical support document
specifies a minimum  exit velocity of 3 meters per second (10
feet  per  second), in order to provide  sufficiently  rapid
mixing that  will minimize organism  exposure time to toxic
material.  In addition, the outfall design  also must meet
three geometric  restrictions for a TDZ  (USEPA,  Technical


                            13

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Support Document  for Water Quality-based  Toxics  Control,
1985):

    -The CMC must be met within 10% of the distance from
    the edge of the  outfall structure to  the  edge of
    the regulatory mixing zone in any spatial direction.

    -The CMC must be met within a distance of 50 times
    the discharge length scale in any spatial direction.
    The discharge length scale is defined as the square-
    root of  the cross-sectional  area  of  any discharge
    outlet.  This  restriction will ensure a dilution
    factor of  at  least 10 within  this distance under
    all possible circumstances,  including situations of
    severe bottom interaction and surface interaction.

    -The CMC must be met within a distance of  5 times
    the local water depth in any horizontal direction.
    The local  water  depth  is  defined as  the  natural
    water depth (existing prior to the installation of
    the discharge outlet)  prevailing under mixing zone
    design conditions (e.g.  low flow for rivers).  This
    restriction will prevent locating the discharge in
    very shallow environments  or very  close to shore,
    which would result in significant surface and bottom
    concentrations.
1.4 Regulatory Assessment of Discharges and the Permitting
Process
1.4.1 The NPDES Permit System

    Any pollutant  discharge into a  navigable watercourse
must have a National  Pollution Discharge Elimination System
(NPDES) permit.  The permit is designed to insure that the
discharge meets  all  applicable  standards.   The  permit is
granted  either by USEPA,  or,   if  the  state has  a  USEPA
approved program, by the state.   The applicant must supply
the  reviewing  agency with  all  data  needed to  grant the
permit.  Data required in the application include:

         Name and exact location of facility

         Nature  of  business  engaged  at  the  facility,
         including what is or what will be manufactured

         The manufacturing  process  and maximum production
         levels

         Schematic of water flow through the facility

         Exact location, flow rates, flow frequencies, and
         chemical composition of each facility discharge
                            14

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         The  waste-water  treatment  currently  or  to  be
         employed for each waste stream

         Pollutant test data
1.4.2 Need for Regulatory Assessment Tools

    Implementation of the mixing zone policy requires that
both  applicants  and  regulators  determine  the  initial
dilution of  the  discharge and the  characteristics  of the
mixing zone.   If  the discharge  is toxic, the CMC value must
be determined for the discharge and  special requirements for
a TDZ must be met within the mixing zone.   Given the large
number   of  possible   ambient  environments,   discharge
configurations,  and  mixing zone definitions,  the analyst
needs  considerable  training  and   experience  to  conduct
accurate and reliable effluent mixing analysis.

    Dilution  of  the  effluent  in  the  receiving  water  is
caused by  different mechanisms  along  its  path.    In the
"near-field" of  the  source,  dilution is caused  mainly  by
jet induced  entrainment.   Further  away, in  the  so-called
"far-field" the jet velocity decreases and ambient diffusion
becomes the primary mechanism of effluent dilution.

    The  most   direct   way   of    determining   pollutant
concentration downstream is by physical measurement.  Non-
polluting tracers also can be injected to give indications
of  effluent   dilution.     Such   field  studies  require
considerable  time  and  effort,  and  field  personnel  need
specialized training  to  perform studies reliably.   Field
studies,  in many  cases,  are impractical and expensive.  For
example,   if  in   situ  observations are  used  they  must
represent  conditions  that  are  present  during  critical
dilutions,  not merely  a  typical  dilution  (USEPA,  Draft
301(g) 1984).  Field  studies  for analyses  of dilution for
toxic discharges are  patently  unacceptable,  so simulation
must be used to determine dilutions.

    Because  of  the  complexity  of the  physical  mixing
process,   permit  writers  are   increasingly  relying  on
mathematical   models  to   analyze  the   transport   and
transformation of pollutants (Tait, 1984).   The difficulty
with  many  present  models  is  that  they  tend to  become
specialized and give accurate results only for a particular
type of outfall.   The user must be careful  to  use a model
that was intended to make predictions under the conditions
with which he is  concerned (USEPA Draft 301 (g) 1984) .

    USEPA has developed a  number of models  to  predict the
initial dilution of discharges.  A few  these are known  as
                            15

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PLUME, OUTPLM,  UDKHDEN, MERGE, and LINE (Muellenhoff et al.
1985).  Applicants are not required to use these models in
the analysis, but must be able to prove that the methodology
chosen gives reasonable estimates of initial dilution.
1.4.3 Motivation for Expert Systems Approach

    In determining the characteristics of the mixing zone,
the  analyst,   either  the  NPDES  applicant  or  regulatory
authority, may choose from  a  wide variety  of  predictive
models.    The  models range  in  complexity  from  simple
analytical formulae to highly intricate numerical solutions
to differential equations.  Although the USEPA has prepared
assessment manuals and actually endorsed certain models in
specific situations,  the average  user has little reliable
guidance  on  which model is  appropriate  for  a  particular
situation, or which is actually best  (Muellenhoff, et al.,
1985).   Examples  of "model  abuse" are  ubiquitous.   Often
unnecessarily  complicated models  are  employed,  creating a
needless burden for both regulators and dischargers.

    Even when a particular  model is appropriate for a given
discharge, the model  may not give reliable  results over a
wide range of  conditions.  Model  developers often fail to
explicitly specify limits of applicability,  or model users
may  simply   overlook important   restrictions   to  model
applicability.   An  example  of  a frequent  error  in  the
application of the  USEPA plume models is the violation of
the  assumption  of  the  infinite  receiving  environment
(Muellenhoff,  et  al., 1985).   In reality,  the  plume  may
attach to the bottom or may become vertically fully mixed,
possibilities that may occur due to changes in the ambient
environment  such  as  low  flow  conditions.   Consequently,
analysts  have  submitted  model   "predictions"  in  which  the
plume diameter exceeds actual water depth!

    Once the correct choice of model is assured, the analyst
often faces the considerable  task of assembling the required
design data base.   This can be  a frustrating and cumbersome
task for the unexperienced analyst who has little guidance
on what design base to choose,  where  to obtain data, which
data are crucial to the analysis,  and  which data may simply
be  estimated.   Because of  these  difficulties,  a large
investment  in  time is required for the  analyst  to become
fully  familiar and proficient with the use of at least one
model, or more likely, a group of models.  The analyst in
reality must become highly  skilled or an "expert"  in the use
and  interpretation of a number of simulation models.  Such
expertise in  model  use requires expensive training and is
rare.   This is the primary  reason for the  development of
expert system  tools to assist the analyst.
                            16

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    In essence, expert systems mimic the  way an expert or
highly experienced person would solve a problem.  An expert
system is a structured computer program that uses knowledge
and inference procedures obtained from experts for solving
a particular type  or class of problem called a "domain".
This  knowledge is  encoded  into a  "knowledge  base"  that
enables inexperienced personnel  to  solve  complex problems
by using  the same  basic reasoning process  that an expert
would  apply.     The knowledge   base  includes  a  set  of
"objective" or  widely accepted facts about  a general problem
area.  This includes the set of parameters  or data an expert
would seek in order  to characterize a specific problem.  The
inference  procedures are "subjective" rules  of judgement
that the expert might use when analyzing the problem.   The
inference  procedures provide the  rules  for  selecting an
appropriate solution to the problem from the knowledge base.
The inference  procedures allow  the expert  system  user to
search rapidly  and systematically through the knowledge base
to obtain a solution to the given  problem.  This element uses
structured search techniques  based upon mathematical logic.

    The development of  an expert  system  for mixing  zone
analysis  promises  significant   advantages   compared  with
existing  conventional   simulation  techniques  for  water
pollution control and management:

         it assures the proper choice of model for a given
         physical situation.

         it  assures that the   chosen  model  is  applied
         methodically without skipping essential elements.

         it guides the acquisition or estimation of data for
         proper model prediction.

         it  allows  a   flexible  application  of  design
         strategies  for a given point source, screening of
         alternatives,   and  if  necessary,   switching  to
         different  predictive models  thus  avoiding  rigid
         adherence to a single model.

         it flags borderline cases for which no predictive
         model  exists suggesting either avoidance  of  such
         designs  or caution by assigning   a  degree  of
         uncertainty.

         it allows a continuous update of the  knowledge base
         as improved predictive models,  experimental data,
         and field experience with particular designs become
         available.

         it  provides a  documented analysis  listing  the
         knowledge and  decision logic that have  lead to the


                            17

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         problem  solution.    Thus,  unlike  conventional
         programs or computer  algorithms  an expert system
         is not a "black box."

         it  provides  a  common  framework  whereby  both
         regulators (federal or state), applicants, and the
         scientific community can arrive at a consensus on
         the  state-of-the-art   hyclrodynamic   mixing  and
         pollution control.

         it gives pollutant concentration at the specified
         regulatory mixing zones.

         finally, and perhaps most importantly, it provides
         a  teaching  environment  whereby  the  initially
         inexperienced analyst through repeated interactive
         use gains physical insight  and understanding about
         initial mixing processes.
1.5 CORMIX1: An Expert System  for  Mixing Zone Analysis of
Submerged Single Fort Aquatic Discharges
1.5.1 Scope and Objective

    The Cornell  Mixing Zone Expert  System  (CORMIX)  is  a
series of software subsystems for the analysis, prediction
and  design of  aqueous  conventional  or toxic  pollutant
discharges into watercourses, with emphasis  placed on the
geometry and dilution characteristics of  the initial mixing
zone.  Subsystem CORMIX1, described in this work, deals with
submerged single port  discharges with  arbitrary discharge
buoyancy  (positive,  negative,  or  neutral)  into arbitrary
water bodies (shallow or deep, stagnant or flowing, uniform
or stratified)  as may be representative for rivers, lakes,
reservoirs, estuaries, or coastal waters.  CORMIX1 assumes
steady state flow conditions, both for the discharge and the
ambient environment.   Another subsystem, CORMIX2, addresses
submerged multiport  diffuser discharges  (Akar  and Jirka,
1989).  CORMIX3, the  third  possible  development,  would be
for the analysis of surface discharges.

    The objective  of  the  expert system  is to provide the
analyst with accurate and reliable  predictions of discharge
mixing processes.   The expert system  should be easy to use,
and should allow for preliminary mixing zone analysis of a
typical design in perhaps 20 minutes  if all necessary input
data is available.  Emphasis is placed on the geometry and
initial mixing of  the  discharge, along with  prediction of
concentration  (or  dilution) values  and  the  shape  of the
regulatory mixing zones.   The expert system should provide
the  analyst with  detailed  hydrodynamic information  and
recommendations for discharge design, including sensitivity
studies.
                            18

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    Since its emphasis is on  initial mixing mechanisms with
their  short  time scales,  CORMIX1 assumes  a conservative
pollutant or  tracer  in the effluent.   Thus any physical,
chemical, or  biological  reaction  or decay  processes are
neglected.  However,  if  first-order  processes are assumed
the predictive results can be  readily adjusted to include
such processes (see Section 7.4).

    It  seems  impossible, and  probably  unnecessary,  to
develop a system that works reliably for every conceivable
mixing  zone   and  discharge  configuration.    The  present
philosophy,  however, was  to  develop  an expert system that
works  for the large majority  (better than 95%)  of typical
discharges,  ranging  from simple to  fairly  complex cases.
The remaining cases may require separate analyses, perhaps
using  sophisticated  numerical  modeling  or  a  detailed
hydraulic model study.
1.5.2 Results of an Earlier Feasibility Study

    A  feasibility  study   (Doneker  and  Jirka,  1988)  was
conducted to  the test  expert  system methodology  for the
analysis  and  design  of submerged  single-port  continuous
buoyant discharges  into a non-stratified  flowing aqueous
environment.  The objective was to test a prototype of the
hydrodynamic  knowledge  base and  simulation model.   This
simplified  expert  system  did   not  include  stratified
environments,   negatively   buoyant  discharges,   and  bottom
attachments.  The system was written in the expert system
shell M.I (Tecknowledge, Inc.)  and in Fortran.

    The results  of  the  hydrodynamic simulation  were found
to be in  good to excellent agreement with available field
and  laboratory data.    In particular,  the  system  proved
flexible  and  reliable  in distinguishing  among  complex
discharge situations  involving boundary  interactions and
buoyant intrusion phenomena.   Many  of the common pitfalls
to model use — incomplete  or contradictory data, choice of
appropriate simulation model, and faulty interpretation of
results — appear to have been  mitigated within the context
of an expert system methodology.  Because of the encouraging
results  of  the  preliminary  system,  the  more  general
hydrodynamic  problems  of  negative buoyancy,  stratified
environments,   and boundary  attachments,  along with  more
sophisticated  user  elements,  have   been  included  in  the
expert system described herein.
                            19

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1.5.3 Summary of Present Study

    CORMIX1  uses  the  expert   systems   shell   VP-Expert
(Paperback  Software,  Inc.)  and  Fortran.   The  following
chapters provide a detailed description of the expert system
CORMIX1.   Chapter  II  provides a detailed review  of basic
hydrodynamic processes of mixing in  buoyant  jets,  buoyant
spreading,   passive   ambient   diffusion,  and   boundary
interaction phenomena.

    A hydrodynamic flow classification system is developed
in Chapter  III.   The classification  system  describes the
physical   discharge/environment   interaction   processes
controlling near-field mixing for a  discharge, and forms the
basis  for  the  construction  of the proper  hydrodynamic
simulation model sequence.

    Chapter IV presents  an outline of the computer programs
in CORMIX1.  This  chapter describes  the  logic  and Fortran
program elements of CORMIX1,  their respective strengths and
weaknesses,  and  how they  are  applied  to  mixing  zone
analysis.

    Chapter  V  discusses the  hydrodynamic model  protocols
used to simulate  a given  discharge/environment condition.
The details of each  simulation  program  element  are also
presented.

    Chapter  VI  is   devoted to  system  evaluation  and
validation.  This  chapter compares  CORMIX1  results with a
wide range  of  laboratory  and field  data.   Comparisons are
given with jet integral  models that are widely used but are
limited to the initial subsurface buoyant jet processes.

    Chapter VII presents design case studies to illustrate
the flexibility and power of the system to evaluate a wide
range  of  typical discharge/environment  situations.   Also
suggestions on extending the applicability of the system to
other possible discharge/environment conditions is given.
                            20

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                        Chapter II

         Hydrodynamic  Elements  of  Mixing  Processes
    The   hydrodynamics   of  an   effluent   continuously
discharging  into  a   receiving   body   of   water  can  be
conceptualized as a mixing process occurring in two separate
regions.     In   the   first  region,   the  initial   jet
characteristics of momentum  flux, buoyancy flux, and outfall
geometry  influence  the jet  trajectory  and mixing.   This
region  will  be  referred  to  as  the  "near-field",  and
encompasses  the jet  subsurface  flow and  any surface  or
bottom interaction,  or in  the case of a stratified ambient,
terminal  layer  interaction.  In  this  region,  designers of
the  outfall   can  usually  affect  the   initial   mixing
characteristics through appropriate manipulation of design
variables.

    As the  turbulent  plume travels further away from the
source, the  source  characteristics  become  less important.
Conditions existing in the ambient environment will control
trajectory  and dilution  of the  turbulent plume  through
buoyant  spreading motions  and  passive  diffusion due  to
ambient turbulence.   This region  will be referred to here
as the "far-field".

    The hydrodynamic analysis treats the  near-field and far-
field regions separately.  An illustration of the near-field
and the far-field of a simple positively buoyant subsurface
plume rising to the surface and traveling downstream appears
in Figure 2.1.

    This chapter represents  the basic hydrodynamic elements
of the several stages within typical mixing processes that
can occur in the water environment.   In  Section  2.1 the
mechanics of buoyant jet mixing are presented, starting with
the simple  jet and plume.   This analysis   is  extended  to
include  the effects  of crossflows,  combined  sources  of
momentum  and   buoyancy,   and  finally  ambient  density
stratification.   Section  2.2 deals  with buoyant  spreading
processes in unstratified or stratified flowing  ambients.
Passive  diffusion,  due to   ambient  turbulent  mixing,  is
summarized  in  Section 2.3.   Finally various  interaction
processes that provide a  transition  between buoyant jet
mixing and  subsequent processes are presented in  Section
2.4.
                            21

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 Plan View
 Side  View
               Near Field
                          o
                   Far Field
 u,
Figure 2.1
Illustrative Near-Field and Far-Field Regions
of Submerged Positively Buoyant Discharge: An
Example  of Unstratified  Ambient  Water  and
Without Bottom Attachment

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2.1. Buoyant Jet Mixing Processes

    A  discharge with  no  buoyancy is  referred  to as  a
"nonbuoyant jet" or "pure jet".  A  release of buoyancy only
(no initial momentum) is called a "pure plume".  A release
containing  both momentum  and  buoyancy  is  designated  a
"buoyant jet" or "  forced plume".   For simplicity, a region
within the actual pure  jet, pure plume, or buoyant jet will
herein be referred  to as a "flow".   Positively buoyant flows
are  defined  as  flows  where  the  buoyancy  force  acts
vertically upwards   against  the  gravity  force;  negative
buoyancy is defined as  acting downwards in the direction of
the gravity force.

    For   a   buoyant  jet   in  a   stagnant   unstratified
environment, List  and  Imberger (1973) propose  three flow
regions  where  buoyant  jet  behavior  is  determined  by
different effects.    In the first  region,  near  the issuing
source, the geometry of the discharge  is important.  In the
second  region,   initial  kinematic  momentum flux of  the
discharge predominates.  In the third and ultimate region,
yet  further away  from  the  source, buoyancy  flux  of  the
initial discharge  becomes  important.    Characterizing  the
flow  by the  predominant mechanism  controlling  the  flow
within  a  region is  the  essence of "asymptotic analysis"
which will be pursued herein.

    The  effects of momentum  and  buoyancy  thus can  be
considered  separately to reduce the number  of  independent
variables under  consideration.  For example,  the solution
for a pure jet can  be applied as an approximate solution to
that  portion of buoyant  jet in  a  crossflow where  jet
momentum dominates  the  flow.   Likewise the results  for a
pure plume can be applied to the buoyancy-dominated regions
for the buoyant jet.

    Additional  factors,   such as  ambient  crossflow  and
density  stratification,  can  also  be  treated   within  the
framework of asymptotic analysis as shown by Wright (1977),
and others.
2.1.1 Description of Turbulent Jets and Plumes

    Most people are familiar with the sight of smoke rising
from a  smokestack into the atmosphere.   The  smoke plume
first rises vertically and spreads narrowly, and eventually
bends over as it is carried away by the ambient wind.  The
smoke plume is an  example of  a  turbulent  buoyant jet,  the
discharge  contains both  momentum  and buoyancy,   and  is
affected, at  least in the final stages by  the crossflow.
                            23

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The buoyancy is produced by the lower density  of the heated
air with respect to the cooler ambient air.

    The discharge of a liquid such as sewage into the ocean
behaves in a similar fashion.  The sewage  flow has momentum
from being  injected through the discharge orifice.   The
sewage  may  have  the density  of  freshwater  and  thus  is
buoyant with respect to the  greater density of the ambient
saltwater.
2.1.2 Dimensional Analysis of Buoyant Jets

    Turbulent  jets  are  characterized  by  a  long narrow
turbulent zone.   Following  release from a nozzle, the  jet
flow becomes unstable at its boundary and breaks  down into
the turbulent motion.  Typically,  the size of the  turbulent
eddies  increases   with   increasing  distance  along   the
trajectory (Holley and Jirka, 1986) .

    Several  assumptions  are made  in order  to reduce  the
independent  variables under consideration.    Only  fully
turbulent jets  are  considered  so  the effects  of  viscosity
can be neglected.  The Boussinesq  approximation is assumed:
density  differences  between  the   jet  and  the ambient
environment are small and are important only in terms of  the
buoyancy force.

    The  three  variables  used to  describe  buoyant   jet
characteristics  are the  kinematic  fluxes  of  mass,  Q0  =
           3~1                        4"2
       uQ  [LT~], momentum  M0 = u0Q0  [LT"] ,  and buoyancy J0
= <30 QQ. [L4"1""3]/  where D [L]  is the diameter  of  the  orifice,
u0 [LT 1]  is the exit velocity,  and g0'  [LT~2]  is the reduced
gravitational  buoyant  acceleration caused  by the  density
difference between  the  jet and ambient environment.  This
term   is  defined   as  g0'  =   g(pa  -  P^/Pa   where  g   is
gravitational acceleration and  pa and  pQ are the ambient  and
jet discharge densities  [ML"3] , respectively.

    If the ambient water is flowing its velocity,  ua [LT"1],
becomes  an additional  variable.   Furthermore,  when  the
ambient density is  not uniform,  the density stratification
may be written in terms  of a buoyancy  gradient defined  as

    e  = -g/P.(d/,a/dz)  [T'2]                             (2.1)

where z is the  vertical coordinate direction.  Note that  the
following assumptions are implicit in the above definitions:
a  uniform exit velocity u0,  a  constant ambient  velocity
(without shear) ua,  and a linear density gradient  with,  at
least  layer-wise, constant e.
                             24

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    For the general case  of  a  buoyant jet discharged into
a  flowing  stratified environment,  dimensional  analysis
proceeds as  follows.   Any dependent variable,  *,  such as
local  centerline  jet velocity,  can  be  expressed  as  a
function of the various independent variables:
where s [L] is the distance along the jet trajectory.  The
function on  the right hand  side of  Eq.  (2.2)  has  to be
dimensionally   consistent   with  the   desired   dependent
variable.

    The following paragraphs  first  present  the  details of
dimensional analysis for the simple case of a pure jet and
a pure plume in a stagnant  environment.  Then, the cases of
jets and plumes in a crossflow are presented.  Finally the
effect of  ambient density  stratification  on flow behavior
is  presented.    In  each case,  the  jet and  ambient flow
variables  can be  combined  into  various  length scales that
measure the  relative  forces affecting a  flow within  a
particular trajectory distance.

    The asymptotic approach will provide solutions that are
valid  only within certain  specified regions and  require
experimentally  determined  coefficients.     However,  the
individual solutions can be linked by appropriate transition
conditions to provide an overall  prediction for the complete
problem.
2.1.2.1 Simple Jet in Stagnant Uniform Environment

    Consider a pure jet in a stagnant ambient  fluid  (Figure
2.2).  Initially as the flow exits the orifice the velocity
profile is near  uniform.   After a  short  distance  s  along
the jet trajectory, the velocity  distribution is observed
to  be  bell-shaped (Gaussian).    The  region where  this
velocity distribution transformation  occurs  is  called the
zone of flow establishment (zofe).   The  details of the zofe
will not be  considered  in any of  the following analysis;
i.e. the jet is assumed to come from a point source.

    The maximum  velocity uc  occurs along the  trajectory
centerline and a  similarity  profile  (Gaussian distribution)
may  be  assumed  for  the  velocity  distribution.   Similar
conditions pertain to the  centerline  concentration  cc  of
pollutant (or tracer)  mass.  The  jet centerline velocity uc
decreases with distance  s  from  the orifice  as the  jet
entrains the stagnant  ambient  fluid.  However, the momentum
flux M at any section  along  the trajectory is conserved and
is equal to the initial momentum flux M0.
                            25

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                   a.   Instantaneous appearance
                 ENTRAINMENT
                 VELOCITY
(Jo. po " p». c0
                                                  CONCENTRA TION
                                                  PROFILE
                                                      c

                                                      «T

                                                AMBIENT DENSITY p,
                     ZONE OF
                     FLOW ESTABLISHMENT
                 b.  Time-averaged conditions
Figure 2.2
                Pure Jet in Stagnant Environment  (Ref. Holley
                and Jirka,  1986)
                                26

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    The  magnitude  and variation  of  the  jet centerline
velocity  depends  primarily  upon   the  initial  kinematic
momentum flux  and the  distance along the trajectory,  uc =
     s).   Therefore, one can deduce on dimensional grounds
    uc = cM

(2. 3) where c is a constant.

    The width b of the jet at trajectory distance s can also
be   expressed   as  b  =  f(M0,s).     The  only   possible
dimensionally consistent equation is

    b = cs                                            (2.4)

where c is a another constant.

    The centerline dilution  S at any cross-section along the
jet is defined by S - CQ/C,.,  where cg is the concentration  at
the nozzle exit.  A mass conservation equation implies c0Q0
a ccucb2, so that  the dilution  S  as a function of  s can  be
expressed as

    S = cM01/2s/Q0                                      (2.5)

where c is a constant.

    The various jet flow constants c in  the above  three
equations must be obtained  from experimental  data.
2.1.2.2 Simple Plume in stagnant Uniform Environment

    A pure  positively buoyant plume  rises vertically  and
experiences  an increase  in vertical  momentum  flux with
distance z from the source (Figure 2.3).  The buoyancy flux
is constant for any cross-section of the plume  as  it rises.
For the pure  plume,  the centerline velocity is a  function
of  the  buoyancy  flux  and  distance,  uc  = /(J0,z).     The
centerline  velocity  of the  plume can  be  obtained from
dimensional reasoning

    uc= cCJo/z)1'3                                      (2.6)

    The width b  of the plume  at  trajectory distance z  is
expressed as

    b = cz                                            (2.7)

where c is a  constant.
                            27

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                    a.  Instantaneous appearance
                              $»z
                                   AMBIENT
                                   DENSITY pa
           EHTRAINMENT
           VELOCITY
                                     CONCENTRA TION AND
                                     BUOYANCY PROFILE
                                       —     9'
                                       cc  '   9'c
                                    VELOCITY PROFILE

                                         u
                                         U-
                   b.  Time-averaged conditions
Figure 2.3
Simple Plume  in  Stagnant Environment  (Ref,
Holley and  Jirka,  1986)
                            28

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    A mass conservation  equation  (similar to the approach
leading to Eq. (2.5)) provides the plume dilution

    S = cJ01/3z5/3/Q0                                    (2.8)

    All plume flow constants  c  in the above equations are
in general different  from  the jet flow constants and must
be evaluated from experiments.
2.1.2.3 Generalizations: Jet/Plume Interactions/ Crossflow
Effects/ and Stratification Effects

    If several parameters influence the flow field, then a
general asymptotic solution for the whole flow field cannot
be found.  However, there  may be individual regions where
specific asymptotic solutions of the type developed in the
preceding sections  still apply.   This is  illustrated in
Figure 2.4.

    A buoyant jet in unstratified stagnant ambient (Figure
2.4a)  is  initially jet-like  and affected by  the initial
discharge orientation.  After some distance the plume-like
behavior predominates, leading finally to a vertical rise.

    The role of an unstratified crossflow is to deflect the
discharge  flow  downstream  into the  current  direction.
However, there is always a  region close to the source where
the flow is  still jet-like  (Figure 2.4b) or plume-like  (Fig
2.4c).   Beyond  some  distance  the jet  or plume becomes
strongly deflected and is advected by the ambient flow.

    The  role  of   ambient   stratification,   given  by  a
continuous linear distribution  in the  present case,  is to
trap the flow at  a certain level (trapping level or terminal
level).  Prior to the trapping the flow may be either jet-
like  (Figure 2.4d) or  plume-like  (Figure  2.4e).   After
trapping the flow forms an  internal density  current with
moderate additional mixing, as discussed in Section 2.2.

    Of course, multiple effects of the types  sketched in
Figure 2.4 can  all occur simultaneously in a  given flow.
In every case it  is possible,  however, to identify dominant
flow  zones  and  spatial  regions.   This  identification is
possible by  means of appropriate  length scales  that are
developed in the  following  sections.    A rigorous  flow
classification  scheme  on  the  basis  of   such  scales  is
described in Chapter 3.
                            29

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                  Transition
                        \
        Discharge
    ua=0

    € '0
                                       Plume-like
Jet-like
             a)  Buoyant Jet in  Stagnant  Uniform Environment
                         \Transition
                0(L
                                 Strongly Deflected Jet

    € = 0       X\     Weakly Deflected Jet

             b)  Pure Jet  in  Uniform Crossflow
   u.
                 ^Transition
                   \
                    \
/                           Strongly Deflected Plume

                         Weakly Deflected Plume
             c)  Pure Plume in  Uniform  Crossflow
Figure 2.4     Examples of Combined Effects of Momentum Flux,
                Buoyancy   Flux,    Crossflow,   and    Density
                Stratification  on Flow Behavior
                               30

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                                Transition
                                     7///7777T7
                                        Density current
                             Jet-like
              d)  Pure Jet in Stagnant  Stratified  Ambient
    ua =
                                         Density current
             e)  Pure Plume in  Stagnant Stratified Ambient
Figure  2.4     (continued)
                              31

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2.1.3 Length Scales

    Length  scales  describe  the   relative  importance  of
discharge volume flux, momentum flux, buoyancy  flux, ambient
crossflow, and  density  stratification in controlling flow
behavior.  The length scales will describe the  distance over
which these dynamic quantities control the flow.
2.1.3.1 Discharge Length Scale

    Initially as the jet exits the port  in the zone of flow
establishment,  port  geometry  controls the  flow.    The
distance over which the port has effect on the flow can be
characterized as a  discharge  length scale.   The discharge
length scale  Lg relates the volume flux to  momentum flux,
and from dimensional reasoning
    LQ -
             1/2
(2.9)
which is proportional to the diameter D of the orifice for
a round jet,  Lg =  (*r/4)1/2D.   For distances  s from the source
less  than  Lg  the  flow  will  be  in  the   zone  of  flow
establishment.   Thus  if  s/Lg  is  less  than  the  order of
unity,  or  s/Lg  « 0(1), the  source geometry will  have a
significant  effect  on the flow  behavior,  but for s/Lg »
0(1)  the  effect  of  the initial  geometry is lost  to jet
momentum or buoyancy which will control the flow behavior.
Similar to the  flow  constants  discussed in Section 2.1.2,
the appropriate numerical value for the  extent of this flow
region must be obtained form experimental data; this holds
for all the following "order of unity" statements.
2.1.3.2 Jet/Crossflow Length Scale

    The presence of a crossflow ua will deflect the jet as
shown  in  Figure 2.4b.   The behavior  of the  pure  jet in
crossflow depends on the relative  magnitude  of  jet momentum
to the crossflow.   The  distance  to the position where the
jet becomes  strongly  affected  (i.e.  deflected in the case
of an oblique discharge) by the ambient crossflow is given
by a jet/crossflow length scale 1^

    T   TUT 1/2 /__                                        / O 1 rt \
    LjT M0  /ua                                       (2.10)

    Thus  for s/L^  « 0(1)  the initial  jet momentum will
dominate and crossflow  is of secondary importance, and for
s/I^ » 0(1)  ambient velocity will have a strong influence
on jet behavior.
                            32

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2.1.3.3 Plume/Crossflow Length Scale

    Arguments presented for the effect of crossflow on the
pure plume flow are  in  analogy  to those for a pure jet  in
crossflow.   The plume/crossflow  length scale  1^  for the
deflection of a vertically rising plume as shown in Figure
2.4c is given by
    Thus  for  z/I^  « 0(1)  the initial  jet  buoyancy will
dominate  and  crossflow is  of  secondary importance, while
for  z/L,.,  »  0(1)   ambient velocity  will  have  a  strong
influence on plume behavior.
2.1.3.4 Jet/Plume Length Scale

    The  distance  from  momentum  dominated  to  buoyancy
dominated flow for a buoyant jet in a stagnant environment
is characterized by a jet/plume length scale 1^  (See Figure
2.4a).    Dimensional  analysis  suggests  the  functional
relationship

    I* = M03/4/V/2                                    (2.12)

    So for z/Ly, « 0(1) flow behavior will be controlled by
momentum  and  for  z/Lj,  »  0(1)   flow  behavior  will  be
controlled by buoyancy, i.e. approach that of a vertically
rising plume.

    In the rare case  that l^ «  Lp,  there will be  no momentum
dominated  flow  and  the  flow  will be  entirely plume-like
except for the region very near the issuing source.
    The ratio of I^/I^ is proportional^ to the usual discharge
densimetric Froude number F0 = UQ/(g0'D)1/2 which relates the
inertial forces to buoyancy forces  within the plume, I^/I^,
= (4/*)1/4F0.  The pure plume has a Froude number of O(l) and
the pure jet Froude number  approaches infinity.
2.1.3.5 Jet/Stratification Length Scale

    The effect of  a  linear ambient density stratification
on a pure jet is to counteract the momentum flux of the  flow
as it travels away  from the source.  This is because the jet
discharging  with  upward orientation  entrains  fluid  of a
greater density and  carries it upwards  where the  ambient
fluid  is  less dense.    A  reverse  condition  holds  for a
downward inclined jet.  The jet/stratification length scale
is given dimensionally by
                            33

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    V- (VO1A                                    (2.13)

For a vertically discharging jet this length scale will be
a measure of the distance to the terminal level of the jet
flow.   For a horizontally  discharging jet L^' will  be a
measure of the distance at  which  collapse  of  the jet flow
will commence,  with increasing  lateral  spreading and damped
turbulent entrainment.
    Thus for distance of s/L/ « 0(1) the effect of density
stratification will  be negligible  on  jet behavior.   For
distances of s/I^,' » 0(1)  the effect of stratification will
be to terminate the  jet motion  and a  density current will
then form at the terminal level.
2.1.3.6 Plume/Stratification Length Scale

    As for the pure jet in stratification, the effect of a
linear ambient density stratification on a pure plume is to
modify both buoyancy and momentum fluxes of the flow as it
travels away from the  source.   The  maximum height of rise
of a simple plume in linear density stratification will be
proportional to the plume/stratification length scale

    V- J0V4A3/8                                    (2.14)

For  a  vertical distance  of z/L^' «  O(l)  the  effect of
density stratification on plume behavior will be negligible.
2.1.4 Typical Flow Regimes of Unconfined Buoyant Jets

    This  section presents  a series  of basic  analytical
results  for  jets  or  plumes  in  a  variety  of  ambient
situations.  All of the results  are perturbation solutions,
in the  sense that a simple  analytical  solution  (e.g. the
pure jet) is being perturbed by assuming a small effect of
an additional variable  (e.g. a weak crossflow).

    For  the following  development  the  simplest  possible
assumptions are being made:  a point source, either vertical
or horizontal orientation, and only one perturbing variable.
The  results can  be readily  generalized to  more  complex
conditions   (e.g.   arbitrary   orientation   or   multiple
influences).  Indeed, such generalizations are implemented
in the predictive elements presented in Chapter V.
                            34

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2.1.4.1 Weakly Deflected Jet In Crossflow

    For a relatively weak  crossflow,  the jet would behave
the same as  if it were in  a  stagnant environment, except
that it is  slightly advected by the ambient current  (Figure
2.4b).  This region is defined for z/I^, « 0(1), where z in
this section signifies  the  coordinate pointing across the
flow (e.g.  vertically) .

    In first order, the vertical  velocity for this jet flow
would be similar to Eq. (2.3).    In  addition,  a kinematic
relationship applies for a jet element moving horizontally
with  the  crossflow  velocity  in  the direction x  of  the
crossflow

    dx/ua = dz/uc                                    (2.15)

Substitution for the vertical velocity given in Eq. (2.15)
and integrating  gives  the  trajectory relationship for the
weakly  deflected  jet  flow  (Wright's   (1977)  "momentum-
dominated near-field", or mdnf1)  expressed in terms of the
jet/crossflow length scale
                                                     (2.16)

where t1 is a trajectory constant.

    Eq.  (2.16)  is  valid for small  source dimensions, i.e.
small values  of L^/L^.   In the special case  that L^/I^ ^s
large,  the  effect  of  geometry is important and Eq.  (2.16)
no longer holds.

    Jet width b is similar to the jet  issuing  in a stagnant
environment given by Eq.  (2.4) or

    b = b,z                                          (2.17)

where b, is the spreading constant.

    The dilution S is  similar to Eq.  (2.5) ,  and is expressed
in terms of L,,
     1In the  following  the  abbreviated  descriptions for
crossflow influenced subsurface flows (mdnf,  mdff, bdnf and
bdff)  as suggested  by  Wright  (1977)  will  be  used for
convenience   since   they  are   frequently   used  in  the
literature.  Care must be exercised in their  interpretation
so as  to avoid  confusing them with the designation  "near-
field"  and   "far-field"   as   used  in  this  study  (see
introductory comments at the beginning of this Chapter).
                            35

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                                                    (2.18)

where s,  is the dilution constant for the mdnf flow.


2.1.4.2 Strongly Deflected Jet In crossflow

    For z/L^ » 0(1) the ambient flow will dominate the flow
pattern.   For a strongly deflected jet the vertical velocity
has  decayed  to  less  than  the value   for  the  ambient
crossflow;   thus   the   ambient   crossflow   will   have
significantly deflected the jet as shown  in Figure 2.4b.

    The  behavior of  the  bent-over  jet  is assumed  to be
roughly  equivalent  to that of a  cylindrical  line impulse
located at the same vertical rise.   Scorer (1954) describes
a line impulse as an  instantaneous  release of nonbuoyant
fluid from a  horizontal line  source.   The characteristic
variables  are the line impulse M'(defined as the kinematic
momentum  flux per  unit length for an infinitesimal period
of  time),  vertical  rise  z,  and time  after  release  t.
Applying dimensional analysis

    M't/z3 = constant                                (2.19)

    To  apply  this  analogy  to   the pure  jet,  MQ/ua  is
substituted for M' and x/ua replaces t in Eq.  (2.19).  The
trajectory relation for  the strongly deflected  jet flow
(i.e.  "momentum-dominated  far-field",   mdff)   is  then
expressed  in terms of the jet/crossflow  length scale

    z/^  = t^x/Lj173                                 (2.20)

where t2  is a trajectory constant.

    The  width  b   of  the gradually  rising  jet element is
proportional to the height  of  rise  z

    b = b2z                                          (2.21)

where b2  is a spreading constant.

    The mass conservation equation is used to  determine the
dilution  at any position z,  c0Q0 «  cfb2ua.  In  terms of the
jet/crossflow length  scale  the dilution  is  expressed as

    S = s2(z'/LA)                                    (2.22)

where s2  is a dilution constant for the mdff flow.
                             36

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2.1.4.3 Weakly Deflected Plume in Crossflow

    For a relatively  weak  crossflow,  the pure plume would
behave the  same  as if it were  in  a stagnant environment,
except that it is advected  with  the  ambient current  (Figure
2.4c) .

    For values of  z/L,, « O(l) ,  the flow will behave as  a
plume in a  stagnant environment but will be advected with
the crossflow.  Proceeding  in analogy to the mdnf  flow, the
trajectory  equation  for the weakly deflected  plume flow
(i.e. "buoyancy-dominated near-field",  bdnf) can be written
in terms of the plume/crossflow length  scale
                                                     (2.23)

where t3 is a trajectory constant.

    Plume  width b  is similar  to  the  plume issued  in  a
stagnant environment and is given by

    b = b3z                                          (2.24)

where b3 is a spreading constant.

    The dilution S  is  similar to Eq.  (2.8),  and is expressed
in terms of L^,  L,,, and 1^ •

     S = s3(Lb1/3z5/3)/(I^L^)                            (2.25)

where s3 is the  dilution constant  for the bdnf flow.


2.1.4.4 Strongly Deflected Plume in Crossflow

    For z/I^ » 0(1) the ambient flow will have a pronounced
effect on  the flow pattern.   When  strongly deflected,  the
plume vertical velocity has decayed to less than the value
for the ambient crossflow; the ambient crossflow will have
significantly deflected the plume as shown in Figure 2.4c.

    The deflected plume should behave as a rising thermal,
i.e. an instantaneous  release of a buoyant cylindrical fluid
mass along a line source.  The important variables  are  J',
the buoyant  weight per unit length, vertical rise z,  and
time t.  Dimensional reasoning implies for the thermal

    J't2/z3 = constant                                (2.26)

Substituting x/ua for  t and replacing J' by J0/ua yields  the
trajectory  relationship  for the strongly  deflected plume
flow  (i.e. "buoyancy-dominated far-field", bdff) expressed
in terms of length scales
                            37

-------
         = t^x/Lj,)2'3                                 (2.27)

where t4 is a trajectory constant.

    Plume width b is analogous to Eq.  (2.21),  or

    b = b4z                                          (2.28)

where b4 is a spreading constant.

    The mass conservation equation is used to determine the
dilution at any position z, c0Q0 & cb2ua,  leading to

    S= s4z2/(LgIJ                                    (2.29)

in analogy  to Eq.  (2.22),  where s4 is a dilution  constant
for the bdff  flow.


2.1.4.5 Horizontal Jet with Vertical  Buoyant Deflection

    For a  horizontally discharging jet with  weak  vertical
deflection  induced by the buoyancy  the centerline  velocity
is given in first order by the pure jet solution, Eq. (2.3) ,
or uc  ss M01/2x"1  in  which x  is  the horizontal  coordinate
direction.  The small vertical deflection  due to the local
buoyancy-induced velocity w is given  by

    dz/dx = w/uc                                     (2.30)

The local buoyant vertical acceleration of a jet element is
given by

    dw/dt * J,/(auc)                                  (2.31)

in which a = b2 is the  local jet  cross-sectional area and b
= x is  the  jet width.  With the  Galilean transformation dt
= dx/uc, and after substitution for b and  uc, Eqs. (2.30) and
(2.31)  can be  solved to  give  the normalized  trajectory
relation

    z/I* = ts(x/V3                                  (2.32)

The appropriate width  and dilution  equations are

    b = bsx                                          (2.33)

and

    S = SX/L)                                      (2.34)
                             38

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where the constants b. and ss should be numerically  similar
to those for the weakly deflected jet  in  crossflow,  b. « bv
and s5 *  s^t respectively.  In either  case the perturbation
effects are small and the equations must  be  identical if no
perturbation is present .  The  above solutions are valid in
the region x/I^ « 0(1).


2.1.4.6 Vertical Plume with Horizontal Momentum Deflection

    The final  phase  of  a horizontal buoyant jet will be a
vertically rising  plume which is  weakly deflected by  the
effect of the  horizontal discharge  momentum   (see Fig.
(2.4a).   This  will  occur in the region  z/I^, » 0(1).   The
plume will have a local  vertical  centerline  velocity given
in first order by the pure solution,  Eq.  (2.6).   The  small
horizontal deflection of the plume trajectory is  given  by

    dx/dz - uh/uc                                     (2.35)

where  uh  is  the  induced horizontal  velocity due  to  the
discharge  momentum  flux  M0.   Conservation  of horizontal
impulse implies

    auh »  M(/uc                                       (2.36)

in which a a  b2 is the local plume  cross-sectional area  and
b  *  z is the  plume width.    The trajectory  relation  is
obtained after substitution and  integration

    x/Ly,  = XF -  t^z/I^r1'3                            (2.37)

in  which  XF   is  the  ultimate  value of  the  horizontal
deflection for  the  final stage (as z approaches  infinity)
of the vertically rising plume.   The width and dilution  are
given  directly by   Eqs.  (2.7)   and  (2.8),  or  using  the
appropriate length scales,

    b - b6z                                          (2.38)

and

    S - s6z5/3/(I*2/3I*)                                 (2.39)

As before, the constants b6 and s6 should  be  the  same  as
those  for  the  weakly deflected plume, b6 *  b3  and s6 *  s3,
respectively.

    The  buoyant trajectory  equations for  the horizontal
buoyant  jet  in  a stagnant  environment, Eqs.  (2.32)  and
(2.37),  are  similar to  those  first derived  by  Abraham
(1963), albeit with  a different methodology.
                            39

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2.2.4.7 Vertical Jet in Linear Stratification

    A vertically discharging jet  in a linear ambient density
environment will ,  in its initial stage,  behave purely jet-
like.   In  the final stage,  however,  as it  approaches the
terminal level,  it will  be increasingly  modified by the
ambient  density gradient.   In  particular  the local  jet
momentum  flux,  M  at uc2b2,  and  local  buoyancy  flux,  J  &
ucgc'b2, where gc'  is the  local centerline  buoyancy (gc'  =
g(pa(z)-pc)/pa(z) ,   where  pc  is the  centerline  density and
pa(z)  is the local  ambient density), will change.

    The conservation equations are

    dM/dz at gc'b2 a bJ/M1/2                            (2.40)

for momentum and

    dJ/dz » -Qe at  -M1/2be                             (2.41)

for buoyancy, in which Q  =  ucb2  is the local jet discharge
(volume  flux) and  e is the  linear  buoyancy  gradient.   In
addition, a linear jet spreading equation  applies in first
order

    db/dz at k                                        (2.42)

where k is the spreading coefficient.  Integration of these
three  equations with the boundary conditions b =  0 (point
source), M  =  M0,  and  J  = 0 (pure jet discharge)  at  z = 0
leads  to the solution

    M/M0 = 1 - m7(z/V)4                             (2.43)

where  m7 is an appropriate constant.   Eq.  (2.43) indicates
that  for Z/LH/  « 0(1)   the jet momentum  is essentially
conserved,  M  =  M0  (pure  jet),  while the terminal  level is
approached at a height, Z^/I^' = (l/m7)1/4, at which point the
local  jet momentum vanishes, M = 0.  Other aspects of the
solution are the linear spread

    b  = b7z                                          (2.44)

and the dilution

    S  =  s7((l-m7(z/Lm')4))1/22/LQ                       (2.45)

where  the constants b7 and s7 should be similar to those of
the pure jet, b7 = b,,  and s7 * s1.
                             40

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    No similar closed-form solutions seem possible for cases
with  a  discharge buoyancy  (non-zero  J0)  including  the
limiting case of a pure plume.
2.2 Buoyant Spreading Processes

    In  the  context  of  this  study,  buoyant  spreading
processes  are  defined  as  the  horizontally  transverse
spreading  of  the mixed  effluent flow  while it  is being
advected downstream by the ambient current.  Such spreading
processes  arise  due to  the  buoyant forces  caused  by the
density difference of the mixed flow relative to the ambient
density.

    The buoyant spreading phenomenon is a far-field mixing
process.   Usually  it  is  preceded by buoyant jet mixing in
the near-field and is followed by passive diffusion, another
far-field mixing process.  If the discharge is nonbuoyant,
or weakly  buoyant,  and the ambient  is unstratified, there
is no  buoyant spreading  region  in  the far-field,  only a
passive diffusion region.

    Depending  on  the  type of near-field  flow and ambient
stratification several types of buoyant spreading may occur:
(i) spreading  at  the water surface,  (ii)  spreading at the
bottom,  (iii)  spreading at  a  sharp  internal  interface
(pycnocline) with a density jump, or  (iv)  spreading at the
terminal level in continuously  (e.g.  linearly)  stratified
ambient.
2.2.1 Buoyant Surface Spreading

    The  definition  diagram  and  structure  of a  surface
buoyant spreading process in unstratified crossflow  is shown
in Figure 2.5.   The  laterally  spreading flow behaves like
a density current and entrains some ambient  fluid in the
"head region" of  the current.   The mixing rate is usually
relatively small.  Furthermore, the flow may interact with
a nearby bank or shoreline (not shown in Figure 2.5).  The
flow depth may decrease during  this phase.  The analysis of
this  region  is based  on  arguments presented  for  surface
buoyant spreading by Jones et al.  (1985).

    The continuity equation for the density current is

    uaabv/3x + 3(vbv)/3y = we                         (2.46)

where we is the net velocity across the interface, ua is the
ambient current,  v(x,y) is the local  transverse velocity,
bv is  the vertical density  current thickness,   x is    the
                            41

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                                            Front
  Plan View
 u,
          Initial
          Condition
 Cross-section A-A
Frontal Zone
                          I   Pa
                                                H
             Buoyant  Surface Spreading
Figure 2.5    Buoyant  Surface Spreading Process
                             42

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downstream distance,  and y is the distance  lateral  to the
crossflow.  Benjamin  (1967) has derived an equation for the
spreading velocity VB

    v.2/(g'bv) = 1/CD                                  (2.47)

where C0 is a drag coefficient that depends on the relative
depth bv/H and is  in the  range of 1/2 to 2.  Combining Eqs.

(2.46) and (2.47)  and  integrating laterally over the density
current width gives

    uad (*>,£„) /dx = q.(x)                               (2.48)

where q^x) is the localized head entrainment representative
of  the dominant  mixing  mechanism, and  bh  is the  lateral
half -width.

    The localized head  entrainment of the density  current
is parameterized as qe(x) = 0vBbv where ft  is a constant with
a range of 0.15 to 0.25 (Simpson and Bitter, 1979; Jirka and
Arita, 1987)  .

    The flow half -width  bh is obtained for  any  downstream
distance  x  by  using   the  boundary  condition  for  the
streamline (VB * uadbh/dx) and integrating Eq.  (2.46)

    bh " Cbhi3/2 + 3/2(V2CD)V2(x - X,-)]2/3              (2.49)
where x{  is  the downstream distance at the beginning of the
buoyant  spreading region, and  bhi  is  the initial  density
current half -width.   This 2/3 power law  of  flow spreading
is  in agreement with  the  previous  work  of  Larsen  and
Sorensen  (1968) .

    The vertical  flow width  bv is  given by integrating Eq.
(2.48) to obtain

    bv -  bviOVbhi)^"1                                 (2-5°)

    Due  to  mixing  the  local concentration c  and  local
buoyancy  g'  gradually change  with distance x.   The  bulk
dilution S,  given by  CQ/C, is equivalent to the ratio g0'/g'
of buoyancy which is a conservative tracer in  this  case.
Buoyancy  conservation  in   the  density   current  can  be
expressed as u^'b^ = constant.  The initial conditions and
appropriate  substitutions   provide  the  expression   for
dilution S

    S= S,.(bh/bhy                                    (2.51)
where S,  is the initial dilution.
                            43

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2.2.2 Buoyant Bottom Spreading

    This  spreading process  is analogous  to  the surface
spreading (Figure  2.5) except  that  the mixed flow density
is pa  + Ap,   i.e.  heavier  than  the  ambient.    If bottom
friction  is  neglected  in the  spreading  process,  then the
same equation system as derived above will apply.
2.2.3 Buoyant Spreading at Pycnocline

    Referring to  Figure  2.6a,  a sharp  density change may
exist separating an ambient lower layer with density pL and
an upper layer with density p^.   A mixed zone may exist as
a result of  a near-field mixing process.   The mixed zone
density is pL  - Lp, so that a difference Lp exists relative
to the lower  layer.  If  the  local  (at any x) thickness of
the  density  current is  bv,  then this  region  extends for
hydrostatic reasons partially over the upper layer, so the
expression for hy is

     hjj = bvAp/(pL-pu)                                  (2.52)

and  partially over the  lower layer,  so that  hL  = by-hy.
Other than  this hydrostatic adjustment mechanism the buoyant
spreading  process at  the pycnocline has  the  same flow
equations,  i.e.  Eqs.  (2.49,  2.50,  2.51), as  the buoyant
surface current.
2.2.4 Buoyant Spreading at Terminal Level

    In  an ambient  stratification with  a  linear density
gradient, a near-field mixing  process may lead to a layer
formation at a  terminal  level  Zt/  i.e.  a mixed current  is
produced whose  density is  equal  to the ambient density  at
the terminal level.   The mixed  zone  perturbs the ambient
stratification  as shown  in Figure  2.6b  and leads  to a
lateral  spreading   while   the  flow  is  being  advected
downstream, qualitatively similar to  Figure 2.5.

    The  spreading velocity VB  for the  stratified case  is
expressed as

    VB2/(ebv2) =  1/(2CD)                               (2.53)

where CD is. the  drag coefficient for the stratified case.

    Proceeding  in the same fashion as in  Section  2.21 gives
the following results, for horizontal half-width  bh
                            44

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Pycnocline
Level
                                     Density current
                                           h
                                 A/5
                        PL
                                            u
         a)  Spreading  at  Pycnocline
                              Ambient
                                   Density  current
        b)  Spreading at  Terminal  Level  of
            Linear  Stratification
Figure 2.6
       Density Perturbation of Ambient Stratification
       Leading to Buoyant Spreading Processes
                           45

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    bh - [+                                      (2-54)
while the expression for the vertical thickness bv is
                 )-                                  (2.55)

Dilution is given by continuity as

    S= S,.(Vbhi)^                                    (2-56)
2.3 Passive Ambient Diffusion Processes

    The  existing turbulence  in  the  ambient  environment
becomes  the dominating  mixing  mechanism  at sufficiently
large distances from the discharge point.   The intensity of
this passive diffusion process depends upon the geometry of
the   ambient  shear   flow  as   well  as   any   existing
stratification.   In  general,  the passively diffusing flow
is  growing  in width and  in  thickness (see  Figure 2.7).
Furthermore, it may interact with the channel bottom and/or
banks .

    The analysis of this region  follows classical diffusion
theory (e.g. Fischer, et al. 1979).   The standard deviation
a of a diffusing plume in crossflow can be  written in terms
of the transverse turbulent diffusivity E

    a2 -  2Ex/U8                                      (2.57)

in which x  is the distance following  the ambient flow with
the point release located at x = 0.  The coefficient  of eddy
diffusivity  depends  on  the  turbulence conditions  in the
environment  and  may  be a function of distance x (or plume
size a) .
2.3.1 Diffusion in Unbounded Channel Flow

    In open channel flow the eddy diffusivity can be related
to the friction velocity u, and the channel depth H

    Ez = 0.2U.H                                       (2.58)

for vertical diffusivity,  and

    Ey = 0.6u«H                                       (2.59)

for horizontal diffusivity.  The friction velocity is given
                            46

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   Plan  View
        i    Initial  Conditions
        X:
Possible Bank Interaction
  Side View
        i

                                              Possible Bottom Interaction
                  Passive Diffusion  Process
Figure  2.7      Passive  Ambient  Diffusion Process
                                  47

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by u* =  (f/8)1/2ua  where f is  the Darcy-Weisbach  friction
factor.  Due to some anisoptropy in a typical channel flow,
the diffusivity  in the horizontal transverse  direction is
usually  larger  than   the  diffusivity   in  the  vertical
direction.   The coefficients  included  in Eqs.  (2.58)  and
(2.59) are average values for  reasonably  uniform channels.
The coefficients may be considerably larger (up to a factor
of 2)  for highly non-uniform cross-sections and/or strongly
curved channels  (see also Holley  and Jirka,  1986).

    Solution of Eq. (2.57) with these diffusivities and with
initial  flow  width conditions specified  at x{  (see Figure
2.7)   gives  the  vertical thickness  bv  and  half-width bh/
respectively

    bv = [7rEz(x-x()/ua)  + bvi2]1/2                      (2.60)

    bh = OE^x-x^/uJ  + bhi2]1/2                      (2.61)

where x,., bvj,  and bh). are the distance, half-width, and depth
of the plume, respectively,  at the beginning of the passive
diffusion region.   The above lengths are related  to the
standard deviations, bv = (*/2)1/2ff2  and bh =  (7r/2)1/2ay,  and
assume  an  equivalent  top-hat plume with same  centerline
concentration and  pollutant mass  flux.

    The  continuity  equation   applied  to  the  plume  in
crossflow 2uabvbh a SQ0  yields the dilution

    S = 2bvbh/(I^|LQ)                                  (2.62)

    Beyond the  distance when the  flow becomes fully mixed
(bv =  H), the dilution expression  is

    S « 2Hbh/(L^)                                   (2.63)


2.3.2 Horizontal Diffusion in  Unbounded Channel Flow

    Many  environmental  flows  without   any  significant
limitation on the transverse dimension (coastal water, large
lakes,  etc.)  exhibit  an  accelerating turbulent diffusive
growth  pattern.    The  horizontal  diffusivity  is  often
specified by  the so called  "4/3 law" (see Fischer et al.,
1979)

    Ey = a(3ay)4/3                                     (2.64)

in  which  a   is  a  coefficient  equal   to  0.01  cm2/3/s
(appropriate  for small plume  sizes)  and  E  is in units of
[cm /s]  and  a   in  [cm] .    Integration of the  applicable
diffusion equation with this variable Ey  yields a solution
                             48

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for plume  growth (Brooks,  I960,  see  also Fischer et  al.,
1979)

    bh = bhi[l +  (7r/3)Eyi(x-x-)/(uabhi2)]3/2              (2.65)

in the  present notation and width convention.   E •  is  the
initial value of diffusivity, so from Eq. (2.64)  at position
xi

    Eyj  = 0.0015bhl-4/3                                  (2.66)

with units of  [m2/s] for Eyi  and [m]  for the initial width
bhj.  The dilution expressions are the same as before, given
by Eqs. (2.63) and  (2.62).
2.3.3 Vertical Diffusion in stratified Shear Flow

    In the presence of a stable ambient stratification  the
vertical  diffusive mixing is  generally  inhibited.    An
expression proposed by Munk and Anderson (1948)  can be used
to specify the reduced vertical diffusivity

    Ez = E0(l +3.33RJ)"1'5                              (2.67)

in which E0 is  the  vertical diffusivity under neutral shear
flow conditions (given by Eq.  (2.59)) and Rf is the gradient
Richardson number.   For linearly stratified shear flow with
a  layer depth  Hs,   a  simple  expression for  the  gradient
Richardson number  is

    Rj = EK2HS2/U.2                                     (2.68)

where  e  is  the buoyancy  gradient,  K  is  the  von  Karman
constant (= 0.4),  and u, is the shear velocity.


2.4 Interaction Processes:  Surface or Bottom Boundaries,  and
Internal Layer Formation

    Ambient water  bodies always have vertical  boundaries:
the water surface and  the bottom, but in addition "internal
boundaries" may exist  in the form of layers  of rapid density
changes  (pycnoclines).    Depending  on the  dynamic  and
geometric  characteristics  of  the discharge  flow, a  large
number   of  interaction  phenomena  can   occur   at  such
boundaries.    Furthermore,  in  the  case   of   a  linearly
stratified  ambient where  flow  trapping may  occur,  other
interaction phenomena may  take place.

     In  essence,   these interaction  processes  provide  a
transition between the jet  mixing process in the near-field
                            49

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(Section 2.1), and between buoyant spreading (Section 2.2)
and passive diffusion (Section 2.3) in the far-field.

    The  analysis  of  several  interaction  processes  is
presented in the following sections.  Many other situations
are  possible   depending   upon  discharge  configuration,
direction of  buoyancy and  other factors; however  all of
these are  related to the  generic  cases and they will be
briefly summarized (without analysis) in Chapter V.

    A control  volume approach  is  used for  the following
sections. When the flow contacts the boundary,  bv and bh are
defined as the vertical depth and horizontal half-width of
the subsequent flow,  respectively.  The variable subscripts
"i" (initial) and "f"  (final)  (e.g.  bf, Sf)  denote control
volume inflow and outflow quantities, respectively.
2.4.1 Near-Horizontal Surface Approach

    In the surface  approach  the bent over flow approaches
the water surface near horizontally at impingement angle 0{
< 45« (Figure 2.8a).  The  flow  is advected with the ambient
velocity field at a  rate equal to ua.   This situation occurs
for crossflow dominated jet-like and plume-like cases that
are  relatively weakly  buoyant, hence the  flow  will  be
strongly deflected when it contacts the surface.

    Experimental  evidence   (Jirka  and  Harleman,  1973)
suggests  that  within  a  short  distance  after  surface
impingement the concentration  distribution  for a 2-D flow
changes from the assumed gaussian distribution to a top-hat
or uniform  distribution   (Figure 2.8a).   Using  a control
volume approach the initial centerline dilution is related
to the  final  bulk dilution,  and a bulk mixing process is
assumed with  Sf = cS{, where c is  of  the order  of 1.5 to
2.0.   An equivalent  cross-section  aspect  ratio  for the
outflow section of 2:1 is  assumed.  The continuity equation
for the control volume in Figure 2.8a  is then

    SfQ0 - ua2bhf*bvf                                   (2.69)

where b, is the initial half-width (radius),  bvf  is the final
flow vertical  width,  and  bhf is  the  final flow horizontal
half-width.   This is evaluated as bvf - bhf = (S^L^/2)1/2.

    A dynamically analogous situation exists for the bottom
approach of a  downward oriented jet or negatively buoyant
flow.  Also the approach process to  any internal pycnoclines
is quite similar, even though the layer configuration will
adjust itself hydrostatically along the pycnocline depending
on the density jump  conditions  (see Section 2.2.3 and Figure
                            50

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      Cross-section
                                        'f (rectangular)

                          i (round)       widtn  bh
                          width b
     a)  Surface Approach (Near-Horizontal)
Figure 2.8     Flow  Interaction  Process with  Water  Surface
              (i  indicates inflow values  in control volume
              and f outflow values)
                           bl

-------
   Side  View
   Plan  View
     Stagnation
     Point
       Inclined Front
 b) Surface  Impingement with Buoyant  Upstream  Spreading
Figure  2.8     (continued)
                             52

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     Side  View
 c) Surface Impingement  with  Full  Vertical  Mixing
   Side View
u,
d) Surface  Impingement  with  Buoyant  Upstream Spreading,
   Full Vertical Mixing, and  Buoyant  Restratification
 Figure 2.8    (continued)

-------
2.6a).   Finally the near-horizontal approaches towards the
terminal  layer in  continuously stratified  flow  will  be
analyzed with a similar approach.
2.4.2  Near-Vertical   Surface   Impingement  with  Buoyant
Upstream Spreading

    In this surface approach condition, the weakly bent flow
impinges on the surface at a near-vertical angle 0,. (Figure
2.8b), where 0f  > 45».   After impingement the flow spreads
more or less radially along the water surface as a density
current.   In particular,  the  flow spreads  some distance
upstream against the ambient flow,  and laterally across the
ambient flow.   This spreading is  dominated  by the strong
buoyancy of the discharge.

    The  lateral  spreading of  the  flow  in  the  surface
impingement region is driven by both the  flow momentum and
buoyancy  force.    Of interest  is  the  upstream intrusion
length  Ls,  dilution  s,  horizontal width  b^,  and vertical
depth bv of the density current at  surface impingement.

    The  analysis  of  this  flow   region   follows  results
presented  by Lee  and Jirka,  (1981),  and Jones  et al.,
(1983).  Lee and Jirka analyze the properties of a buoyant
subsurface discharge in stagnant water including the effects
of recirculation  and buoyant restratification.   Jones et
al. presents a methodology to predict the upstream spreading
of a buoyant radial discharge in crossflow.

    A  length scale  1^  representing  the  turbulent mixing
action  of the horizontal  momentum flux  versus stability
effect of buoyancy force is given by

1^ = (defected  horizontal momentum  f lux)3/4/J01/2       (2.70)

For the weakly deflected plume, Holley and Jirka,  (1986)
give an expression for the vertical momentum of a plume

    M * 0.85J02/V/3                                   (2.71)

where,  z  (= H)  is the  vertical  distance along the flow
trajectory.    Substituting  appropriate  values into  Eq.
(2.70), the length scale for a weakly  deflected plume at
impingement becomes

    L,, * 0.367H(l-cos0j)                              (2.72)

where  the  factor  (1-cos^)  accounts  for  the deflected
horizontal  momentum  flux,  in analogy  to the vane equation
in classical fluid mechanics.
                            54

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    Jones  et al. define  an intrusion  length scale L: ,  by
the interaction of buoyancy force with the crossflow force

    L, = J0/(2ffC0u.3)                                  (2.73)

where CD is a drag coefficient of O(l) .

    Thus, for a weakly deflected plume at surface approach,
the ratio  of length scales  obtained from Eqs.  (2.72) and
(2.73)

    Lj/Ly, =  0.54(VH) (l/(l-cos0,.))                    (2.74)

which  describes  the relative  importance  of buoyancy  to
momentum forces  at surface impingement.

    Jones  et  al.  provide a  numerical  solution  for the
upstream intrusion length (their Figure 5-14) which can be
summarized  as  follows

    LS/L, =  4.2(LI/LN)'2/3  for  LJ/LH  3.3              (2.76)

Noting that Lt =  Lj/5 with CD  =  1 and since  the  flow is a
weakly deflected plume  at surface approach,  the upstream
intrusion length Ls  in  Eq. (2.75) can be  expressed in the
present notation  as
    Ls = 1.26Lb((l-COs5i)/(VH))                       (2.77)

    Ls = 1.91^                                        (2.78)
for the  conditions L^H  <  6. 11 (1-cos^-)  and Lj/H > 6.11(1-
COS0,.)  in Eqs. (2.75) and  (2.76), respectively.

    Jones et  al.  (their  Figure 7-8)  also give the dilution
for a radial  surface discharge

    S/FS = 1.6(L,/LN)1/3                                (2.79)

where Fg is  a radial surface spreading Froude number.  This
Froude number is  defined as

    Fs = ur/(g'L0)1/2                                   (2.80)

where ur is  the discharge velocity of the radial  jet  and L0
is a characteristic length scale defined by
    L0 = (2wr,h,)                                      (2.81)

with TJ  and h, are the radius and depth of the buoyant radial
surface spreading  flow,  respectively.


                             55

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    The results of Lee and Jirka can be used to evaluate the
surface spreading  Froude number F ,  so the dilution S  from
Eg.  (2.79)  can be  found.   In this  analysis, the initial
radial surface  spreading  region  uses a simplified control
volume to relate  the  properties  of  the vertically buoyant
jet at the  entrance of the  surface  impingement region to
the characteristic parameters of the horizontal axisymmetric
buoyant surface jet at the exit of this region.

    Lee  and Jirka define  the Froude  number  at surface
impingement

    F, «  ur/(g'h,)1/2                                  (2.82)

where ur  is  the radial surface spreading velocity and h, is
the depth after impingement.   For large values of H/D,  the
value F,  *  4.62 and the value h,/H a  0.0775.   The  radius of
the flow TJ  is  r,  a  «H,  where e a  0.11.   By substituting
these asymptotic values into Eg.  (2.81), the  characteristic
length scale L0 becomes

    L0 *  0.23H                                       (2.83)

which when  combined with  asymptotic values  for Eq.  (2.82)
gives

    Fs =  F,(h,/L0)1/2 a  2.65                           (2.84)

indicating  that  the  flow   in this  region  is  jet-like.
Finally,  note  that  the  radial  surface  spreading  Froude
number Fs can be  expressed  in terms  of the  discharge  flux
variables as QJ01/2/M0  .

    This  result  can   be  then used  to  determine  a  bulk
dilution at the end of the region Sf.   From Eqs.  (2.79)  and
(2.84) the  expression  for  final dilution  in the surface
impingement region is
    Sf - a^gS^V*1)1-008*,-)"                      (2.85)

    The  geometry  of the surface flow as computed  by Jones
et al. will be used to determine the width and depth within
the  region.    From Jones et  al.  (their  Figure 7.1),  the
width, bhf, at impingement is about 2.6 times larger that L8,
or

    bhf  - 2.6LS                                       (2.86)

The  typical  depth  of  the flow  in the upstream  intrusion
region  hs, is  found using the  vertical length scale from
Jones et al. where
                             56

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                                                     (2.87)
 s
                                           where  Sf
                                               2
with CD = 0.8.  With  the  definition g'=  g0'/S
the total bulk dilution,  and using the  identity u Q,j/J0  =
ua QoMo  / ( ^Wo  )  * VW the stagnation flow thickness hs
hs =
                                                     (2.88)
The  final depth  bvf  (at x=0)  is  found using  again  the
continuity equation, bvf  (x=0)  = Q0Sf/ (2bhfua) ,  leading to

                    )                                 (2.89)
2.4.3 Near-Vertical Surface Impingement with Full Vertical
Mixing

    In this surface approach  region,  the weakly bent  flow
impinges  on  the  water surface  at a  near-vertical angle
(Figure 2.8c).  Given  a  shallow ambient water depth and  a
weak buoyancy of the discharge, the flow may become unstable
after impingement, and may recirculate.

    The recirculation  region  causes  the  flow  to  entrain
ambient fluid from the flow itself causing  dilution within
the flow  to  decrease.   Because  of unstable recirculating
flow, the centerplane dilution increases to Sf = RSf , where
R is a mixing factor.   Experimental data indicate R ranges
from l.o to 4.0.  The  final  flow width,  bhf, is found  from
the continuity equation
bhf =
and final outflow location xf is approximated as
       + H
                                                     (2.90)
                                                     (2.91)
where  xf  is the  flow  position  at  the beginning  of  the
region.  The additional distance  H accounts for the typical
length of a recirculating zone.

    For  more buoyant  yet unstable  discharges,  the  full
vertical mixing in the near-field can occur  in combination
with upstream spreading as discussed in Section 2.4.2.  This
is illustrated in Figure 2.8d.
2.4.4 Bottom Interaction Processes

    A submerged buoyant jet discharging in the vicinity  of
the water bottom  into  a stagnant or cross-flowing ambient
can experience two  types  of dynamic interaction processes
                            57

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that lead to rapid attachment of the effluent plume to the
water bottom (see Figure 2.9).  These may be wake attachment
forced by the crossflow or Coanda attachment forced by the
entrainment demand of the effluent jet itself.  A physical
description of these processes is given below.  Appropriate
criteria for the occurrence of such attachment processes are
discussed in Chapter III.
2.4.4.1 Wake Attachment

    In wake attachment  (Figure  2.9a),  the presence of the
discharge outfall  structure  and the jet efflux interrupts
the ambient velocity field and causes a  recirculation region
in the wake downstream from the discharge.

    The  appropriate  length  scale  measuring  the outfall
structure/jet efflux combination  is given by  Lg = (hgLg) 1/2
where  h0  is the  port height or  by Lg  = L,,  for  a  flush
discharge  (zero port height) .  The downstream  extent XR of
the recirculation region is a few multiples of Lg,

    XR = CLg                                         (2.92)

where  C  = 5.0.   Furthermore,   in many such recirculation
processes the dilution is limited  to low values, SR & 2 . 0 to
4.0 (see Jirka et al., 1975).  Thus  by  continuity  the width
of the attached (semi-circular)  cross-section at the end of
the recirculation zone is given by
    bR = [(2A)SRLJ^]                                 (2.93)

with virtual source conditions assumed for the discharge.

    A wall jet, with initial width bR/ is formed downstream
from the recirculation region.  If boundary friction in that
wall jet is neglected  - a reasonable assumption as indicated
by  the data  summarized  in Rajaratnam,   1976 -  then  the
dynamics of the  attached  wall  jet are similar to those of
the free jet as discussed earlier.  Further details  of such
jet models are presented  in Chapter V.

    Depending on discharge buoyancy, the wall jet may adhere
to  the  bottom for long distances (weak,  zero or negative
buoyancy)  or  it may  lift-off  form  the  bottom  at some
distance (strong positive  buoyancy) .  Such possibilities are
considered in the classification  scheme in Chapter  III.
                            58

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    UQ
U,
    i)  Free Deflected  Jet/Plume     ii) Wake  Attachment of
       in  Cross-flow                   Jet/Plume

                a)  Wake  Attachment
    i)  Free Jet                    ii)  Attached Jet

                b)  Coanda  Attachment


Figure 2.9     Near-Field  Attachment Processes
                           59

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2.4.4.2 Coanda Attachment

    When a jet discharges parallel (or near-parallel)  to a
boundary that is located nearby,  rapid dynamic attachment
can occur.  This process is often referred to as a "Coanda
effect".   It occurs because of the entrainment demand of the
jet  flow at  its periphery.   If a  boundary  limits  the
approach  flow  of ambient water then  low  pressure effects
cause the jet  to be deflected towards that boundary thereby
forming  a wall  jet.   Thus the  mixing process  of  Coanda
attached  flow is governed by wall jet dynamics.  Criteria
for  the  occurrence  of  Coanda  attachment under  the  added
influences of buoyancy  or weak crossflow  are discussed in
the following chapter.
                            60

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                        Chapter  III

             Hydrodynamic Flow Classification
    The previous  chapter has presented  a summary  of the
multitude of  distinct  flow and mixing processes  that can
occur with effluent discharges into the water environment.
Obviously,  depending  on the  interplay  of  these  mixing
processes, the  size  and appearance of any  discharge flow
field and its associated mixing zone may vary greatly from
case to case.

    In this chapter,  a rigorous flow classification scheme
is developed that classifies any given discharge/environment
situation into  one of  several flow classes  with  distinct
hydrodynamic  features.   The classification  scheme places
major emphasis on the near-field behavior of the discharge
and uses  the  length scale concept  as  a measure  of the
influence of each potential mixing process.   Flow behavior
in  the   far-field,  mostly  in  the  form   of  boundary
interactions, is also discussed herein.
3.1 Ambient and Discharge  Data: Geometry and Flow Variables

    Given  the  diversity of possible  ambient environments
(e.g. highly varying water depth, curved channels, unsteady
flow   conditions,    etc.)   some   form   of   engineering
simplification, or schematization,  is necessary to perform
predictions  of effluent  flow  conditions  and  mixing  zone
analyses.
3.1.1 Ambient Geometry and Flow Conditions

    Ambient conditions are defined by the hydrographic and
geometric conditions in the vicinity  of the discharge.  For
this purpose, typical cross-sections normal to the ambient
flow direction at the discharge site  and further downstream
need to be  considered.   The cross-section  can  be defined
as:  i)  bounded  cross-section:  If  the  cross-section  is
bounded on  both  sides by  banks  - as in  rivers,  streams,
narrow estuaries, and other narrow watercourses -, then the
cross-section  is  considered  "bounded",  and  ii)  unbounded
cross-section: In some cases  the discharge is located close
to one boundary while  the  other boundary  is for practical
purposes very far away. This would include discharges into
                            61

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wide lakes, estuaries and  coastal  areas.  These situations
are defined as "unbounded".

    The  following   flow   classification   and  subsequent
predictive models assume a  rectangular cross-section that
is given by a width  and a  depth  which are constant in the
downstream direction following the  ambient  flow.   Thus if
the actual ambient is curved  or  meandering,  it is assumed
that the schematic rectangular cross-section represents a
straight "stretched-out"  counterpart.   The  discharge and
ambient schematization for a typical single-port discharge
appear in Figure 3.1.

    This   schematization   may   be   quite    evident   for
well-channeled and regular  rivers  or artificial channels.
For highly irregular cross-sections or unbounded sections,
it  may require  more  judgement  and  experience,  perhaps
combined with an iterative use of  the classification scheme,
to get a better feeling on  the sensitivity  of the results
to different schematizations.

    The hydrodynamic classification assumes  steady  state
ambient flow  conditions.    Thus  for time varying ambient
flows,  as in  tidal currents,  a quasi-steady analysis must
be  conducted  choosing  certain  design  flow  conditions.
Generally this  is acceptable because  the time  scale for
variation in  ambient currents (e.g. the  tidal period)  is
usually much  larger than  the time scale  for near-field
mixing  processes   (in  the  order of minutes  to tens  of
minutes).    Furthermore,  any shear  effects  in the ambient
flow are  neglected  and  a uniform  velocity equal to the
depth-averaged value is assumed.
3.1.2 Ambient Density Stratification

    Ambient  density stratification  occurs  frequently  in
aqueous environments.  A stable density profile occurs when
density increases vertically with  increasing  depth from the
water surface to the bottom.   If the density decreases with
depth, the water column is unstable, and subsequent overturn
mixing will  eventually  yield a  stable or uniform profile.
In the unstable density profile,  water  of lesser density
located below water of greater density would rise towards
the surface,  and water of greater density  would sink towards
the bottom.  Density stratification may be associated with
variations of salinity  or  temperature within the vertical
water profile.

    Stable density  variations in  ambient environments can
arise in many possible profiles.  Four  simple representative
                            62

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                  PLAN  VIEW
                            CROSS-SECTION
      w
            f T>/ / t , ;m s\ | i/ f s
/
/
/
/
/
/
C0
   Flux quantities:   Oo - discharge


                   Mo= U00O = momentum flux


                   J0 = ( A/o0//)Q) q 00 = buoyancy flux
Figure 3.1
Definition  Diagram for Single Port Discharge

Geometry  in Ambient Channel with rectangular

Cross-Section.   Width W of the water body may

be finite or unlimited.
                              63

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density  profiles  are  illustrated  in  Figure  3.2.    Any
existing  ambient  stratification  is  approximated by  the
schematic  profile  that  most  closely  resembles  it.    A
dynamically correct approximation of the actual distribution
should keep a balance between over- and under-estimation of
the actual density data.

     The simplest case  is a  linear density profile shown in
Figure 3.2a (Stratification  Type A).  Figure 3.2b describes
two  uniform density layers with a  density  jump between
layers (Stratification  Type  B).  This density jump is often
referred to  as  a pycnocline or thermocline.   Figure 3.2c
illustrates a two layer profile in which the upper layer is
uniform,  the  lower layer has  a  linear stratification,  and
a density  jump  occurs  between  layers  (Stratification Type
C).  Finally, Figure 3.2d presents a two layer system with
a uniform upper  layer and a linearly stratified bottom layer
with no density  jump between layers (Stratification Type D) .
The uniform upper  layers in Stratification  Types B,  C,  or
D is representative  for  the well  mixed upper layer (often
referred to as the epilimnion)  that is found in many types
of ambient water bodies  and occurs due to wind induced
turbulent mixing.
3.1.3 Discharge Parameters

    The salient  discharge conditions are  shown  in Figure
3.1.  The discharge geometry is given by the diameter D of
the port or nozzle, its height h0 above the bottom, and its
orientation angles 00  and OQ.

    The vertical angle of discharge  00 is the angle of the
port centerline  measured from the horizontal  plane.   For
practical applications,  this  angle may range between  -45°
and  90°.  As examples,  the vertical angle  is 90°  for  a
discharge pointing vertically upward, and  it  is  0° for a
horizontal discharge.   The horizontal angle of  discharge  CTO
is  the  angle measured  counterclockwise from  the ambient
current direction  (x-axis)  to the plan  projection of the
port centerline.  This angle may range between 0°  and 360°.
As examples, the horizontal angle  is 0° if the port points
downstream with the ambient flow  (co-flowing discharge), it
is 90° or 270° if it points across the ambient flow  (cross-
flowing discharge) , and it is 180°  if  it  points upstream
opposing the ambient flow  (counter-flowing discharge).

    The important dynamic variables of the discharge are its
momentum  flux  M0,  its buoyancy  flux J0/  and  to  a lesser
degree, the  discharge flow (volume  flux)  QQ.   These bulk
parameters,  first derived  in Chapter  II,  are  listed on
Figure 3.1.  Note  that in case of stratified ambients, the
                            64

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              H









<


is,
\
\
,*\
\
\










hint









N \
\ \ _
<*NA
A
A

V
\
\«
\
y., , rT7 7 ^ A-7-r
      Linear
Two-Layer
Figure 3.2    Representative Stable Density Profiles  (Four
              Stratification Types)
                            65

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discharge  buoyancy  g0'  refers  to  the  ambient  density
conditions at  the  level of the  discharge,  h0/  i.e.  g0' =
3.2 Near-field Flow Classification

    The purpose of the hydrodynamic flow classification is
to predict for a given discharge/environment situation the
type of flow configuration that will occur.  Once a reliable
classification has been established,  it becomes much easier
to provide actual predictions  for flow properties including
pollutant concentration distributions within the distinct
hydrodynamic zones pertaining to each flow class.

    The  present  flow  classification procedure  uses  the
length   scale   concept.     The  dynamic   length   scales
characterizing the discharge  are  summarized  in Table 3.1.
There are six major  scales: Lg,  1^,, 1^,  1^' ,   and   1^' .
It   should   be   noted   that   there   are   functional
interdependences, e.g.  1^ = L^//I    and 1^' = I^'/!*   / and
it can be readily shown that there are only four independent
length  scales.    These  length  scales  interact  with the
geometric properties of  the  ambient water  body,  its  layer
depth Hs,  stratification e,  and orientation angles  8Q and a0.

    Thus  in  total  at  least  seven  independent  length
parameters plus two angles  seem  to influence the near  field
flow  configuration,  even  within  the  relatively  simple
rectangular channel schematization discussed in Section 3.1.
Assuming  two values  (high  and  low)  for  each  of  these
lengths, two values of 0 or 90°  for 8Q, and three values of
0°, 90° (or 270°) , or 180°  for CTO,  it appears that there  exist
at  least  27"1  x 2  x  3  =  384  possible  different  flow
configurations!  Indeed such a simple calculation gives an
indication of the  potential  variety of flow patterns that
can occur in environmental conditions.

    In fact, many of these  potential configurations  are not
possible on theoretical grounds, and many will not  occur for
practical reasons.  The classification procedure presented
below yields  35 generic flow configurations.   The actual
number of flow classes that can be  modeled with the full
predictive methodology  (Chapter V)  is considerably larger
(about 100  flow classes) since:  i)  each of the 35  generic
flow classes may apply to a layer corresponding to the full
water depth  or  to the region below a pycnocline, and ii)
certain  sub-processes  may  be   present or   absent  in   a
particular  flow classes  (a typical example is the  absence
of a weakly deflected jet region close to the discharge port
if the ambient velocity is very large) .
                            66

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Table 3.1      Flow  Classification  Variables  and  Length
               Scales
Ambient and Discharge  Variables:
H =  ambient depth  at  discharge
h0 = discharge port height above bottom
hint = ambient internal density jump height
H8 = stratified layer height  (equal to  H or hjnt)
ua = ambient velocity
f = Darcy-Weisbach  friction  factor for ambient shear  flow
9Q = discharge vertical angle
a0 = discharge horizontal angle relative to current
Length Scales:
LQ = Qo/M01/2   = discharge  (geometric)  scale (Eg. 2. 9)
LH = M03/4/J0V2  -  jet/plume transition scale  (Eq.2.12)
1^, = M01/2/ua =  jet/crossflow scale (Eg. 2. 10)
LH, = Jo/ua3 = plume/crossflow scale  (Eg. 2. 11)
L/- (Mo/e)174 - jet/stratification  scale  (Eg. 2. 13)
      1/A/e3/8 - plume/stratification scale (Eg. 2. 14)
                             67

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3,2.1 General Procedure

    The flow classification is a 13 step procedure that is
summarized  in Table  3.2.    This  procedure  is  used  to
determine which  of four major  flow categories the  given
discharge will exhibit.  The four major  flow categories are:
i)  flows affected by  linear  stratification  leading  to
internal trapping (S classes, Figure 3.3),  ii) buoyant flows
in a uniform  ambient layer  (V and H classes,  Figure 3.4),
iii) negatively  buoyant  flows in a  uniform ambient  layer
(NV and  NH  classes,  Figure 3.5), and  iv) bottom  attached
flows (A classes, Figure 3.6).

    Even though  a stable  ambient density profile may  be
specified for a  given situation,  that  profile may be weak
or  even dynamically  impossible  in the  presence of  the
destabilizing effect of an ambient flow with mean velocity
ua.  In Step 1 of Table  3.2  a flux  Richardson criterion (see
Appendix A)  is used to check for such destabilization which
would enforce a uniform profile.

    Steps 2 through 8 in Table 3.2 determine the effect of
ambient  density  stratification  (if present) on the  flow.
In general,  if the predicted terminal height of rise  Zt for
near-field flows is greater than the actual layer height Hs/
then  the effect  of  the  linear  stratification  will  be
unimportant and the buoyant jet  will traverse this layer as
if it were in fact of uniform density.

    If the terminal height  of  rise Zt is less than the layer
height Hs additional tests  (Steps  3 through 7,  Table 3.2)
are performed.  In the case of a  profile with a density jump
(Stratification  Types B  and C in Figure  3.2) these  tests
determine if the flow will  be  trapped by the pycnocline, or
in  the  case  of Stratification Type  C,  trapped  within the
lower  density  layer.    If the  flow  is trapped by  the
pycnocline,    the   details   of  stratification   below  the
pycnocline  are  unimportant  and  the  region  below  the
pycnocline will be represented by a uniform density layer
in all cases.

    Step 9  is the detailed flow  classification  for those
flow classes whose dynamics are  directly affected by linear
ambient  stratification.  The  linearly stratified layer may
extend  over  the  full  water  depth  or  be confined  to the
region  below  the pycnocline.    Further  details  on this
classification are given in Section  3.2.2.

    Steps  10  to  12  examine  the  flow   behavior  for those
categories  in which  the  ambient layer  can  be  taken as
uniform  (either  existing or because any stratification is
                            68

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                                                      72

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Table 3.2     Near-Field Flow Classification Procedure
Step 1:  Test for density profile stability.  If the ambient
         is  unstratified  or  the  given  stratification is
         dynamically   impossible   according  to   a   flux
         Richardson number  criterion,  approximate ambient
         density  with  mean value and  recompute  discharge
         parameters.    Conclude   stratification  is  not
         important and go to Step 10.

Step 2:  Ambient has stable density stratification.  Check
         for density step  change.  If the ambient does not
         contain  a  density step change  (Types  A  or  D in
         Figure 3.2) go to Step 4.

Step 3:  Ambient density profile contains step change. Since
         the Stratification Type is  B or  C, approximate the
         actual  lower  layer  stratification  and  the  step
         change  with  a surrogate   linear  stratification
         (Figure 3.2).   Calculate surrogate gradient e* and
         surrogate stratification length  scales 1^' and 1^'.

Step 4:  Possible   flow   trapping   in   linear   density
         stratification. Test for internal layer formation
         (flow trapping),  using the scheme outlined in the
         upper portion of Figure 3.3. Use height  Hs (Hs = H
         for Stratification Type A,  and  Hs = hint  for Types
         B,  C  or  D) .  If  (Zt+h0)/Hs  >  0(1),  density
         stratification  will  not  trap  flow.   Therefore
         conclude  ambient  density  stratification is  not
         dynamically important.  Approximate ambient density
         with mean  value,  recompute discharge parameters,
         and go to step 10.

Step 5:  Stratification is important and flow trapping may
         occur. If there is no density jump in the profile
         (Types A or D) go to Step 8.

Step 6:  Test for trapping  at  density  jump or in linearly
         stratified layer.  If  Stratification  Type  is C,
         perform a second test for internal layer formation
         using the scheme outlined in the upper portion of
         Figure 3.3 based on the actual density gradient e.
         If  (Zt+h0)/Hs < 0(1),  conclude  the flow will become
         trapped in the linearly stratified layer below the
         density jump,  go to Step 8.
                            73

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Table 3.2     (continued)
Step 7:  Trapping at  the  density jump  (pycnocline) .   The
         linear stratification  below the density  jump is
         dynamically unimportant.  The  effluent flow will
         be confined to the  lower  layer of Stratification
         Types B or C due to the strong density jump. For
         Type C,  approximate  linear ambient density profile
         of lower layer with mean,  and recompute discharge
         parameters.  Set Hs  = hjnt and go to Step 10.

Step 8:  Check for  flow interaction  with bottom for flows
         influenced by linear density stratification. Flow
         may  interact  with   bottom  if its  buoyancy  is
         negative or jet is  directed downward. If Zt  +  h0 <
         0, flow will interact with the bottom. Proceed to
         Step 12.

Step 9:  Complete flow  classification  for buoyant  jet in
         linearly stratified  layer.  Five flow  classes exist
         (SI to S5) as shown in Figure  3.3. Go to Step 13
         for final check on near-field bottom attachment.

Step 10: Test  for  discharge  buoyancy  in  uniform  ambient
         density  layer  height Hs.     If discharge  is
         negatively buoyant go to Step 12.

Step 11: Perform flow classification  for positively buoyant
         (or neutral)  jet in uniform density layer.  Fifteen
         major flow classes  (VI to V6,  HI  to  H5)  exist as
         shown in Figure 3.4. Go to Step 13 for  final check
         on near-field bottom attachment.

Step 12: Perform flow classification  for negatively buoyant
         or downward directed jet in  uniform density layer.
         Ten major  flow classes exist  (NV1 to NV5, NH1 to
         NH5) as shown in Figure 3.5.  STOP.

Step 13: Perform  flow classification for  bottom attached
         effluent flows. Five major  attached  flow classes
         exist  (Al  to A5)  in the form  of  wake and Coanda
         effects as shown in  Figure  3.6.  STOP.
                            74

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weak and dynamically unimportant compared to the discharge
fluxes).  The detailed classification  for positively buoyant
(or neutral) discharges in such a layer is  contained in Step
11 (see Section 3.2.3) and for negatively buoyant discharges
is given in Step 12  (see Section 3.2.4).

    The  final  Step  13  performs  an  additional  test  and
classification  for dynamic  bottom  attachment (see Section
3.2.5).  Most (but  not all) of the  flow  classes that may
have been concluded  in Step  8, 11,  or 12 may experience such
attachment effects which then radically alter  the near-field
flow configuration  leading  to a new  category  of attached
flows.

    The  detailed classification   schemes for  each  flow
category (Figures 3.3 to 3.6) are discussed in the following
sections.   It is stressed  that all  criteria presented in
this chapter and listed on  Figure 3.3 to 3.6 are "order of
magnitude" relations.  The precise form of the criteria as
well as the numerical constants are given in Chapter V.
3.2.2 Flow Classes B for Linear Ambient Stratification

    Referring to  Figure  3.3,  the first test  level of the
flow  classification  for  a  buoyant  jet  in  a  linearly
stratified layer is to determine whether the flow is mostly
jet-like or mostly plume-like  as  it rises in the stratified
layer.   This is  achieved  through  the  comparison  of the
stratification length scales,  Lm*
    The next  determination is the  relative  importance of
crossflow  on  these   stratified   flows.     For  jet-like
stratified flows, if  ^\' <  0(1),  the crossflow will have
strongly deflected  the buoyant jet flow by the  time the
stratification starts  to  influence the flow leading to a
"crossflow dominated"  regime.   But for  l^/l^'   >  0(1)  the
crossflow  is  weak  and  the  flow  is  "stratification
dominated. "
    For plume-like stratified flows,  if   Lj/1^'  < 0(1) the
crossflow will  have  strongly deflected  the  buoyant plume
flow before  the stratification  begins to  affect the flow
leading to a "crossflow dominated" regime.   On the other
hand, L^LI,'  >  0(1)  signifies a  "stratification dominated"
flow.

    The terminal  height of  rise  Zt  predicted  for  any of
these flows is  indicated on Figure 3.3. Detailed discussion
and references for these equations are in Section 5.3.  In
general, the height  of  rise depends on L,/ or 1^'  with an
added influence of L,,, or  l^ for crossflow affected stratified
flow.  The sketches at the bottom of Figure 3.3 indicate the
                            75

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schematic flow configuration for each flow class.  Once the
terminal height has been reached,  some flows  (SI or S4) are
further deflected  by  the strong  crossflow leading  to far
field buoyant spreading and diffusion phases.  Other flows
(S2 or S5)  have weak crossflow and are more nearly vertical
in approach  ("impingement")  to  the  terminal  layer with an
ensuing upstream spreading phase.  Flow class  S3 with strong
horizontal   momentum    experiences    a   (near-) horizontal
"injection" into the terminal layer.


3.2.3  Flow Classes V  or  H for  Buoyant Discharges  into
Uniform Ambient Layers

    The flow  classification  system  for positively buoyant
discharges in uniform  ambient layers appears  in Figure 3.4.
Two  major   branches   occur within  this  classification
depending on the vertical angle  of the discharge 00 as shown
in Figure 3.4.  The vertical discharge angle  80 is used to
define the  sub groups of  (near-) vertical  (V classes)  and
(near-) horizontal discharges (H  classes).  This distinction
is necessary because V classes may have surface contact with
strong  vertical momentum,  while for the  H  classes  the
momentum is directed in the horizontal plane.

    The flow  classification  system  then  uses the ratio of
IV/HS  to characterize  the  discharge  as  "deep water"  or
"shallow water"  based on the momentum of the  flow as it
contacts the surface.    A deep  water  discharge  will have
relatively weak momentum as the flow contacts the surface,
while a shallow discharge will have strong momentum as the
flow is influenced by, or impinges on, the surface.

    The next  level of the classification assesses the role
of buoyancy  with respect to the  ambient layer height  H8.
For LI/HS > 0(1) the flow will have a strong buoyancy effect
when contact  with the surface or  upper layer  occurs, while
for Lfc/Hg < 0(1)  the buoyancy influence will  be minor.
    An additional  determination  needs to be made in those
cases where  both  momentum and buoyancy effects have found
to be weak, or both to be strong,  respectively.  A criterion
LH/HJ  is  used  to  determine which  one of  the  two effects
predominates.

    As a result,  discharges can  be classified as "stable"
or "unstable" .  Flows with strong momentum and weak buoyancy
occurring  in shallow water  layer tend to be unstable  (V4,
V6,  and  H5) .   In this  case the  jet is  affected  by the
shallowness and an unstable recirculation zone occurs around
the  jet  as it re-entrains the fluid  already mixed.   In a
stable  discharge, buoyancy  tends  to have  a  stabilizing
                            76

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effect on the flow as it contacts the surface, causing the
flow to form a stratified layer on the surface.

    Discharges  into  deep  water  layer  have  stable  flow
classes (VI,  V2,  V3, HI, H2, and H3) ,  with strong similarity
among the  V  and H  classes in  this  case,  as  well  as the
shallow water cases  V5 and H4  that  have extremely strong
buoyancy as  a  stabilizing factor in an  otherwise shallow
layer.   Some  of these  stable  flow classes  with  strong
buoyancy (V3, V5, H3,  and H4) experience  upstream spreading
once surface contact has occurred.

    An important aspect of such a classification scheme is
its  robustness  under   extreme  conditions.    Two  such
conditions are of interest; i)  zero  discharge buoyancy (g0'
= 0 and thus  J0 = 0) , and ii) stagnant ambient  (ua = 0) .  In
the first  case,  the  length scales are L^ =  0, and 1^ goes
to infinity.   In the  second case 1^  goes to infinity.  In
the combined  case (zero buoyancy flux and ambient velocity)
1^ is  indeterminate.

    Case i)  Non-buoyant  discharges  into  a flowing ambient
    lead to flow classes V2 or H2.   A special  sub class of
    this flow is a  rapidly  deflected  small "passive source"
    (well below the layer surface) with  a rapid transition
    to far-field ambient diffusion.

    Case  ii) Stagnant ambient  conditions  lead to  flow
    classes V5,  V6, H4, or H5, respectively.   In particular,
    if the discharge is weakly  buoyant (or,  in  the extreme,
    nonbuoyant)   flow   classes  V6    or  H5  will  occur.
    Obviously, far-field mixing process are absent for these
    situations,   which   rarely  occur  anyway  in  actual
    environmental conditions.

    The flow  classes H4 and H5  contain a  sub-classificatieon
depending on whether the discharge  is coflowing  (a0 a  0°) ,
cross-flowing  (a0 as  90°) ,  or counter-flowing  (a0 »  180°) .
This  is  necessary  since the strong  horizontally oriented
momentum  flux  in  these shallow  environments leads  to a
drastically different  flow  configuration as a function of
discharge direction relative to the crossflow.  In fact some
of these configurations  (e.g. the counter-flowing ones) lead
to complicated recirculation zones that may  be  difficult to
analyze and undesirable in actual design practice.
3.2.4  Flow  Classes  NV  or  NH  for  Negatively  Buoyant
Discharges in Uniform Ambient Layers

    The  classification   system   for  negatively  buoyant
discharges (Figure 3.5)  bears some similarities to that for
positively buoyant  discharges described above.   Several


                            77

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negatively  buoyant  flow  classes  have  a  "mirror  image"
analogy to positively buoyant flows which appear in Figure
3.4.

    Again,  the flow  classification system  has two  main
branches;  for discharge  angles  90  >   45°  the  flows  are
classified as  near-vertical  (NV-classes), while  for -45° <
9Q  < 45° the flows are classified  as near-horizontal  (NH-
classes).

    The first level is to determine if momentum or buoyancy
dominates with respect to  the ambient  layer depth H .   If
I^/Hg  <  0(1)  the  flow will be buoyancy  dominated  after a
short distance and  therefore will  not have  any  surface
interaction.   If  it  is discharged  upward,  it will quickly
fall back towards the bottom.   If 1^/H8  > 0(1) the flow will
be momentum dominated in relation to the ambient layer depth
Hs.  For near-vertical jets, surface interaction will occur.
For near-horizontal  discharges, the potential  for surface
interaction will  depend on the horizontal angle of discharge
CTo-

    Additional tests  for   flow  behavior are based  on  the
crossflow  scales  Lra  and  1^.   The  negatively buoyant  flow
classes are  separated into those  without layer or surface
interaction  (NV1,  NV2, NH1,  NH2,  NH3,  and  NH4)  and those
with interaction (NV3, NV4, and NV5).  The extremely strong
negative buoyancy causes upstream spreading in flow classes
NV2 or NH2.  Unstable discharge configurations with vertical
mixing and recirculation zones exist in flow classes NV4,
NV5,  and NH5.    Finally,  it  should be noted  that  this
classification also applies for a  downward  oriented jet  (00
<  0°, regardless  of  buoyancy)  that is  trapped  by linear
ambient stratification near  the bottom of  the water layer
(see  Step  8  of   Table  3.2).    In this  instance,  flow
configurations NH1 to NH3 may result.
3.2.5 Flow Classes  (..)A for Bottom Attached Flows

    Two types of flow attachment appear in  Figure  3.6: wake
attachment and  Coanda  attachment.   The physical  processes
for  these have  been described  in the  previous  chapter.
Several  flow  classes appear to  be prone  to  some kind of
     1Strictly speaking  1^ and  1^  are  negative quantities
for negatively buoyant  discharges  since g0'  <  0,  and thus
J0 < 0 .  In this clas
quantities are used.
J0 < 0 .  In this classification the absolute values  of these
                            78

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attachment while  others are not  as shown  in  Figure 3.6.
For example,  a vertical discharge cannot experience Coanda
attachment.

    Wake attachment will not occur if the effluent intrudes
sufficiently far away from the boundary.  An estimate of the
intrusion distance is given  by the sum of port height h0 and
the crossflow length scale 1^, for  jet-like  or L^ for plume-
like flows,  respectively. If these  intrusion distances are
small relative to the source dimension,  (1^, + h0)  <  Lg, and
(1^ + h0) <  Lg,  then wake  attachment  to  the  bottom will
occur.    A  supplementary  criterion  based  on  a  local
Richardson number condition tests  for  potential buoyant
lift-off  (flow class  Al)  following the recirculation zone
in the wake of the discharge  (see Figure 3.6) .  For weak (or
negative) buoyancy no such lift-off will occur (flow class
A2) .

    Jet-induced Coanda attachment depends primarily on the
vertical angle 8Q  of  the  (near-)horizontal  discharge and on
the  initial  jet  separation  given by  the  total  spreading
angle  (with  a  tangent of 0.2  for a jet flow).   A simple
criterion for  attachment is indicated by  tan0Q   <  (0.2  -
h0/L)  where  L is the distance of the jet region.   For weak
crossflow (stagnant)  conditions, L is given by the jet/plume
scale LH leading  to  flow  classes A3  or A4, depending on the
strength of buoyancy.  In a  strong crossflow, L is given by
the  jet/crossflow length scale L^,  leading  to flow class
A5.

    As has been noted earlier, the flow class is checked for
wake and Coanda  attachment after the primary classification
(S, V, NV, or NH)  has been completed.   In the actual expert
system  implementation  of   this  scheme,  if  the  flow  is
attached, it is  given  the   appropriate  attachment  suffix
(e.g. A2) to the already determined  flow class  (e.g. V1A2).
This  is  done for practical  reasons as a  guidance  to the
analyst: simple modification of the discharge geometry  (e.g.
a larger angle 9Q) can often  lead to  avoidance of attachment
in which case the  primary flow class (e.g. VI) will describe
the flow.
3.3 Far-Field Flow Behavior

    After the effluent  flow  has  interacted with the water
surface, bottom, pycnocline,  or terminal  layer and has thus
completed its near-field phase, the -far field mixing begins.
This  region  consists   of  one  or  two  mixing  processes,
depending on discharge characteristics.    In  the  general
case, the discharge  flow  contains sufficient buoyancy and
there will  be  a  buoyant  spreading  region followed  by a
passive diffusion region.   The buoyant spreading region is


                            79

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characterized by dynamic horizontal  spreading and gradual
vertical thinning  of  the mixed effluent  flow while being
advected  by  the  ambient  current.     Vertical  boundary
interaction may occur, and  the  flow may contact one or both
lateral boundaries (shorelines).   In the passive diffusion
region, the dilution is controlled by the turbulent mixing
action of the flowing ambient water body.  Again, boundary
interaction  may  occur,  and  the  flow  may  become  both
laterally and vertically fully mixed within the layer height
Hs in this region.   If the flow is  non-buoyant  or weakly
buoyant there is no buoyant surface spreading region, only
a passive diffusion region.

    In contrast to the near-field flow there is no need for
an advance classification scheme to determine the behavior
of the  far-field  flow  for a  given  discharge/environment
situation.   Since the effluent  flow in  the  far-field is
always advected in the direction of  the ambient flow, the
various interaction processes are simply  calculated as part
of the downstream  modeling process of  the applicable far-
field  solutions.    This applies  also  to the  transition
between  buoyant spreading and passive  ambient  diffusion
(based  on a  flux Richardson  number  criterion).   These
aspects are directly implemented in the predictive elements
for the detailed effluent flow and mixing zone predictions
as summarized in Chapter V.
                            80

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                        Chapter IV

         Expert  System  CORMIX1:  General  Framework
    The  Cornell  Mixing  Zone Expert  System,   Subsystem  I
(CORMIX1) contains  a  series of software  elements  for the
analysis and  design of conventional or toxic  single port
submerged buoyant or  nonbuoyant  pollutant discharges into
stratified or unstratified  watercourses,  with  emphasis on
the geometry  and dilution characteristics of  the  initial
mixing  zone.    It  is intended  as  an  analysis tool  for
environmental  regulators,  discharge  designers, and more
generally,  students of hydraulics.  The system is designed
for use under the MS-DOS  operating  system on  an IBM-PC/XT
with a  hard  disk and  a  math co-processor as  the  minimum
hardware configuration.

    The user  supplies CORMIX1 with information about the
discharge  and   ambient   environment.     CORMIX1  returns
information   detailing   the    hydrodynamic    mechanisms
controlling  the  flow,  dilution,  geometric  information
concerning the shape of the pollutant plume or flow in the
ambient water body,  and design recommendations allowing the
user to improve  the dilution characteristics  of the flow.
If specified by the  user, CORMIX1 also presents information
about the legal mixing zone dimensions and dilution, toxic
mixing   zone   requirements,   and   zone   of   interest
characteristics for the flow.

    The purpose  of  CORMIX1  is to obviate for  the  novice
analyst the need for detailed understanding and experience
in hydrodynamic mixing processes.  A general environmental
science or engineering background at  the  BS  level  appears
to be the minimum educational requirement  needed to compile
and supply relevant  data,  interpret the system information,
and  ultimately   learn   and  become   knowledgeable   about
hydrodynamic mixing through repeated interactive use.  Two
working days appear  to be required for a first time user to
gain initial facility with system requirements, limitations,
and interpretation of results.

    Depending  on the computer  configuration,  a  typical
CORMIX1 session for  one discharge/environment condition may
take about  5  minutes  for  an advanced  80386-based  micro-
computer to 20 minutes for  an  IBM-PC/XT,  if  all necessary
input data is at hand.
                            81

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4.1 Background on Expert Systems and Logic Programming

    CORMIX1 is implemented in two programming languages: VP-
Expert (Paperback Software,  Inc.)/  and Fortran  .  VP-Expert
is  an  expert   systems  programming   language,   or  more
precisely, a "shell".  A shell is a  self-contained inference
engine that  does not  contain the  knowledge base,  but has
facilities   for  both   forward   and  backward  reasoning,
debugging  aids,  consistency  checking,   input and  output
menus, and explanation facilities.   The  two programming
languages  are  used  to exploit  their  respective  strengths
while avoiding their respective weaknesses.  VP-Expert, as
a knowledge  base language,  is very efficient  in knowledge
representation  and  symbolic  reasoning;  however  it  is
relatively weak in numerical computational  ability.  On the
other hand, Fortran is ideal for  computation of mathematical
functions  (Fortran  stands  for  formula translator)  but is
poorly  suited  for  the tasks   associated with  symbolic
reasoning.   Thus VP-Expert  is  employed to implement the
knowledge  acquisition,  simple  length  scale   and  dynamic
variable calculation,  model selection,  and analysis of the
hydrodynamic  simulation portions  of the  expert  system.
Fortran is used for  the  hydrodynamic flow simulation, which
is called  from a VP-Expert program element.

     It is interesting to note that the entire system could
have been programmed in a language  such as  Fortran, or even
assembly  language;  the real  issue is one of programming
efficiency.  For instance,  a routine written in 5 lines of
Fortran code might take 100 lines of assembly level source
code.    Since  VP-Expert  was  developed  to  encode  and
manipulate symbolic  logic, it does so with great efficiency,
allowing the programmer to  write in 5 lines  of  code what
might take  100 lines  in Fortran or 1000  lines of assembly
language.   In essence  the  selection  of VP-Expert  as the
language   for  the  symbolic  reasoning  tasks  gives  the
programmer significant leverage.  A VP-Expert knowledge base
is very similar in structure to a PROLOG  (PROgramming LOGic)
program.  PROLOG was developed in Europe  and is designed to
manipulate logical expressions (Clocksin and Hellish, 1984).
A VP-Expert program  is built  from  statements containing
facts and  if-then rules about  facts.   This is called the
knowledge base.  The knowledge base is constructed with an
expert  in the problem  domain,  in this  case  hydrodynamic
mixing processes.

    Logic  programs,  such  as VP-Expert,  are  driven  by a
"goal" which the program tries to validate  by searching the
knowledge  base  to  construct  a "proof".   The proof  is
constructed  by using  the facts  and rules in the knowledge
base  to  deduce  the  goal   as  a valid  hypothesis.    The
following paragraphs give a more detailed explanation of how
this  is  accomplished,  using the  CORMIX1 knowledge base
                            82

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AMBIENT as an illustrative example.  AMBIENT is a knowledge
base designed to gather  information  on ambient conditions
at the discharge site.

    The execution of each knowledge base program is driven
by attempting to satisfy a goal.  In the AMBIENT knowledge
base this is written in VP-Expert as:

    FIND = ambient_conditions                         [1]

Here the  goal  is to  satisfy  or find a valuation  for the
expression "ambient_conditions".

    All rules in VP-Expert are stated as: if {expression(s)
or clauses called the  "premise"  or "head"   of the rule}  -
then {an  expression  or clause called  the  "conclusion"  or
"tail" of the rule}  statements.   The  premise  of a rule in
VP-Expert can contain more than one expression connected by
and/or statements.   VP-Expert will try to satisfy the goal
(here the expression  "ambient_conditions") by searching for
a rule in the knowledge base whose conclusion contains the
expression "ambient_conditions =  (valuation)".

    A rule in AMBIENT that has "ambient_conditions = known"
in its conclusion is:

    if ambient_advice <> UNKNOWN and
      bounded_section = yes and
      channel_width <> UNKNOWN and
      depths <> UNKNOWN and
      nearest_bank <> UNKNOWN and
      ambient_velocity_field <> UNKNOWN and
      friction_factor <> UNKNOWN and
      ambient_density_field <> UNKNOWN
then  ambient_conditions = known                      [2]

Here,  in  the  conclusion  of  the  rule  the  expression
"ambient_conditions" is assigned the valuation "known".

    First, an explanation is given on  how  VP-Expert uses
information  contained within  if -  then  rules  to  assign
valuations  to  expressions.    VP-Expert always tries  to
satisfy a valuation in the conclusion of the  rule by proving
its  premise.    Thus,  VP-Expert  tries  to  satisfy  all
expressions  in   the  premise  of  the  rule,  beginning  in
statement [2] with the first expression "ambient_advice <>
UNKNOWN"  (the "<>" in  [2]  stands for "not  equal to").  If
the  valuation  of  the  variable  in  the  first  clause  is
satisfied, i.e.  the expression site_description does indeed
have a valuation other than "UNKNOWN", then VP-Expert tries
to satisfy the second expression, "bounded_section = yes".
If  this valuation  is  satisfied,  VP-Expert  will try  to
satisfy  the  remaining expressions in  the premise  of the
                            83

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rule.   Whenever  in the  premise the  valuations for  all
expressions are  satisfied,  the rule succeeds  or "fires".
When the rule  fires, the expression in the conclusion of the
rule can be given a  valuation and this information is added
to the facts known in the knowledge base.

    So   how   does   VP-Expert    know   the   expression
"ambient_advice"  has  a  valuation  other  than  "UNKNOWN"?
Because there is  another  rule  in the knowledge base which
is:

    if ambient_query = yes
then  ambient_advice = yes                       [3]

This statement is invoked by statement  [2] when it tries to
find a valuation for the  first expression "ambient_advice".
Since  there is  no  present valuation  for the  expression
"ambient_advice", VP-Expert locates statement [3] with the
expression  "ambient_advice" in  its conclusion.    If  the
expression "ambient_query" in the premise of statement [3]
can  be assigned a valuation  equal  to  "yes",  then  the
expression  ambient_advice  is assigned  the  valuation "yes"
(which is not equal to "UNKNOWN").  VP-Expert will now try
to find a valuation for  ambient_query,  the  first and only
expression in the premise of statement  [3].  Within AMBIENT
there is another rule:

    ASK ambient_query: "Do you want a detailed
description of the ambient environmental data needed?" [4]

This rule is  a  treated as a "fact", and VP-Expert prompts
the user for a valuation of "ambient_query" with the message
within the quotes of statement [4].  The user  enters a value
(yes or no) which is bound to  "ambient_query".  VP-Expert
continues  to  find  valuations  for  the  remainder  of  the
expressions in statement  [2] in a similar manner.  When all
expressions in the premise of statement [2]  are assigned  a
valuation,  the  conclusion "ambient_conditions  = found" is
added as a  fact to the knowledge base.

    Thus,  as  was  shown  with  the  previous  example,  the
knowledge base  AMBIENT  is built  from  rules  which contain
expressions that force  VP-Expert to seek  valuations from
other  rules.     The  process  of  seeking  valuations  of
expressions continues until either  all the valuations are
found  or the  rule base  is exhausted  without  finding   a
valuation.  VP-Expert will never assign a valuation which
is  in  contradiction  within  a  rule,  so  one   is  assured
whatever  valuations are   concluded  are taken  from  a rule
within the  knowledge  base.  Care must  be taken in program
structure however,  since  the  search strategy of VP-Expert
may not consider all  rules needed to find a valuation for
a  given  expression.   In general, the  rule  base should be


                            84

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programmed in a "tree"  structure, with the most general and
independent rules at the beginning of the program, and rules
which depend on valuations from other rules following in the
program.  The most dependent and nested rules should occur
last in the knowledge base.

    When a valuation for a clause in the premise of a rule
is  found  not to agree with  the valuation given  for  that
clause  within  the rule,  e.g.  the expression  "depths"  in
statement [2] is  found to have the valuation "UNKNOWN", then
the  rule  fails,  no  valuation  can be  assigned  to  the
expression "ambient_conditions" from that rule.  VP-Expert
will stop trying  to satisfy the remaining expressions in the
premise of  that  rule.   VP-Expert will continue to try to
satisfy the expression "ambient_conditions"  by looking for
another rule in the knowledge base with "ambient_conditions"
in the conclusion of the rule.

    Rules in AMBIENT contain additional  clauses that control
the manner in which intermediate conclusions are stored in
memory, messages  are  displayed on the monitor,  and other
statements which create and  manipulate  external  files for
use in other CORMIX1 modules.
4.2 Structure of CORMIX1

    Figure 4.1  shows  the overall structure  of  the system
elements of CORMIX1.  The  program  elements  of CORMIX1 are
DATIN, PARAM,  CLASS,  HYDRO,  and SUM.  During system use the
elements are loaded automatically  and  sequentially by the
system.   Table  4.1  outlines the  directory  structure  of
CORMIX1 and contains comments about program files.

    The system  runs  entirely under the  VP-Expert program
shell.  The hydrodynamic simulation  Fortran program HYDRO
is executed  from the knowledge  base  program HYDRO.   All
program elements execute sequentially.   For example,  when
a rule in a program element  DATIN  corresponding to statement
[2] fires, the  "cache"  of  DATIN  is written  to an external
DOS file.   The cache is a list of all expressions within a
program element that have been assigned a valuation.  This
cache file is  read  by  the next sequential element in DATIN,
the  knowledge  base  PARAM,  and  so on  for  the  remaining
program elements.
4.2.1 Data Input Element: DATIN

    DATIN is a VP-Expert program for the entry of relevant
data  and  for  the  initialization  of  the  other  program
elements.  DATIN consists of four program segments or
                            85

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VP-Expert

      DAT IN
    User Input
Iteration
Alternatives
Corrections
VP-Expert
     PARAM
    Parameter
    Computation
VP-Expert
     CLASS
    Flow
    Classification
VP-Expert   Fortran

     HYDRO
Prediction/Simulation
     Program
VP-Expert
       SUM
Summary
Evaluation
Recommendations
(Legal/Engineering)
Figure 4.1     System  Elements  of CORMIX1
                              86

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Table 4.1

Directory
CORMIX1 Program File Directories

               Comments
C:\crnx
     system root directory, contains VP-Expert
     system  files  and  the  knowledge  base
     program CORMIX1 (system driver)
c:\cmx\advice

c:\cmx\bat



c:\cmx\cache


c:\cmx\data



c:\cmx\desc


c:\cmx\kbs

c:\cmx\pgms


c:\cmx\sim
     contains all user-requested advice files

     contains   batch   files   for   program
     execution, data  file  manipulation,  and
     program control

     contains cache "fact" files exported from
     knowledge base programs

     contains   constants   used   in   flow
     classification and other knowledge base
     programs

     contains flow descriptions for each flow
     class

     contains all knowledge base programs

     contains Fortran hydrodynamic simulation
     and file manipulation programs

     contains simulation results
                            87

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knowledge base sub-elements which execute sequentially.  The
knowledge base sub-elements  are,  in execution order, ASITE,
AMBIENT, DISCHARG, and ZONES.  The user executes DATIN by
invoking the CORMIX1 expert system by entering the command
"CORMIX1"  at  the  DOS  prompt  .    DATIN program elements
automatically prompt the user for needed information.

    The  purpose  of  DATIN  is  to  specify  completely  the
physical environment of the discharge, as well as legal or
regulatory requirements  on  the discharge.    The following
data  groups  need  to be  entered:  general  site and case
identifier  information  (knowledge  base  ASITE),  ambient
conditions  (geometry  and   hydrography,   knowledge  base
AMBIENT),  discharge conditions   (geometry  and  discharge
fluxes, knowledge base DISCHARG),  and information desired
including legal mixing zone definitions and toxic dilution
zone  criteria  (knowledge  base  ZONES).   DATIN provides
consistency checks and  gives advice  for input  parameter
selection.

    CORMIX1 assumes a deeply submerged single port discharge
into  the water body.    The  system  assumes  a  schematic
rectangular cross-section bounded by two banks - or by one
bank  only  for  coastal  or  other   laterally  unlimited
situations.  The user receives  detailed  instructions  on how
to  approximate actual  cross-sections  that  may be  quite
irregular  to   fit  the  rectangular  schematization.  The
representative schematization with all relevant hydrodynamic
variables that  DATIN gathers, was given in Figure 3.1.

    DATIN contains advice on how to  enter  data values and
rejects inappropriate or  incorrect values.  A listing  of the
input advice  available  on-line to the  user  of  CORMIX1 is
given in Appendix B.   DATIN will also flag unusual  design
cases.   For  example,  in the  knowledge base  sub-element
DISCHARG, if the user specifies a  discharge horizontal angle
which directs  the effluent  towards the  nearest bank,  the
following message is displayed:

    "The discharge port or nozzle points towards  the nearest
    bank. Since this is  an unusual design,  make sure you
    have specified the discharge horizontal angle correctly.
    CORMIX1  will  continue   with  cne  analysis  with  the
    horizontal angle as specified, but be aware that CORMIX1
    may  predict  a  hydrodynamically  unstable  discharge
    because of  the interaction of the discharge  near field
    with the bank."

    At  its termination  DATIN triggers the next  program
element PARAM.
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4.2.2 Parameter Computation Element: PARAM

    PARAM  is  a  VP-Expert  knowledge  base  that  computes
relevant  physical  parameters  for  the  given  discharge
situation.   This  includes various  fluxes;  Q0, M0, and  J0/
length  scales  Lg,  1^,  1^,,  1^,  l^',  L^',  as  well  as  other
values needed by the remaining CORMIX1 elements.  As PARAM
executes,   the   user   is   notified   about   important
characteristics of the flow.  For example:

    "The effluent density (1003.2 kg/m**3) is greater than
    the surrounding ambient water density at the discharge
    level  (  997.3  kg/m**3).  Therefore,  the  effluent  is
    negatively buoyant  and  will tend to  sink towards the
    bottom."

    At  its  termination  PARAM triggers  the  next program
element, the knowledge base CLASS.
4.2.3 Flow Classification Element: CLASS

    CLASS is an VP-Expert program that classifies the given
discharge into one of the many possible flow configurations
that have  been presented  in  Chapter III  (Figures  3.3 to
3.6).  CLASS  contains two program elements,  the knowledge
base sub-elements CLASS and FLOWDES.

    The  goal  of  CLASS  is to  find a  valuation  for  the
expression   "flow_class"   in   relation  to   the    flow
classification  scheme.     Each  of  the   possible   flow
classifications has an alphanumeric label(e.g. VI, SI, H1A1,
etc.).  CLASS inputs a cache created by PARAM that contains
the length  scales and other dynamic variables needed for
flow classification,  and  uses the knowledge  base rules to
assign the appropriate classification to the flow.  CLASS
first tries to satisfy the goal of "flow_class"  by initially
seeking  a  value  for  "flow_type".    For  example  a   rule
corresponding to  flow case V2 would appear  in simplified
form for illustration purposes as:

    if   flow_type = UNKNOWN and
         uniform_layer_flow = yes and
         flow_direction = upward and
         THETA > 45.0 and
         THETA <= 90.0 and
         C4 > (Lm /(0.8*(HS-HO))) and
         C6 > (Lb /(0.8*(HS-HO))) and
         C9 <= (LMM /(0.8*(HS-HO)))
then     flow_type = V2
         coanda_attachment = no
    find wake_attachment                         [5]
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in which  C4,  C6,  and  C9 are  constants.    If all  of  the
conditions in the premise of  [5] are true, then "flow_type"
is assigned  a value  of  V2.   The  possibility of  coanda
attachment does not exist for this case, but wake attachment
can occur.   The  system then looks  for rules  in  which to
satisfy  a  valuation  for  Mwake_attachment".    If  wake
attachment does not occur, other rules within the knowledge
base will  fire and a value "flow_type"  (i.e.  V2)  will be
assigned to "flow_class".  If the knowledge base rules fire
that conclude wake  attachment with buoyant lift-off from the
bottom, V2A1 will be  assigned to "flow_type".

    As an example  of the  output  from  CLASS,  the following
would  represent  some of  the  information presented  for a
discharge trapped by  the pycnocline in a two-layer density
stratified environment:

    "The  near field  flow  configuration will  have  the
    following features:

    The specified two layer ambient density stratification
    is dynamically important. The discharge near field flow
    will  be  confined to  the lower layer by  the  ambient
    density stratification.   Furthermore, it is trapped in
    the lower layer  by  the ambient  density jump  at  the
    pycnocline.

    The  following conclusion  on  the flow  configuration
    applies to the  lower layer only of  the  specified ambient
    stratification condition B.

    Note  that the lower layer  will  be  overlaid  by  the
    surface layer  of the ambient  density stratification.
    The surface  layer will  remain  undisturbed by  the near
    field  discharge   flow  (with  the exception  of  some
    possible intrusion along the pycnocline).

    The flow class is V2  for the design case represented by
    the DOS file name EXAMPLE."

    A  detailed  hydrodynamic description of  the  flow is
available  to  the  user  in the  knowledge  base sub-element
FLOWDES.  This detailed output includes a  description of the
significant near  field mixing processes, or the hydrodynamic
mixing  zone  (HMZ) .    The complete  listing  of the  flow
descriptions  for all major  flow  classes is  contained in
Appendix  C.   Typically,  the HMZ  is the  region  of strong
initial mixing where the particular design  of the outfall
can have an effect on initial dilution.  The HMZ is defined
to give additional information  as  an  aid to understanding
mixing processes and to distinguish  it  from purely legal
mixing zone definitions.
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    CLASS also creates a cache output file that supplies the
next CORMIX1 element HYDRO with instructions for running the
appropriate simulation.  At its termination CLASS triggers
the next program element HYDRO.


4.2.4 Hydrodynamic Simulation Element: HYDRO

    HYDRO  is  a knowledge base that  runs the hvdrodynamic
simulation  program for  the  flow classification  program
specified in CLASS. The  actual simulation program HYDRO is
written in Fortran. The  simulation program  is based on the
analytical  description of  the  physical  mixing  processes
presented  in  Chapter  II and  discussed  in  more  detail  in
Chapter V.

    HYDRO  consists  of control  programs or "protocols" for
each  hydrodynamic  flow classification  (e.g.  VI,  S2,  H3,
etc.)  as  specified by  CLASS.    Each protocol executes  a
series of subroutines  or "modules" corresponding to the flow
phenomena  (e.g weakly deflected  jet  in  crossflow  (mdnf),
surface  spreading, etc.)  which   may occur  in  that  flow
classification.    Thus  HYDRO  assembles the  appropriate
simulation sequence by picking the correct flow modules.

    HYDRO  creates  a tabular output file  of the simulation
containing information on geometry (trajectory, width, etc.)
and  mixing (dilution, concentration) .   The user  has the
option to view the tabular  output file.   An example of such
an output file is given in Appendix D.

    At  its termination HYDRO  triggers  the  final  program
element SUM.
4.2.5 Hydrodynamic Simulation Summary Element: SUM

    SUM  is  a   VP-Expert   program  that  summarizes  the
hydrodynamic  simulation   results  for  the   case  under
consideration.     SUM  describes  mixing  characteristics,
evaluates how applicable legal requirements are satisfied,
and  suggests  possible  design  alternatives  to  improve
dilution.  Thus, SUM may be used as an interactive loop to
guide the user back to DATIN to alter design variables.

    The  output  of SUM  is  arranged  in four  groups;  site
summary, hydrodynamic simulation summary, data  analysis, and
design  recommendations.  The site, summary  gives  the site
identifier information, discharge  and ambient environment
data,  and  discharge  length  scales.    The  hvdrodynamic
simulation  summary  lists  conditions  at  the  end of  the
hydrodynamic mixing  zone,   legal  mixing zone conditions,
toxic dilution zone conditions, region of interest criteria,


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upstream   intrusion   information,   and   bank   attachment
locations, if applicable.  The data analysis section gives
further  details  on  toxic dilution  zone criteria,  legal
mixing   zone  criteria,   stagnant  ambient   environment
information, and region of interest criteria.  Finally, the
design   recommendations   section   gives   suggestions  for
sensitivity studies and design changes for improving initial
dilution.    An  example  of   a  case  summary  and  design
recommendations appear in Appendix E.

    At the completion of SUM, the user is given the option
to exit  to  DOS,  start  a new  design example,  or modify the
discharge  and  mixing zone data for the  design case under
consideration using the same general ambient data base.
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                         Chapter V

      CORMIX1: Flow Protocols and simulation Modules
    This chapter provides the  hydrodynamic  details of the
effluent  flow predictions  and  mixing  zone  analysis  as
performed  in  program element  HYDRO  of the expert system
CORMIX1.

     First, detailed flow protocols for each of the 35 flow
classes defined in program element CLASS (see Section 3.2)
are give*h.  The full hydrodynamic description of these flow
classes  (which is  available on-line  to the  system user)
appears in Appendix C.  In Section 5.2 the actual prediction
modules for each flow  zone,  including  near-field and far-
field processes,  are discussed.  Finally,  in Section 5.3 the
appropriate transition  criteria  that  define the  spatial
extent of each flow zone  (module) are presented, along with
all constants  used  in the flow classification and simulation
modules.
5.1 Plow Protocols

    The hydrodynamic prediction of  the effluent flow and of
associated mixing zones in program  element HYDRO is carried
out by appropriate flow modules that are executed according
to  a  protocol   that   pertains to   each  distinct  flow
configuration as  determined by the  classification scheme
CLASS.

    CORMIX1 contains 22 separate flow modules that apply to
each of the diverse mixing processes that can occur in the
near- and far-field of  an  effluent  discharge.  The physical
background of these mixing processes has been discussed in
Chapter  II.   Table  5.1 summarizes the  flow modules.   A
detailed description of each module is given  in Section 5.2.

    The sequence of module execution is governed by a flow
protocol for  each flow class.   These  flow  protocols have
been constructed  on  the basis of  the  same  arguments that
have been  presented in  Chapter III  to  develop  the flow
classification.   Detailed  flow protocols for  each flow class
are presented in  the following sub-sections with extended
explanations on their formulation.

    The spatial extent  of each flow module  is  governed by
transition rules.  These determine  transitions  between
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Table 5.1     Flow Prediction Modules of CORMIX1
Module
(MOD)              Description
         Modules for Buoyant Jet Near-Field Flows


01       zone of flow establishment (zofe)

11       weakly deflected jet in crossflow (mdnf)

12       weakly deflected wall jet in crossflow  (mdnf-wj)

13       near-vertical jet in linear stratification
         (mdls-v)

14       near-horizontal jet in linear stratification
         (mdls-h)

16       strongly deflected jet in crossflow (mdff)

17       strongly deflected wall jet in crossflow (mdff-wj)

21       weakly deflected plume in crossflow (bdnf)

22       strongly deflected plume in crossflow (bdff)


         Modules for Boundary Interaction Processes


31       near-horizontal surface/bottom/pycnocline approach

32       near-vertical surface/bottom/pycnocline impingement
         with buoyant upstream spreading

33       near-vertical surface/bottom/pycnocline impingement
         with vertical mixing

34       near-vertical   surface/bottom/pycnocline
         impingement, upstream spreading, vertical mixing,
         and buoyant restratification

36       terminal  layer  stratified  impingement/upstream
         spreading

37       terminal layer  injection/upstream spreading
                            94

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Table 5.1     (Continued)
Module
(MOD)              Description
         Modules for Buoyant Spreading Processes


41       buoyant layer spreading in uniform ambient

42       buoyant spreading in linearly stratified ambient


         Modules for Attachment/Detachment Processes


51       wake recirculation

52       lift-off/fall-down


         Modules for Ambient Diffusion Processes


61       passive diffusion in uniform ambient

62       passive diffusion in linearly stratified ambient
                            95

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different  near-field and  far field  mixing  regions,  and
distances  to  boundary interaction.   Section 5.3  gives  a
detailed summary of the transition rules.
5.1.1 Flow  Protocols  for Buoyant Discharges  into Uniform
Ambient Layers (Flow Classes V and H)

    The classification  scheme discussed  in  Section 3.2.3
with its associated criteria (see Figure 3.5) already gives
an indication of which  flow processes  will occur for each
of  the  flow  classes,   and  hence  which  sequence of  flow
modules is necessary for simulation.  The  length scales are
the basis for the sequence determination in the near-field.
As an example,  consider flow class VI.   In the submerged
phase of that flow  there are four possible flow zones (i.e.
mdnf, mdff,  bdnf,  or bdff)  that  might be  involved.   The
question  is,  which will   occur  and  in what  sequence?
Provided that L,,, and 1^  are  both substantially larger than
Lg two possible transitions  can occur (see Figure 5.1):

    i)   For  Lfo/Lb  » 0(1)  the buoyancy  in the  plume  is
    relatively  weak compared to  momentum,  and a  large
    distance  is required   for  the  buoyancy to  generate
    additional momentum to  control  flow  characteristics.
    Therefore the  flow  will  develop  as:  mdnf  ->  mdff  ->
    bdff.  This is the  initial sequence for the subsurface
    flow modules in flow class VI.
    ii)   If  L^/^j  < bdnf -> bdff.  This  is an
    alternate initial sequence (labeled VI') which has not
    been illustrated in Figure 3.4.

    In  each of the preceding cases  boundary interaction
interrupts  the  sequence of  flow regions.    When boundary
interaction occurs, the sequence  will  change to include the
appropriate boundary interaction effect and then continue
as  a  surface  far-field flow.   The  listing of  the  flow
protocols for the flow categories V and H is given in  Table
5.2.

    No  protocols  are given  for  flow  classes  H4-180, H5-
90, and H5-180.   These discharge types lead to a complicated,
irregular,  and  perhaps  time-dependent (pulsating)  flow
behavior for which no reliable predictive methodology exists
and which  also seem undesirable  in engineering practice.

    Additional  criteria  are  also imbedded  into the actual
flow modules which  may lead to   by-pass of  certain  flow
                            96

-------
                               Transition]
            Transition
                N
                 N
           z=0
              a) Lm»Lb ;  Momentum Dominates
             Z=0-L-
              b) Lm«Lb;  Buoyancy Dominates
          General Behavior for  Buoyant  Jets  in Unconfined

          Crossf low (Assuming Near-Vertical Discharge)
Figure  5.1
General Behavior for Buoyant Jet in Unconfined
and Unstratified Crossflow
                            97

-------
Table 5.2     Flow  Protocols  for Buoyant  Discharges into
              Uniform Ambient Layers
Flow
Class
VI, HI






vi SHI'






V2,H2





Flow
Zone
discharge
mdnf
bdnf
bdff
surface approach
surface buoyant spreading
passive diffusion
discharge
mdnf
mdff
bdff
surface approach
surface buoyant spreading
passive diffusion
discharge
mdnf
mdff
surface approach
surface buoyant spreading
passive diffusion
MOD
01
11
21
22
31
41
61
01
11
16
22
31
41
61
01
11
16
31
41
61
TR
0
1
3
5
10
17

0
2
4
5
0
7

0
2
5
0
7

MOD = module, TR = transition rule
                            98

-------
Table 5.2     (continued)

Flow     Flow                               MOD     TR
Class    Zone
V3,H3    discharge                          01           0
         mdnf                               11           1
         bdnf                               21           6
         surface impingement with buoyant
           upstream spreading               32           0
         surface buoyant spreading          41           7
         passive diffusion                  61

V4       discharge                          01           0
         mdnf                               11           5
         surface impingement with full
           vertical mixing                  33           0
         surface buoyant spreading          41           7
         passive diffusion                  61
V5, H4-0 discharge                          01           0
H4-90    mdnf                               11           1
         bdnf                               21           6
         surface impingement with
           buoyant upstream spreading       32           0
         surface buoyant spreading          41           7
         passive diffusion                  61
                            99

-------
Table 5.2     (continued)
Flow
Class
H5-0





Flow
Zone
discharge
mdnf-wj
surface impingement with
full vertical mixing
surface buoyant spreading
passive diffusion
MOD
01
12

33
41
61
TR
0
9

0
7

V6       discharge                          01           0
         surface impingement with
           unstable recirculation, full
           vertical mixing, buoyant
           upstream spreading, and
           buoyant restratification         34           0
         surface buoyant spreading          41           7
         passive diffusion                  61
                            100

-------
modules.  For example,  if the  source dimension is large and
the crossflow is strong, i.e.  L^ » Ly, then the weakly
deflected jet (MOD11) may be omitted in some flow classes,
and a strongly deflected jet or plume may  follow the initial
discharge.    For  a non-buoyant  discharge,  the  buoyant
spreading regime  (MOD41)  will  be absent  in the applicable
flow  classes  (V2 or H2) .   Given  all  these  possible sub-
classes the actual variety of  flow configurations that will
be modeled  is much  larger  than  indicated by  the primary
classes (see also Section 3.2)
5.1.2 Flow Protocols for Negatively Buoyant Discharges into
Uniform Ambient Layers  (Flow Classes NV and NH)

    The  flow  protocols  for negatively  buoyant discharges
into  uniform  ambient  layers,  corresponding  to  the  flow
classes  NV and  NH as  discussed  in  Section 3.2.4  and
illustrated in  Figure  3.6,  are listed in Table 5.3.  Some
of the unstable discharge  protocols  bear some resemblance
to  those  for  positively  buoyant discharges except  for
restratification  and  buoyant  spreading  in  the far-field.
This is reflected in different transition criteria.

    Also some  protocols for stable discharges  classes (e.g.
NV1,  NH1)  appear  similar to  their  positively  buoyant
counterpart (e.g. VI,  HI) .  However,  some  differences in
transition criteria as well as the downward acting buoyancy
force act to produce entirely different flow configurations
(see sketches in Figures 3.5 and  3.6 , respectively).
5.1.3  Flow Protocols  for  Discharges Trapped  in Linearly
Stratified Ambients  (Flow Class S)

    Table  5.4  summarizes the protocols for  the  five flow
classes S  (refer  to  Section  3.22  and Figure 3.4) in which
the ambient stratification causes an internal trapping of
the effluent flow leading to  a terminal layer formation and
subsequent  far-field   processes.     All  stratification
dominated  flow (see Fig.  3.4)  use  special  modules that
account for the ambient  stratification in the initial jet
or plume phases of the flow.

    For instance,  in the jet-like stratification dominated
flows  (classes S2, and  S3)  the mdnf will be replaced by its
stratified  counterpart,  the mdls,  before  terminal  layer
interaction.

    When  terminal  layer  interaction  occurs  the  normal
sequence of flow  regions is  interrupted,  and the sequence
will  change  to   include  the appropriate terminal  layer
interaction (see Section 3.2.2)  and then  continue  as  an
                            101

-------
Table 5.3     Flow   Protocols   for   Negatively   Buoyant
              Discharges into Uniform Ambient Layers
Flow
Class
NV1






NH1





NV2 , NH2






Flow
Zone
discharge
mdnf
mdff
bdff
bottom approach
bottom buoyant spreading
passive diffusion
discharge
mdnf
bdff
bottom approach
bottom buoyant spreading
passive diffusion
discharge
mdnf
bdnf
bottom impingement with
buoyant upstream spreading
bottom buoyant spreading
passive diffusion
MOD
01
11
16
22
31
41
61
01
11
22
31
41
61
01
11
21

32
41
61
TR
0
2
16
17
0
7

0
16
17
0
7

0
16
17

0
7

MOD = module, TR = transition rule
                            102

-------
Table 5.3     (continued)

Flow     Flow                               MOD         TR
Class    Zone
NV3 discharge
mdnf
mdff
surface approach
fall down
bdff
bottom approach
bottom buoyant spreading
passive diffusion
01
11
16
31
52
22
31
41
61
0
1
5
0
0
17
0
7

NH3      discharge                          01           0
         mdnf                               11           2
         bdnf                               21          17
         bottom approach                    31           0
         mdnf-wj                            12          18
           flow turning                     31           0
         bottom buoyant spreading           41           7
         passive diffusion                  61
NV4      discharge                          01           0
         mdnf                               11           5
         surface impingement with
           full vertical mixing             33           0
         surface buoyant spreading          41           7
         passive diffusion                  61
                            103

-------
Table 5.3     (continued)
Flow     Flow                               MOD         TR
Class    Zone
NH4 discharge
mdnf
mdff
bdff
bottom approach
bottom buoyant spreading
passive diffusion
01
11
16
22
31
41
61
0
2
16
17
0
7

NV5      discharge                          01           0
         bottom impingement with
           unstable recirculation, full
           vertical mixing, buoyant
           upstream spreading, and
           buoyant restratification         34           0
         bottom buoyant spreading           41           7
         passive diffusion                  61

NH5      discharge                          01           0
         mdnf                               11           5
         bottom impingement with
           full vertical mixing             33           0
         surface buoyant spreading          41           7
         passive diffusion                  61
                            104

-------
Table 5.4     Flow  Protocols  for  Discharges  Trapped  in
              Linearly Stratified Ambients

Flow     Flow                               MOD         TR
Class    Zone
SI       discharge                          01           0
         mdnf                               11           2
         mdff                               16          10
         terminal layer approach            31           0
         internal buoyant spreading         42          11
         passive stratified layer
           diffusion                        62
S2       discharge                          01           0
         mdls-v                             13          12
         terminal layer impingement with
           upstream spreading               36           0
         internal buoyant spreading         42          11
         passive stratified layer
           diffusion                        62

S3       discharge                          01           0
         mdls-h                             14          13
         terminal layer injection with
           buoyant upstream spreading       37           0
         internal buoyant spreading         42          11
         passive stratified layer
           diffusion                        62
MOD = module, TR = transition rule
                            105

-------
Table 5.4     (Continued)
Flow     Flow                               MOD         TR
Class    Zone
S4 discharge
mdnf
bdnf
bdff




terminal layer approach
internal buoyant
spreading
01
11
21
22
31
42
0
1
3
14
0
11
passive stratified layer
diffusion

62

S5       discharge                          01           0
         mdnf                               11           1
         bdnf                               21          15
         terminal layer impingement with
           buoyant upstream spreading       36           0
         internal buoyant spreading         42          11
         passive stratified layer
           diffusion                        62
                            106

-------
internal layer far-field flow.


5.1.4 Flow Protocols for Bottom Attached Flows  (Flow Classes
    The flow protocols  corresponding  to  Section 3.2.5 and
Figure 3.7 are listed in Table 5.5.  The first flow module
following the discharge refers to either wake recirculation
for wake attachment classes  (Al and A2) ;  or to wall jet flow
for Coanda attachment classes  (A3 to A5) .   Flow class A3 has
a sub-class A3'  (determined  by using an internal criterion)
depending on whether a weakly deflected  jet  flow (MOD17)
exists.  Whenever a lift-off occurs due to positive buoyancy
the remaining flow regimes  after  lift-off  are  similar to
the parent flow class given by the prefix (..).

    For wake attached jets,  the near-field flow regimes are
replaced  by  a wake-recirculation  module as described in
Section  5.3.3.8.    In  the  (..)A1  class,  buoyancy  is
sufficient to cause lift off,  so the wake recirculation is
followed by  a bdff.   For negatively  buoyant  flow classes
with no lift off  ((..)A2 class), the wake recirculation can
be followed by a buoyant bottom spreading module.

    In the Coanda attached jet, the usual mdnf and mdff are
replaced by their attached counterparts,  the mdnf -wall jet
and the mdff -wall jet, respectively. If sufficient buoyancy
is present,  as in attachment classes A3, A3', and A4 ,  lift-
off will occur.
5.2 Hydrodynamic Simulation Modules

    This section provides the  salient  details for each of
the modules listed  in Table 5.1 which provide the predictive
element for a particular mixing  process.   The modules are
grouped into the different flow phases (from near-field to
far-field)  as indicated in Table 5.1

    There are two types of flow modules:

    i) The  continuous types describe the evolution of a flow
    process along  a trajectory.   Depending on user input,
    a small or  large  step interval can be used  to obtain
    flow and mixing information along that trajectory.

    ii)   The control  volume  type  uses  a control  volume
    approach to  describe  outflow values  as a function of
    inflow values based on conservation principles.

    For either type, the beginning values  are denoted by the
subscript  "i"  (e.g.  S,- is  beginning dilution)  and  final


                            107

-------
Table 5.5     Flow Protocols for Bottom Attached Flows
Flow     Flow                               MOD         TR
Class    Zone
         discharge                          01           0
         wake recirculation                 51           0
         lift-off                           52           0
         bdff                               22           5
         surface approach                   31           0
         surface buoyant spreading          41           7
         passive diffusion                  61
(..)A2   discharge                          01           0
         wake recirculation                 51           0
         bottom buoyant spreading
            (NV and NH only)                 41           7
         passive diffusion                  61
         discharge                          01           0
         mdnf-wj                            12          18
         lift-off                           52           0
         bdff                               22           5
         surface approach                   31           0
         surface buoyant spreading          41           7
         passive diffusion                  61
MOD = module, TR = transition rule
                            108

-------
Table 5.5     (continued)
Flow     Flow                               MOD         TR
Class    Zone
( . . ) A4 discharge
mdnf-wj
lift-off/fall down
bdnf
surface impingement with
buoyant upstream spreading
surface buoyant spreading
passive diffusion
01
12
52
21

32
41
61
0
8
0
6

0
7

(,.)A5   discharge                          01           0
         mdnf-wj                            12           2
         mdff-wj                            17          19
         surface approach                   31           0
         surface buoyant spreading          41           7
         passive diffusion                  61
                            109

-------
values are  denoted by the  subscript "f"  (e.g.  bf  is the
final flow half-width).
5.2.1 Simulation Modules for Buoyant Jet Near-Field Flows
5.2.1.1 Introductory Comments

    The flow  equations  in this module  group describe the
trajectory (x,y,z) of the jet/plume centerline and provide
values along that trajectory for the flow half-width b, the
local concentration c, and the local dilution S.

    The half-width b is defined here as the  "1/e width" as
a typical  convention for Gaussian jet-like profiles  (see for
example Holley and Jirka,  1986).  Thus,  b is  the half-width
(radius) of the jet/plume flow where the  local concentration
is  1/e, or 37%,   of  the  centerline concentration.   Since
alternate width definitions are  sometimes used in pollution
analysis,  the width definition when multiplied by 0.83 gives
the 50% width, by 1/21/2 gives the  standard deviation (61%
width), and by 2 /2 gives  the 14% width, respectively.  In
the case of atmospheric plumes the later  definition  is often
taken as the "visual width" of the plume.

    The local concentration in this group of  modules refers
to the maximum centerline  concentration  cc at the jet/plume
centerline.  Thus, the corresponding dilution refers to the
minimum dilution CO/GC in which  c0 is the initial discharge
concentration.  It is important to keep in mind these flow
definitions since they differ, in general, from those found
in modules for subsequent flow zones.   These differences are
unavoidable due to different profile shapes  for the effluent
flow distribution governed by the various mixing processes.

    In CORMIX1 a  global Cartesian coordinate  system (x,y,z)
is placed  at  the  bottom of the  water  body  with the origin
(0,0,0) located directly below the center of the discharge
orifice.   The height of  the discharge  orifice above the
bottom is hQ.   The positive x-axis  is  located at the bottom
and  directed  in  the downstream  direction  following the
ambient flow.  The positive y-axis  is  located at the bottom
and points to the  left, normal to the ambient  flow direction
(x-axis).    The positive  z-axis points^ vertically upward.
The angle  between  the discharge axis  y* and  its projection
on  the  horizontal plane  (i.e.  the discharge  angle above
horizontal) is 8Q.   The discharge-crossflow angle aQ is the
angle between the projection of y*  on  the x-y plane and the
x-axis  (a0 =  0°  for co-flowing discharges,  afl  =  180° for
counter-flowing discharges).

    A primed  coordinate  system,  (x',y',z'),  within a given
buoyant jet  flow region is  specified with  respect to the
virtual source for that flow region.   A virtual source is


                            110

-------
needed  for  each  flow  region  because  the  perturbation
analyses  used  in  each  module  assume  a  point  discharge
source,  which  is  physically  unrealistic.     The  primed
coordinate system is related to  the global coordinate  by

     (x,y,z) =  (x',y',z') +  (xv,yv/zv)                   (5.1)

where (xv/yv,zv) is the global position of the  virtual source
for  that  flow  region.   The position of the  virtual source
(xv/yv,zv)  is computed by taking  the known  flow solution at
the transition, as given from the previous flow region, and
then back calculating the source position using the dilution
equation for the given flow region. This  procedure assures
continuity  of  the dilution  and concentration  predictions
from one  module to  another.   However,  ocassionally slight
discontinuities in the predicted half-widths can  occur.

     In general, the simple analytical  results of Chapter II
are extended to non-vertical three dimensional trajectories
within the  ambient  crossflow.   A  supplementary transverse
coordinate >j is defined here inw a plane  given by the z-axis
and  rj  is the  projection of y*  into  the  z-y plane.   Any
vertical  motion of  the  jet  flow is  controlled  by  the
vertical  component of  the  discharge momentum  flux  as  well
as the buoyancy flux (which always acts vertically) .   The
transverse  (horizontal)  motion of the  jet flow  is solely
controlled  by  the horizontal  component  of  the  discharge
momentum flux.

     Defining 7* as the angle between  the  discharge axis y
and  the  crossfl^ow  (x-axis) , and the  angle  60  between the
projection of  y* on the yz-plane  (transverse coordinate ^)
and  the y-axis the  relationships for the discharge angles
8Q  and  CTO  are

    70  =  sin'1(l - cos200cos2<70)1/2                       (5.2)

    60  =  tan"1 (tan^o/sinCTg)                             (5.3)
5.2.1.1 Discharge Module  (MODOl)

    This module begins every flow sequence.   In  the  module
the flow is converted from a uniform velocity distribution
to a  Gaussian profile,  with equivalent volume  flux  (note
that momentum flux conservation is assured due to  the  bulk
flow parameters used in the analysis) .  The  representative
final flow width bf for  the discharge module  is

    bf = (a,/*)*                                       (5.4)

where a0 is the port cross sectional area.   No dilution  is
assumed to occur, so that Sf = 1.0 and  cf = CQ, where Sf  is


                            111

-------
final dilution  and cf and c0 are  the  final and  discharge
concentrations, respectively. The  final x- and y-coordinate
are 0, but zf = h0.
5.2.1.2 Weakly Deflected Jet In Crossflow  (MODll,  mdnf)

    The results  for  the mdnf presented in Section 2.1.4.1
are extended to  include the general  3-D trajectory.   For a
cross-flowing  discharge  (70  > 45°)  the  trajectory  is  a
function  of  ij  as  the independent variable.   Writing  the
trajectory equations  in the virtual coordinate  system  for
the mdnf in terms of the supplemental coordinate ^ gives the
crossflow induced deflection

                                                      (5-5)

where  T^  is  the  trajectory constant  for  the  mdnf.  The
expression for the transverse coordinate y is simply

    y' = rj'cosSg                                       (5.6)

    The  vertical   coordinate,   however,   experiences   an
additional perturbation due to buoyant deflection, or

    z' = r,'sin*0  + T^^signJo/d^sin^)               (5.7)

where T11B is a constant for the buoyancy correction in  the
mdnf, and  signJp is  equal to +1  for a positively buoyant
discharge  and  is  equal  to -1  for  a  negatively  buoyant
discharge.

    The flow width  (radius)  is

    b - Bu'/siivy,                                    (5.8)
where Bn is a width constant for the mdnf.  The dilution is
expressed as

    S = S11f?//(Vin7o)                                 (5.9)

where sn is the dilution constant.

    If the discharge is co-flowing (70 < 45°) , the simulation
should step in  x as the primary  independent coordinate and
the trajectory,  width,  and  dilution relationships are

    z' = r,'sin6Q + T11Bx/3signJ0/(I^2cos370)             (5.10)

    •»' = x'tan7o - x'2tanV(Tn2LJ                    (5.11)

    b = B1tX'/COS70                                   (5.12)
                            112

-------
    S = S11X//(LQCOS7o)                                (5.13)


5.2.1.3 Weakly Deflected Wall Jet in Crossflow  (MOD12, mdnf-
wj)

    In this  flow region unequal entrainment  and spreading
will be neglected  in directions parallel and normal to the
boundary wall.  The attached flow has a horizontal momentum
flux Mw two times the discharge momentum  flux  MQ to account
for the mirror image of the attached  flow  with the bottom
symmetry plane,  so the horizontal wall  momentum flux MH =
          This assumption also results in Qw  = 2Q0.
    For a cross-flowing discharge (a0  >  45°) , the trajectory
equation for y' in terms of x'  (z = 0 for the attached case)
becomes

    y' = T12(2cos00)1/V/2(*'  -  y'cota0)1/2             (5.14)

where T12  is a  trajectory constant  for the mdnf-wj .   The
width and dilution are  given by

    b = B12y'/sina0                                   (5.15)

    S = s12y'(cosV2)1/2/(LQsina0)                     (5.16)

respectively,  where  B12  a width  constant,  and  S12  is  a
dilution  constant for  the  mdnf-wj .    A  similar  equation
system  holds for  the  co-flowing  wall  jet (a0 <  45°)  in
analogy to the  free  jet (previous  sub-section) .
5.2.1.4 Near-Vertical Jet  in Linear Stratification (MOD13,
mdls-v)

    For  jets   issued   (near-) vertically  into  a  density
stratified environment,  70  is  greater than 45° so the xyz-
coordinates  of  the flow in the virtual  coordinate system
are given in first order by a  straight line trajectory
                                                     (5.17)

    y' = r,'cosS0                                      (5.18)

    z' = T)'sin6Q                                      (5.19)

respectively.  The width  and  dilution are expressed as

    b = B^'/sin^                                   (5.20)

    S = S13C(l-S13Asin^0r7'4/(sinS0LIn'4)]f?'/(I^sin50)     (5.21)
                            113

-------
respectively, where B13  is a  width constant, and S13 and S13A
are dilution  constants  for  the  mdls-v.   For  the physical
background see Section  2.2.4.7.
5.2.1.5 Near-Horizontal Jet in Linear Stratification (MOD14,
mdls-h)

    The simulation of this module (occurring in flow classes
S3^ is limited to  the co-flowing design, with 70 less than
45 .   The  trajectory in  the virtual coordinate system is
given by

    z' = x'tan7osin$0  + [T14BvV (VcosV4*0) ]3        (5.21)
    y' = x'cos
-------
5.2.1.8  Strongly Deflected Wall Jet in  Crossflow  (MOD 17,
mdff-wj)

    The assumption for jet attached momentum flux MH is the
same as  in previous  section  for the mdnf-wj .   Expressing
the trajectory  equations for y' in  terms of x' (z  = 0 for
the attached case) gives in  analogy to the free jet

    y' - T17(2cos*0)2/\2/3(sina0)1/3x'V3                 (5.29)

The dilution is

    S - S14y'2/ (21^)                                  (5.30)

where Su is a dilution constant.


5.2.1.4 Weakly Deflected Flume in Crossflow (MOD21,  bdnf)

    The bdnf trajectory  coordinates  are a generalization  of
the perturbation solutions  presented in Section 2.1.4.6.
With z' as the primary  coordinate the trajectory  equations
are

    x' = (zV(T21Lb1/4))4/3+                            (5.31)
             2/31/1/3'1/3
    y' = T21I^cossina0x'    +                    (5.32)
where T21 is a trajectory constant for the bdnf, and T21M1  and
T21M2  are  momentum  correction coefficients.     Width  and
dilution are given  by

    b = B21z'                                          (5.33)

    S = S^L^'V5'3/^!*)                              (5.34)
respectively,  where B21  is a  width constant  and  S21 is  a
dilution constant  for  the bdnf.
5.2.1.9 Strongly  Deflected Flume in Crossflow  (MOD22/bdff)

    The bdff trajectory coordinates, written in the virtual
coordinate system as  a  function of x'  are
    z/ = TsignJo                             (5.35)

    y' = T16Lln2/3cos1/3?0sin1/3a0x'1/3                       (5.36)
                            115

-------
where T22  is a  constant  for  the  bdff,  and T-6 is a constant
for the mdff  since the transverse  deflection  is momentum
induced.

    Width and dilution are given by

    b = B22z'                                         (5.37)

    S = S22z'2/(W                                  (5.38)

respectively.


5.2.2 simulation Modules for Boundary Interaction Processes

    When the flow  interacts with  any  boundary  such as the
surface,  bottom,   or  pycnocline  density jump,  a  similar
interaction module will be  used  to describe the process.
The only difference is the centerline height  of the flow as
well as any hydrostatic adjustment  process for pycnocline
flows (see Section 2.23).

    In  all of the  following  modules  a control  volume
approach is used.   Generally, a bell-shaped jet/plume inflow
is transformed to a more uniform (top-hat) outflow zone that
follows the boundary (surface, bottom,  pycnocline) or flows
in   the   stratified    terminal   layer.     Thus,   after
transformation the  final geometric values are  the trajectory
(xf,  yf,  zf) ,   the  total  vertical thickness  b,,  and  the
horizontal  half-width bhf of  the top-hat profile.   Also
concentration  and  dilution  values refer to average values
which,  within  the  top  hat  profile, tend to  be  close to
extreme (maximum or minimum, respectively) values.
5.2.2.1 Near-Horizontal Surface/Bottom/Pycnocline Approach
(MOD31)

    In this simplest approach condition,  the bent over  flow
approaches the  interface  near-horizontally at impingement
angle 9{  < 45°  (Figure 2.8a and Section 2.4.1).

    The final x-coordinate is given by a geometric shift due
to the size of the in-flowing jet/plume

    xf = x,. + 2b,.                                     (5.39)

yf is set equal to ys,  and zf equal to z-.   The final  bulk
dilution  is

    Sf = 883,8,                                        (5.40)
                            116

-------
where SB31  is  a  bulk mixing conversion factor.


5.2.2.2 Near-Vertical Surface/Bottom/Pycnocline Impingement
with Buoyant  Upstream Spreading (MOD32)

  In this  surface  approach condition,  the weakly bent flow
impinges on the surface at a near-vertical angle  &. ,  where
0j  >  45°.   The physical  process has  been  summarized  in
Section  2.42  with  reference  to  Figure  2.8.b.    After
impingement the flow spreads more or less radially  along the
water surface as a density current.  In particular,  the flow
spreads some distance upstream against the ambient  flow, and
laterally  across  the  ambient  flow.   This   spreading  is
dominated  by  the  strong buoyancy of  the discharge.

    The dilution  is  expressed as (see Eq.  2.85)

    sf = SiSSB32[V(Hs(l-cos^iCOSai))]1/3                 (5.41)
where SSB32 is a dilution constant.   The upstream intrusion
length Ls is given by
    Ls = A^I^l-COSfljCOSajtVHs)                  (5.42)

          for  (Lb/Hs)  <  165(1- COSfljCOSaj)

and

    Ls = AL^Lfe                                       (5.43)

          for  (Ifc/HJ  >  165(1- cos0jCos<7j)
where AL^  and ALj28 are  constants.   The  typical vertical
thickness within the upstream stagnation region is
    hs - CD^S^V^                                  (5-44)
where CD32 is a constant.   The dimensions  of the effluent
flow are

    bhf =  BH32LS                                        (5.45)

    bvf =  SfLfcV(2bhf>                                  (5-46)

The final flow coordinates  are xf  =  x1 +0.5bvf,  yf =  y( , and
xf  = X,- .
                            117

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5.2.2.3 Near-Vertical Surface/Bottom/Pycnocline Impingement
with Pull Vertical Mixing  (MOD33)

    In this  surface  approach region, the weakly  bent  flow
impinges  on the  water surface  at  a  near-vertical  angle
(Figure 2.8c).  Because of the unstable recirculating flow,
the centerplane dilution  increases

     Sf = SR33S,.                                       (5.47)

where SR33 is a recirculation factor.  The final flow width,
bhf/ is found from the continuity equation
    bhf =  SfI^V(2H8)                                (5.58)

and final outflow location xf is approximated as

    xf = x, + Hs                                      (5.49)

where  x,-  is  the  plume position  at the  beginning of  the
region, and yf = yf  and zf = z-.


5.2.2.4 Near-Vertical Surface/Bottom/Pycnocline Impingement
with Unstable Recirculation, Buoyant Restratification,  and
Upstream Spreading  (M0034)

    In this surface approach region,  the flow  rises  near-
vertically and impinges on the water surface (Figure 2.8d) .
After  impingement  the mixed  flow recirculates  over  the
limited water depth and becomes partially re-entrained into
the flow.  The final  dilution Sf is given by

    sf * S34H,5/3/(I*2/3lM)                               (5.50)

where  S34 is  a dilution  constant.   The upstream  intrusion
length Ls is  given by

    LS = AL^                                       (5.5i)

The upstream intrusion thickness  hs is

    hs - C^SfW^,                                 (5.52)

The final  half-width bhf  and  thickness bvf  and  coordinates
are analogous to  those for MOD32.
5.2.2.5 Stratified Terminal  Layer  Impingement with Buoyant
Upstream Spreading  (MOD36)

    In  this  condition,  the  flow becomes  trapped  in  a
stratified  terminal  layer  before surface  contact.   This
                            118

-------
terminal  layer  approach  is  defined   for  near-vertical,
strongly buoyant stratified flows that  do not interact with
the  surface or  pycnocline  density jump.   The detailed
equations   are  similar   to  the   previously  presented
unstratified case  (MOD32) and are not presented  here.
5.2.2.6  Stratified Near-Vertical  Surface  Injection with
Upstream Spreading  (MOD37)

     This module  simulates a terminal  layer approach  for
near-horizontal, strongly stratified jet-like flows that do
not interact with  the  surface or pycnocline density jump.
With the  exception of  an added effect  on  the horizontal
discharge momentum, the development is similar to MOD36  and
is omitted for brevity.
5.2.3 Simulation Modules for Buoyant Spreading Processes

    The  flow  distribution inherent  in  the two  buoyant
spreading modules is again mostly uniform (top-hat).  Hence,
the same interpretations on geometric (width) and dilution
(or concentration) values apply (see introductory comments
to Section 5.2.2) .
5.2.3.1 Buoyant Surface/Bottom Spreading  (MOD41)

    The physical background  for  buoyant spreading process
at  the boundary  of an  flowing  abient was  discussed in
Section 2.2.1.  Thus the flow equations are

    bh = tbhiV2 + l.5(V(2CD41))1/2(x - x,.)]2/3          (5.53)
    bv = bvi (Vbhi~                                 (5.54)

    S = S,(b/bvi)^                                    (5.55)

    The trajectory is a straight line  following the ambient
flow  and located  at  the  appropriate  vertical  boundary.
Also, if the plume contacts a lateral boundary (shoreline)
the trajectory centerline shifts over to that boundary and
the  further  spreading process  is  limited  to  one frontal
zone.  These coordinate switching functions  are included in
MOD41.
                            119

-------
5.2.3.2 Buoyant Terminal Layer Spreading  (MOD42)

    Referring to Section 2.8.4, the flow  equations  are

    bh = [bhi2"^+                                      (5.56)
    bv " bvi(Vbhi~                                  (5.57)

    S = Sjb^/tb^b,,,.)                                 (5.68)

MOD42 also contains boundary interaction  features.


5.2.4 Simulation Modules for Attachment/Detachment Processes

    The variable  definitions  in the following section  are
similar to those  for jet/plume processes  (Section 5.2.1).


5.2.4.1 Wake Recirculation  (MOD51)

    This module describes the recirculation process for wake
attached flows  (see  Section 2.4.4.1).   The  flow equations
are for minimum dilution
    Sf = »/2bvf/(V*)                                 (5.69)

the flow half -width

    bhf  = BV51xf                                       (5-70)

with bvf = bhf,  and the longitudinal extent

                                                     (5.71)
5.2.4.1 Lift-Off/Fall-Down  (MOD52)

    This is the reverse of MOD31 and performs  a  conversion
form a uniform (top-hat) profile to a final Gaussian profile
as a buoyant plume separates  form a. boundary.
5.2.5 Simulation Modules  for Ambient  Diffusion Processes

    The  physical  processes  underlying  the  two  ambient
diffusion modules  have  ben presented in Section  2.3.   The
following flow definitions  apply here:   The  passive plumes
have  a Gaussian  profile,  the vertical  thickness  bv  and
horizontal  half-width  represent the 46% width value (i.e.
(7r/2)1/2 times the standard deviation of the Gaussian passive
                            120

-------
diffusion profile).  This width convention is equal to the
width of  a top-hat profile  that has  the  same centerline
concentration.  This  difference  relative to the jet/plume
regimes arises due to the different mass flux conservation
equations  for passive  versus active  (discharge induced)
effluent  flows.   The representative  concentration  is the
maximum centerline concentration,  and the  dilution is the
corresponding minimum.
5.2.5.1 Passive Diffusion in uniform Ambient  (MOD61)

    The passive plume trajectory is straight  following the
abient flow.  The geometric expressions are

    bv =  [*Ez(x-x,.)/ua  +  bvi2]1/2                        (5.72)

    bh =  [*Ey(x-x,.)/ua  +  bhl.2]1/2                        (7.73)

with  the  appropriate  diffusion  coefficients  Ez  and  Ey
discussed  in  Section 2.31  for  bounded channel  flow.    In
unbounded channel flow,  the  "4/3  diffusion law" coefficient
(Section 2.3.3)  is used,  and  Eq. (2.65)  is the expression
for the half-width bh.  Changes in centerline trajectories
occur  when the plume  interacts  with  vertical  or lateral
boundaries.
5.3.5.4 Passive Diffusion in stratified Ambient  (MOD62)

    The flow  expression for this module  are analogous to
MOD61  with  the  substitutions  of  a  Richardson  number
dependence  for  the vertical diffusivity  (Section 2.3.3).
Also there are more complex interaction possibilities with
vertical boundaries.
5.3  Transition Rules/  Flow Criteria and Coefficient Values

    This section  provides the detailed  equations for the
transition rules listed in the flow protocols that control
the spatial extent of  each flow  module.   It also provides
the complete  functional  form for  the  criteria,  including
terminal height evaluations that  have been used  in the flow
classification  presented  in Chapter III.   Furthermore,  a
listing and justification of all numerical coefficients is
supplied.
                            121

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5.3.1 Transition Rules

    Transition  rules  are  needed  to  give  the  spatial
expressions  as to  where  each  flow  region  ends.   Each
subsequent  flow region  is assigned  initial  values that
correspond to the final values of the preceding flow region.
Transition rules used in the simulation appear in Table 5.6,
and the associated constant values appear in Table 5.7.

    For example, Transition Rule I gives the  final  value of
a weakly deflected jet coordinate when  it is followed by a
weakly deflected plume.  The transition from one region to
the other is characterized  by the jet/plume length scale L,,,.
If the  discharge  angle relative to the x-axis  is -y0,  the
final  supplementary  coordinate  r?f',   and   the  final  x-
coordinate xf'  are  given  by Transition Rule 1 as
    r,f'  = CTIVI'LH       7o  > 45                      (5.74)

    Xf'  = CT1V2-I^       7o  < 45°                      (5.75)
where CT1V1 and CT1V2 are constants (Constant for Transition
rule I, first Value and second Value, respectively) .

    Note that some transition rules apply within the primed
coordinate  system (limiting  xf',  yf',  zf',  or r?f')  while
others apply to the global coordinate system (limiting xf/
Yf/  zf/ or r/f) .
    As shown in Table 5.6 the proper transition rule depends
on the sequence of current flow module to next flow module.
In general,  flow transitions between flow regimes are smooth
due   to   matching  volumetric  dilutions.     There  may
occasionally be slight discontinuities in the predicted flow
width.
5.3.2 Flow Classification Criteria

    A summary of the detailed classification criteria that
have been shown in "order of magnitude"  form on  Figures  3.4
to 3.7 is provided  in  Table 5.8.   The labels Cl, C2, etc.
correspond  to  the  labels  used  on  those  figures.    The
detailed  criteria  often  contain  factors   (e.g.  0.8 that
describes the thickness  of  a buoyant layer formation at  a
boundary  after  impingement)  that effectively  reduce  the
existence of certain flow zones which are being  tested for.
The values of the numerical constants are also  included in
the first column of Table 5.7 with reference or  comments on
how they were obtained.
                            122

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Table  5.6     Transition  Rules

TR   CMOD NMOD Equation
1    11   21   70 >  45    ijf' =
               70 <  45°    xf' =  CT1V2-LM
                                            V2_
2   11    16   7o ^ 45    r,f' = CT2Vl.Lmsin'/S0
    12    17   7Q < 45°   Xf' = CT2Vl-LmCOS1/270
3    21   22    zf' =
4    16    22    xf' =  CT4Vl'L)l((Ll/I^)1/6
5    22    31    zf  =  Hs
     16    31
     11    33
6    21    32    zf  =  0.8HS 4-  0.2hQ
7    41    61   Xf  =  X,- +  (23/2/3) -CD411/2
                      ,h 3/2/T 1/2* , r ,R
                      (°hi   /-hs   M I (8
8    17    52   aQ ^  45    yf' =
     12    52   a0 <  45°   xf' =  CT8V2-L>,
TR  =  Transition Rule, CMOD = Current module,
NMOD = next module
                              123

-------
Table  5.6      (continued)
TR   CMOD NMOD Equation
9    12    33    <70  >  45°   yf'  - (H./B,,) sinaQ
                *   <  45°     '  = (
10   16   31    zf = h0 + CTlOVl«I^,1/3Lill/2/3sin«01/3signtf0

11   42   62    Xf  = x,  + (2CD42)1/2/(2-/3)(V2bhi/Vbvi)
12   13   36    zf  = h0
13   14   37    7o  >  45°   »?/  - CTISVI'L/
                70  <  45°   Xf'  = CT13V2-Lm/

14   22   31    Zf  -  h0 + CT14Vl-LbV9Lb'8/9signJ
15   21   36    zf  = h0 +
16   11   22    70  > 45°   ijff  = CT16V1-L,,
                7  < 45°   X'  =
17   22   31    Zf - 0
     21   31
18   12   31    a0  > 45°   yf' = CT18V1-L,,,
19   17   31    Xf'  = CT19V1'L^(COS00)V2
                               124

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Table 5.7

Coefficient
Coefficients Used In Transition Rules

     Value          Data Source, References,
                    or Comment
CT1V1, CT1V2
CT2V1, CT2V2
CT3V1
CT4V1
CT8V1,CT8V2
CT10V1
CT12V1
CT13V1,CT13V2
CT13V3
CT14V1
CT15V1
CT16V1
CT16V2
CT18V1
CT19V1
RfC
2.5
2.0
1.0
2.7
1.5
2.1
2.1
3.0
2.0
2.6
2.5
1.75
2.5
1.5
30.0
1.0
A) From trajectory and
terminal height equations
given by Wright (1977),
List (1982), Wong (1984),
and Hoi ley and Jirka
(1986) .
See A
See A
See A



Sharp (1977), Sobey et
al. (1988)
B) From terminal
equations given
(1982) and Wong
(See Table 5.8)
See B
See B
See B
See B
See B
See A
See A
See A
See A
height
in List
(1984)









Critical flux Richardson
                                  number
                           125

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Table 5.8

Criterion
and Value
              Flow Classification Criteria

              Equation Used  Data Sources,  References,  or
              in CLASS       Comments
Cl - 1.0
                             A)    From   trajectory    and
                             terminal    height   equations
                             given  by Wright  (1977),  List
                             (1982),   Wong    (1984),   and
                             Holley and  Jirka (1986) .
C2 - 1.8
C3 = 3.0
C4 - 0.65
C5 - 0.65
CIO = 2.0
              Lm/Lm'*C2
              SC4
                             See A
                             See A
                           ] See A
                       j-hg) ] See A
              5C5
C6,C7,C8      Lb/[0.8(Hs-hQ) ] See A
   - 1.0      S(C6,C7,C8)

C9,C11        Lb/[0.8(Hs-h0) ] See A
   = 0.4      *(C9,C11)
                              B)  Lee and Jirka (1981)
              SC10
C12,C13
   - 0.65      *C(12,13)
                              See  A
C14,C15,C16   LM/H8           Sobey et al.  (1988)
   = 4.3      *(C14,C15,C16)

C17 = 0.55    V[0.8(H,-h0)]  See A
              SC17
                            126

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Table 5.8  (continued)
Criterion     Equation Used   Data  Sources,  References, or
and Value     in CLASS        Comments
C18 = 0.4     L/CO.S^-ho) ]  See  A
              SC18
C19,C22
  = 0.6
                              See  A
              5(C19,C22)
C25 = 2.5
C20 = 1.0
C21 = 0.65    Ln/Hs^C21
                              See  B
                              See  A
C23 = 0.65    Lm/[0.8(Hs-h0) ]  See  B
              SC23
C24 = 0.65    L|]/HS*C24
              SC25
              SC25
                              See  B

                              Derived on basis of data
                              comparison for wake attached
                              jets/plumes
C26 = 1.0     I^/fS-LgL^       Richardson number
              (f/8) ]*C26     criterion for buoyant lift-off
C27,C28
 = 0.20
                              Knudsen and Wood (1990)
              S(C27,C28       Sharp (1977)
C29 = 1.0
                              See  B
                            127

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5.3.3 Terminal Layer Expressions

    Table 5.9 lists the detailed terminal height equations
used in Figure 3.4 of the flow classification scheme.  The
equations differ from the usual equations available in the
literature  through  geometric  factors  that  measure  the
vertical or horizontal momentum strengths and through
factors measuring the direction of the buoyancy force.  The
first column also gives the adopted numerical values.
5.3.4 Model Coefficient Values

    Any predictive model describing turbulent flow processes
contains a number of constants that must be determined from
experimental data.  The coefficient values for flow modules,
transition rules,  and classification criteria of CORMIX1 are
listed in Tables 5.10,  5.7,  and  5.8, respectively.  A large
number  of  constants appear  as  required by  the  different
physical processes  in the various flow zones.

    The  consistent procedure   used   in  evaluating  the
numerical values of the coefficients was to refer to basic
experiments reported (or summarized) in the literature that
deal with  specific  flow processes.   The majority  of the
coefficients values  have been chosen in this  fashion without
any adjustment.   If conflicting data  were reported in the
literature, a mean  value was adopted  or seemingly dubious
data were  rejected.   In  several  instances  (notably for
recirculation zone  estimates for full vertical  mixing)  no
reliable data, or no data at all, has been reported in the
literature.  Often these processes are difficult to measure
and some judicious  estimation was made.   Subsequent system
evaluation and  validation  (see  next  chapter) led  to some
adjustment of coefficients  in that  category.  Ultimately,
it is expected  as more detailed experiments are conducted
in the future that those system  coefficients  that currently
have a limited data base can be confirmed or modified.

    Furthermore,  it  should  be  noted   that there   is  a
considerable overlap among flow constants for various
modules (Table 5.10), the transition rules  (Table 5.7), the
flow  criteria   (Table   5.8),   and   the  terminal  height
expressions  (Table  5.9).   Care has been taken  in setting
values  so  that there  is consistency between the various
coefficient types.

    Of  course,   the ultimate  validation  of the  present
predictive   methodology   together   with   the   relevant
coefficient  values must come from the ability to simulate
complex  flow  and  mixing  phenomena  in  agreement  with
available data.   This is addressed in the  following Chapter.
                            128

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Table 5.9
Stratified Terminal Height Expressions
Constant
Value
CT1 =2.1
Equation Used
in CLASS
Zt = (CTl-Lj^L /2/3sin001/3)sini90
+ (CT4-Lb1/9Lb'8/9)cos00
References or
Comments
Coef
f i c i ent
values adapted
CT2 =2.1

CT3 =2.0

CT4 =2.6
CT5 =2.9
Zt = CT2-Lm'sin001/4

Zt = CTS-Lj/VfV30083'4^)

Zt = CT4'Lb1/9Lb/8/9
Z^ = CT5-L '
from
List
and
Wong



(1982)

(1984)


                            129

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Table 5.10
Module Constants
Coefficient   Value
          Data Source, Summary Reference, or
          Comment
Tii,T12
S11'S12
Bn,B12
T11B
S13
S13A
B13
Su
Bu
T14B
?16'T17
S16'S17
B16'B17
B21
T16B
T21
T21M1
T21M2
T22
S22
B22
2.3
0.18
0.11
0.07
0.18
0.0058
0.11
0.18
0.11
2.0
1.6
0.30
0.3
0.11
0.5
1.5
5.6
7.5
1.0
0.35
0.3
A) Adapted from Wright (1977),
Fischer et al. (1979), List (1982),
Holley and Jirka (1986) , Lee et al.
(1987) .
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
See A
                            130

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Table 5.10    (Continued)

Coefficient   Value     Data Source, Summary Reference, or
                        Comment
SB31'SB33
SB32
ALj2A
AL32B
CD32
TJtJ "DU
BH32 , BH34
SR33
SB34
AL,,
CD34
SB36,SB37
HSS36
CD36,CD37
css36
AL36'AL37B
BH36 , BH37
HSS37
AL37A
CD,,
1.7
1.4
11.4
0.38
1.0
2.6
2.0
1.3
0.1
2.0
1.4
0.5
1.2
0.65
0.26
2.0
1.7
0.69
2.0
Center line/bulk dilution
conversion, Holley and
Jirka, (1986), Leeetal.
B) Upstream intrusion in crossflow,
Jones et al. (1982), Chu and Jirka
(1986)
See B
See B
See B
See B
See B
See B
See B
See B
Wong (1984)
See B
See B
See B
See B
See B
See B
See B
C) Density current . spreading,
                        Simpson  (1982) ,   Jirka  and  Arita
                        (1987)
              0.25      See C
                            131

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Table 5.10    (Continued)
Coefficient   Value
Data Source, Summary Reference, or
Comment
CD42
E«2
BV51
XR51
EZ61/EZ62
EY61 , EY62
E061/E062
2.0
0.25
0.3
5.0
0.2
0.5
0.0015
See C
See C
D) Based on data comparison
recirculation
See D
E) Fischer et al. (1979)
and Jirka (1986)
See E
See E


for wake

, Holley


                            132

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                        Chapter VI

            System Evaluation and Verification


    In  this  chapter  the  predictions  of  CORMIX1  will be
compared with laboratory and  field  data.   This chapter is
not meant  to  be an exhaustive validation  of all possible
CORMIX1 flow classes and associated  predictions, but rather
a test of key CORMIX1 modules  which  are common to many  flow
protocols  (flow  classes)   and  an  illustration  of  the
flexibility of  the  system  in  handling complex environment
and discharge conditions.

    While  CORMIX1  can  accommodate  many  possible   flow
configurations,  actual  available  laboratory or field  data
are quite limited.   In Section 6.1 comparisons are made  with
data for the  initial  subsurface  regimes  (buoyant jets) of
mixing processes  in the absence of any  boundary effects.
This  validation for  the  initial   flow  modules  (MODs 11
through  23)  is  important  in  view  of the  strong  initial
mixing common in most (but  not all)  environmental discharge
situations and  in view of the  larger body of literature
concerning the behavior  of unconfined buoyant jets.  Section
6.2 addresses more  complex flows  where different forms of
boundary interaction processes play a significant role.

    In  all  of  the  comparisons  shown below the numerical
constants and coefficients values have be consistently set
to the values summarized in Chapter V.

    To facilitate comparison with the non-dimensionalization
that  is  frequently used in the available  literature the
following parameters are introduced:
Densimetric Froude Number

    F0 = u0/(g0'D)V2 = (x/4)1/4VLQ                      (6-D

Jet/Crossflow Ratio

    R = uo/ua =  VLQ                                  (6-2)

Stratification  Parameter

    T = APo/[D(-dPa/dz)]  =  VV(I*V>                 (6'3)
                            133

-------
6.1 Buoyant Jets in Unconfined Ambient
6.1.1 Comparison With Experimental Data

    The following sections will  present  analyses of near-
field  flows,  starting  with  buoyant  jets  in  a stagnant
uniform ambient,  followed by neutrally,  positively,  and
negatively buoyant jets in uniform crossflows, and finally
flows in a stratified stagnant ambient.  To validate these
buoyant  jet  near-field  flows,  CORMIX1  predictions  are
compared with laboratory data from Anwar (1972), Cederwall
(1963) Fan (1967), Jordinson (1956),  Wright  (1977), Margason
(1968), and Anderson et al.  (1973).
6.1.1.1 Stagnant Ambient

    Figure 6.1 shows two  cases  of Fan's (1967)  trajectory
data  for a  buoyant  jet   in  a  stagnant uniform  ambient
compared with  CORMIX1  projections.   Fan released  a dyed
buoyant jet horizontally  (0Q =  0°)  into  a  uniform ambient
density tank.   Photographs recorded visual plume outlines.
For this stagnant environment  (for which  both 1^ and 1^ tend
to  infinity)  CORMIX1  classifies  the  flow  as H4-0 (see
section  5.1.1),  since for finite  depth H (equal  to  the
laboratory  tank  depth)   some  boundary  interaction  will
inevitably occur.  However, Fan does not report any detail
on these interaction processes.

    Figure  6. la  shows Fan's  buoyant jet  with  relatively
strong horizontal momentum flux  (F0 = 66) . The flow travels
horizontally at  first, after  some distance  the  buoyancy
force  deflects  the  flow  vertically.    For this  stagnant
condition the predicted trajectory is in excellent agreement
with  the observed  plume   outline.   As  noted  in  Section
5.2.1.1,  CORMIX1  predicts  a  plume  half-width  b  that
corresponds to a  local concentration of 1/e  =  37% of  the
centerline  concentration.   Assuming a   10% width  for  the
photographically recorded plume boundary (as traced by Fan)
these  values may be expected to  be wider by  a factor of
about 1.5.   This  interpretation  appears in good qualitative
agreement with the predictions.

    In contrast,  Figure 6.1b shows a horizontal buoyant jet
with relatively weaker momentum (F0 = 10)  .  In  this case the
horizontal  intrusion of  the  jet  is  small,  and  the flow
exhibits a strong vertical deflection,  which appears to be
slightly under-predicted by CORMIX1.

    CORMIX1 results for horizontal buoyant  jets  in stagnant
ambients with  a  wide  range of  Froude   numbers  appear in
Figure 6.2 in comparison with three different experimental
data sources.  This  figure seems  to illustrate two  facts:
                            134

-------
      120
      Data:
      	 Fan (1967), Visual Boundary
      CORMIX1
      	Centerline
 Z/D
                             (a)
 2/D
I20


100


 80


 60


 40


 20


  0
                                                   200
                        Data:
                        	 Fan (I967)  Visual Boundary
                             F0»IO,  V°°
                        CORMIXI :
                        — •— Centerline
                        	Width b
        0     20   40    60   80    IOO
                      x/D

                      (b)

Figure  6.1     Horizontal Buoyant Jet Trajectory in Stagnant
               Ambient, a)  Weak jet, b) strong jet.
                            135

-------
      220

      200

      180

      160

      140

      120
r  R
 z/D
    o
    4
    8
   I I
   14
   20
   33
   42
A
A
O
Experiments
Anwar (1972)
Anwar (1972)
Anwar (1972)
Fan (1967)
Cederwall (1963)
Fan (1967)
Fan (1967)
   Horizontal  Round
   Buoyant Jet

— CORMIX1  Centerline
               20
40
60
X
/D
80
IOO
I20
I40
Figure 6.2
     Horizontal   Buoyant  Jet   Trajectories   in
     Stagnant  Ambient  Over  a  Range  of  Froude
     Numbers
                           136

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i) the agreement of CORMIX1 with the observed trajectories
is good, within ±  20%  for the horizontal penetration, and
ii)  the disagreement  among  different  experimental  data
source is at least  as  large.   This can be seen indirectly
using CORMIX1 as the standard since in some cases an over-
prediction and in  others  an under-prediction is apparent.
Such discrepancies, or  levels of  accuracy,  are typical in
predictions and/or experiments with turbulent flows, and may
be related to the experimental setup,  some unsteadiness, the
exact method of determining centerline position, and other
factors.  In summary,  Figure 6.2 shows  that overall CORMIX1
predictions are  quite  good,  and  well within  the  normal
scatter evident from the experimental results.

    It should be noted that all the buoyant jet trajectories
displayed in Figure 6.2 could have been collapsed  into a
single curve  (at  least for  sufficiently large FQ)  if the
appropriated  length scale  1^ was  used  in  normalization
instead of D.   This was avoided in order to better display
the  jet  behavior  and data  scatter.    The  appropriate
normalization  has  been  used  in  Figure  6.3  in  which
centerline dilution data  form three  experimental  sources
covering  a  wide  range of  F0 is  displayed  in  a  compact
fashion   (Note that DFp=  [ (4/*) 1ALM]) .   The  agreement is
satisfactory in the entire jet/plume transition range.
6.1.1.2 Flowing Unstratified Ambient
6.1.1.2.1 Pure Jets In Crossflow

    Figure  6.4  shows  the centerline  trajectory  from an
experiment  of  Jordinson  (1956)  for a  pure jet  (F0  = «)
discharging vertically  in  a  crossflow  with velocity ratio
R = 6.2  (R  = Ug/uJ .  Here,  the  CpRMIXl predictions (flow
class  V2)  show    slightly  more  jet  deflection  than  the
experimental data near the orifice,  and  slightly less after
the flow becomes strongly deflected.

    Again, such disagreement has to be interpreted in the
light of the experimental  methods employed.  The centerline
used by Jordinson was  defined as the maximum velocity point
which  for  a cross-flow deflected  jet  (especially  in the
weakly deflected stage) is always considerably upstream of
the point half-way between the upstream and the downstream
jet boundary.  This factor, related to the horse-shoe like
concentration distribution in the  cross-section  of  such
jets,   is also addressed by Fan (1967),  Rajaratnam (1976),
and Jirka and Fong (1981).

    Two other examples  of  jet  trajectories in a crossflow
are given in Figure 6.5 in comparison to Margason's (1968)
data.     Figure   6.5a   illustrates   a  slightly  co-flowing
discharge (8Q = 60°, a0  =  0°) for two  crossflow  ratios (R


                            137

-------
      100
       10
S/F,
      O.I
      i  i i i T r
           ,rj    ,   r T  T in,|

Data:
 •  Liseth (1970)
 A  Hansen and  Schroder (1968)
 a  Cederwall (1968)
CORMIX1
	 Centerline Dilution
        O.I
                            10
                                z/OR,
too
Figure 6.3     Horizontal Buoyant Jet Dilution in Stagnant
               Ambient
                          138

-------
12
             Jordinson, 1956, data
             F0=oo,  R = 6.2
             CORMIX  Centerline
Z/D
               .
      O1-^
                      J	I	I	I
                                 8

                                 /D
                                             J	I
                                                  16
Figure  6.4
         Non-buoyant   Jet   Trajectory
         Crossflow
                                                in   Uniform
                           139

-------
       a)
               10
           z/0
Data:
• O Margoson (1966)
CORMIX1
    Centerlines
                                        R»IO
                                        10
                                 x/D
       b)
              20
          z/D
               10
                       OatO:
                P_IQ    • O Morqoson (1968)
               .***     CORMIX1
            •             Centerlines
                  ^-   	Width b
  • I   '
                                        ."O
                                            R=5

-5
                                     5
                                    x/D
                           10
Figure 6.5     Non-Buoyant Jets  at Various Discharge Angles
                in  Uniform Crossflow
                               140

-------
= 5 and R  = 10) .   Excellent agreement can  be  seen.    The
more severe test oof a slightly counter-flowing discharge (00
= 60°, CTO  = 180°)  is  shown  in Figure  6.5b for  the same
crossflow  ratios.   For the strong crossflow case,  R = 5,
the predicted jet trajectory is somewhat more deflected than
the observed one.
6.1.1.2.2 Buoyant Jets in Crossflow

    The effect of adding buoyancy to the jet flow will now
be  considered.     Figures   6.6   and  6.7  present  Fan's
trajectory,  dilution,   and  width  data  for a  vertically
discharging buoyant jet, 00 = 90°,  in  crossflow.  Figure 6.6
shows Fan's  experiment  with  F0 =  20 and R  =  12.   CORMIX1
(flow class VI, mdnf, mdff,  bdff)  predictions are in good
agreement with trajectory, dilution,  and width data. Figure
6.7 shows a jet with similar buoyancy  (F0 = 20)  but with a
considerably stronger cross-flow (R = 4), causing the flow
to deflect more strongly.  Excellent  agreement is apparent.
    Figure 6.8 shows a CORMIX1 trajectory prediction  (flow
class VI mdnf, mdff, bdff)  for a laboratory experiment by
Wright (1977).  Figure  6.8  employs a logarithmic scale  (as
used by Wright) to show the trajectory data for a vertical
buoyant jet  (R = 37 and  F0  =  67)  into a  crossflow.   The
logarithmic   scale   display   exhibits   the   different
trajectories laws (slopes in Figure 6.8, equivalent to the
exponents of the power laws) that are used in CORMIX1.  As
opposed to Fan's data,  CORMIX1  shows for this case a slight
over-prediction  (factor of  1.5)  in  the predicted vertical
rise of the flow.
6.1.1.2.3 Negatively Buoyant Jets in Crossflow

    Figure  6.9  shows  the  results  of  an  experiment  by
Anderson et al.  (1973)  for a negatively buoyant jet into a
slightly co-flowing crossflow (00  = 60  , aQ = o°,  F0 = 11.0,
and R =  5.5) .   In this case CORMIX1 predicts an NV1 flow
class (mdnf, mdff, bdff)  with numerical results that are in
good agreement with trajectory,  dilution,  and width data.
In  particular,   note  that  CORMIX1   predicts  the  flow
trajectory decreasing in  elevation in the bdff as  is typical
for negatively buoyant flows.
6.1.1.2.4 Buoyant Jets with Three-Dimensional Trajectories

    Figure  6.10  presents   Ayoub's  (1971)   buoyant  jet
experiment with a transverse horizontal  discharge in a weak
crossflow  (F0 = 15,   R = 15,   9Q =  0°,  a - 90°) .      The
                            141

-------
  a)
     z/D
                                           100
                             x/D
   b)
          	Fan (1967), Visual Boundary
           O  Dilution
           D  Width  b

          CORMIX1
          	Centerline
         	Width b
                    0.5
          100
           10
       D



                                       O''
                                       '0.5
                    10
                       100  200
                            S/D
Figure  6.6
Buoyant Jet Discharging Vertically into  Weak
Crossflow.   a)  Trajectory,   b)   width   and
dilution.
                           142

-------
    a)
          40
       z/D
          20
             0                50

                                x/D


            —-— ' Fan (1967), Visual  Boundary
             O  Dilution
             D  Width b
            CORMIX1
            --- Centerline
            --- Width b
                                   IOO
                      05
   b)
60
       D
                   1    '  '
                                      X
                                         S po
                                        o*
                                               g

                /
              /'
                          10
                                  100  200
                               s/D
Figure 6.7     Buoyant Jet Discharging Vertically into Strong
               Crossflow.  a)   Trajectory,   b)   width   and
               dilution.
                            143

-------
     10
z(m)
     10
             '   '  rl     r
           O Wright 1977 data
          - - CORMIX1 Centerline
             F0>67   R=37
Lm« 0.0664m
Lb'O.OI85m
LQ*0. 0018m
                   10
                    -2
                       10
                         -I
                                x (m)
Figure 6.8
  Buoyant  Jet Discharged Vertically  into Weak
  Crossflow (Logarithmic presentation)
                           144

-------
a)
 5r
       10
   z/D

         Did
         0
          10
20       30       40       50
    x/D
b)    100
10
   b/D
                   R»O.I8
                            o  /'
                        o ./
            S~"     A *•
                 b/D A^
                  . i . . . ,i
                       0
                             s/D
                                  Data:
                                  O A Anderson et al.
                                     (1973)
                                  CORMIX1:
                                  	Prediction
                             IOO
                        000
Figure 6.9
      Negatively Buoyant Jet Discharging Obliquely
      Upward  in  Uniform Crossflow.  a)  Trajectory,
      b) dilution and width.
                          145

-------
 0)
    z/D
          10
Data.-
  o  Ayoub (1971)
Centerline  Predictions
	CORMIX1
	 UDKHDEN
                   20      40      60

                              x/D
80
                                    IOO
 b)
         80r
         60
    y/D
                  = 30,
Figure 6.10
Three-Dimensional  Trajectory  of  Transverse
Horizontal Buoyant Jet in Weak Crossflow.
a) Side view, b) plan view.
                           146

-------
experimental  trajectory  results  are  compared  to  CORMIX1
predictions as well as to the jet integral  model  UDKHDEN
(see Muellenhoff,  et  al.  1985).    CORMIX1  predicts  an HI
flow class  (mdnf,  mdff,  bdff)  for this discharge.    The
observed transverse penetration (Figure 6.10b)  is reasonably
well predicted by  both models.   The vertical rise, solely
due to  buoyancy effects, however,  is under-predicted by both
models  (Figure 6.10a).  Unfortunately  no detailed data or
photographs  are  available  for Ayoub's  data,  but  it  is
suspected that this flow may be influenced by flume boundary
(shallowness) effects.

    Much better agreement, with both predictive models, is
obtained for a case of stronger crossflow (or alternately,
for the  same  crossflow,  a weaker buoyant jet so that the
shallowness will have less influence) .  This is shown in
Figure 6.11 for the conditions F0  = 15  and R = 5.
6.1.1.3 Buoyant Jet in Stratified Stagnant Ambient

    The effect of ambient density stratification on buoyant
jets is illustrated in Figure 6.12.  Figure 6.12a shows the
plume  boundary  for  Fan's  buoyant  jet  experiment  for  a
linearly stratified stagnant ambient.  This plot represents
a horizontal  discharge  (00  =  0°, <70  = 0°)  with  a Froude
number  F0  =  26  and  stratification parameter  T  =  1200.
CORMIX1 predicts a plume-like  flow  class  S5  (mdnf, bdnf).
Trajectory data, including  the terminal  level,  zt/D  = 76,
agree well with Fan's visual results.

    In  the absence  of  any  specified  ambient  crossflow
CORMIX1 does  not  predict  any  properties  of the  buoyant
spreading regime except the thickness of the terminal layer
of bv/D =  38  which is  in  good agreement with  the visual
data.  As  discussed in Section  2.2 this process is strongly
influenced  by the  crossflow  strength and  for  stagnant
conditions no  steady-state solution is possible.  Hence, the
layer  thickness  (shown on  the left and right  margins of
Figure 6.12a)  are not comparable to any steady-state model
predictions.  CORMIX1 however provides some results of the
near-field "boil" produced by the vertically rising plume,
such as the maximum "boil" elevation of z^/D = 116 (see Fig.
6.12a)  which  is slightly  greater  than  the visual  plume
outline.

    The effect of ambient density stratification  (T = 1200)
on a stronger jet (F0  = 51)  discharging near-vertically (8Q
= 45°, a« = 0°) is shown in Figure 6.12b.   CORMIX1 predicts
a jet-like flow class S3 (mdnf, mdls-v)  and its trajectory
data agree well with Fan's  results.  The predicted terminal
level, zt/D &  43, the maximum elevation of rise z^D = 43,
and the width b/D  = 44 at  the  terminal level are  all   in
                            147

-------
 a)
    z/D
         80
         60
         40
         20
Data:
  o  Ayoub (1971)
Centerline  Predictions
	CORMIX1
	 UDKHDEN
                                                   IOO
b)
   y/D
         80
         60
        40
 F0 -• 15 ,  R = 5
 V0°.  
-------
  a)     '20
    z/D
                               100
               Fan, 1967, Visual Boundary
               CORMIX1  Centerline
               Width b
                           x/D
200
 b)
        80
    z/D
        40
                                              , T = 2IO
                          0=45°
                               IOO
                                            j	I
                           x/D
200
Figure 6.12
Buoyant Jet Trajectory in Stratified Stagnant
Ambient, a) Horizontal discharge, b)  oblique
discharge.
                          149

-------
agreement with Fan's visual results.


6.1.2 Comparison of Predictions with Jet Integral Models

    Because experimental data  on  buoyant  jets is limited,
this section presents CORMIX1 predictions in comparison with
some  common  jet  integral  models.    Several such  model
formulations exist and  have been extensively tested against
various data sources (Muellenhoff  et al. 1985, Wong, 1984).
Of course, such integral models are limited to buoyant jet
flows in unconfined  ambients and cannot address any boundary
interaction.
6.1.2.1 Buoyant Jet in Uniform Crossflow

    Figure 6.13 presents a  comparison  of CORMIX1 with the
integral jet models  by Jirka and Fong  (1981)  and UDKHDEN
(Muellenhoff,  1985).    Model  predictions for  trajectory
(Figure 6.13a)  and dilution (Figure 6.13b) are given for ao
buoyant jet (F0 -  10)  in a  crossflow (R = 10)  with 00 =  90°
and 0Q = 0°.   The trajectory relationships for  the three
models appear to be in general agreement, with CORMIX1 and
UDKHDEN predicting a  stronger  bending by  the crossflow than
the model  of Jirka and  Fong.   CORMIX1  predicts  the most
conservative dilution values  of the three models as shown
in Figure 6.13b.  It  should  be noted that the bulk dilution
values from  UDKHDEN  were adjusted  by  dividing by  1.7  to
represent centerline  dilution as  shown  for the  other two
models.

    Another comparison with the jet model UDKHDEN already
has been  included in  Figures  6.10  and  6.11  as  discussed
earlier.
6.1.2.2 Buoyant Jet in Stratified Crossflow

    Figure  6.14  illustrates  the effect  of  a  stratified
crossflow on buoyant jet behavior for the three previously
discussed  models.    No  fully  documented  experiments  are
reported  in the literature  for this  flow configuration.
Figure 6.14 represents the effect of a strong crossflow  (R
= 3.0) with a  mild density stratification (T = 1000) on a
weakly buoyant jet (F0  =  40) .  CORMIX1 predicts a crossflow
dominated flow class SI (mdnf, mdff) with  a terminal height
of  zt/D =30 which is obtained at a downstream distance x/D
=  1210  as seen   in  Figure  6.14a.    In  this  case,  the
trajectory  and stratified terminal height  of  CORMIX1  are  in
good  agreement  with  the  integral models,   with  CORMIX1
predicting  the highest  terminal  level and the model  of Jirka
                            150

-------
      a)
         z/D
10
                                	CORMIX1
                                	Jirka 8 Fonq,l98l
                                	UDKHOEN
           20    30
                X/D
                                     40    50    60
      b)    ioo
            80
            60
            40
            20
                    20    40    60    80    100
                               x/D
                                  120
Figure 6.13
Comparison   of   CORMIX1   Predictions   with
Integral   Buoyant  Jet   Models   in   Uniform
Crossflow
                           151

-------
     a)
       z/D
                                                       Terminal
                                                       levels
10-
                                        CORMIX1
                                        Jirko S Fong, I98I
                                        UDKHOEN
                  FQ = 40
                                                 IOOO
                          500
                              1000
                              x/D
    b)    200 -
                           500
                              IOOO
                               x/D
Figure  6.14    comparison   of   CORMIX1   Predictions   with
               Integral  Buoyant Jet  Models  in  Stratified
               Crossflow
                           152

-------
and Fong the lowest, zt/D  =  26 at x/D - 1350.  Figure 6.14b
shows again that CORMIX1 predicts the most conservative
centerline dilutions, with a difference of about 50% among
the three models.
6.2 Complex Flows With Boundary Interaction

    This section  is  intended  to  illustrate the ability of
CORMIX1 to correctly classify and predict flow dynamics in
the presence of various boundary interaction processes.
6.2.1 Jet Flows in Shallow Receiving Waters

    Figure 6.15 presents the laboratory data of Abdelwahed
and Chu (1978)  for vertical discharges into shallow uniform
crossflow.  Figure 6.15a and 6.15b show a pure jet (F0 = «)
in weak crossflow  (R = 12, Test 2001) and strong crossflow
(R = 6, Test 2004), respectively.  CORMIX1 predicts a flow
class V2 (mdnf,  mdff,  surface approach, passive mixing) for
both cases where the subsurface regions are limited and the
surface passive mixing occurs  shortly downstream  of the
discharge.   Passive surface plume dimensions  are in good
agreement  with  visual  plume  outlines  for  both  of  these
nonbuoyant cases.  Figure 6.15c illustrates the additional
influence  of  buoyant  surface  spreading for  a  buoyant
discharge  in  strong crossflow  (F0 = 12,  R =  6).   CORMIX1
predicts a flow class V2 but with a buoyant spreading region
before passive mixing occurs.   Again the plume prediction
agrees well with  the  visual surface  plume boundary.   This
documents  the  importance  of  including  both  far-field
processes, namely buoyant spreading and passive diffusion,
in a predictive methodology.
6.2.2 Strongly Buoyant Jets in Shallow Receiving Waters

    Fischer et  al.  (1979)  present field data  for the San
Onofre nuclear power plant.  The San Onofre Unit 1 discharge
is a thermal discharge from a 4.3 m diameter outfall located
5.5  m below  the  surface  in  9.6  m  deep  water off  the
California  coast.   The  temperature difference between the
ambient current and the discharge  is 11.1°C giving rise to
a buoyant acceleration of g'0 = 0.032 m2/s.  CORMIX1 predicts
a flow class  of V5, which represents  an  stable discharge
with  buoyant  upstream  intrusion  and  subsequent  buoyant
surface spreading as the plume travels downstream.

    Figure  6.16a  shows  the CORMIX1 results  compared with
actual field results obtained  from a tracing of an infrared
picture  of the  actual  plume.    Two   different  crossflow
velocities were used to account for possible  variation in


                           153

-------
  a)
         -20H
                       = 7.62cm
                                        100	x(cm)
                                        R = I2
  b)
y (cm)
   20
	 Visual  boundary
     Abdelwohed  and Chu (1978)
	CORMIX1, width b
                     Lm = 2.l6 cm
                     Lb = 0cm
                        = 2.l6 cm
                     Lb=0.48 cm
Figure 6.15
       Vertical Jet Discharge into Shallow Crossflow,
       Plan view of plumes at water surface.
                           154

-------
                   CORMIX1 width b
                   	ua=0.2 m/s
                   	un = 0.25m/s
        z(m)4
          IO--
!!
L^
5
L- 	
Cl^"*
I -^—Discharge
D = 4.3m
50=25.2
00""""* 0 ™ 1 00
"S~n J^^ ' — "•" ' TTn* * *™*™"
m3/s
i i i
200 300 400
i — -
x (m)
Figure 6.16
Cooling Water Outfall from San Onofre Nuclear
Power Plant (Unit 1) . a) Comparison of CORMIX1
prediction  for  surface plume,  b) predicted
subsurface flow pattern (side view).
                         155

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the ambient data and  to  illustrate  the sensitivity of the
model.  For a crossflow velocity of 0.2  m/s CORMIX1 predicts
a buoyant upstream intrusion of 42 m with a flow half-width
of 110 m at surface impingement.  Using the slightly higher
crossflow velocity of 0.25 m/s, as reported by Fischer et.
al., CORMIX1 predicts a smaller buoyant upstream intrusion
of  22  m  with  a  flow  half-width  of  56  m  at  surface
impingement.   The field data indicate an upstream intrusion
and half-width at surface impingement of about 30 m and 85
m,  respectively.    Overall  CORMIX1  agrees  well with the
photographic surface data.

    No  field  data  are available for the  sub-surface flow
region as well as for the induced temperature field.  Figure
6.16b  illustrates  model  predictions from CORMIX1  for the
discharge cross-section for  the two ambient velocities.  The
upstream  intrusion  and gradual thinning in  the downstream
direction  due to buoyant  spreading  is  demonstrated and is
consistent  with   the  information   from the  plan  view
photograph.
6.2.3 Flows with Wake Interaction

    A discharge operating  in  a strong crossflow can cause
wake attachment.   CORMIX1  was applied to data for cooling
tower experiments  from Viollet  (1979); as reported by EPRI
(1981) and illustrated  in  Figure  6.17.   Dilution data are
also included in Figure  6.17,  as indicated by concentration
isolines.  Figure  6.17a represents an unattached flow with
a strong buoyancy  (F0 =  0.8)  and weak crossflow (R = 2.0).
CORMIX1  predicts  an  unattached  flow  class  VI.    The
experimental data show slightly stronger  deflection than is
indicated  by the  CORMIX1  prediction.   The concentration
decay CC/CQ along the centerline of the CORMIX1 predictions
(indicated by  arrows)  is  in  excellent agreement  with the
experimental contour values C/CQ.

    The effect of  a much stronger crossflow is illustrated
in Figure  6.17b with  F0 =  0.8  and  R  = 0.33.  Here CORMIX1
predicts an attached flow  class V1A1  (wake recirculation).
This is in agreement to the attachment of the experimental
cooling tower plume indicated  in Figure 6.17b.  CORMIX1 also
predicts   the  plume  will  contain   enough  buoyancy  to
subsequently lift-off from the ground  at x/D =6.4.  However
experimental  data  further downwind  are  not  available to
fully verify this aspect.   The concentration predictions of
CORMIX1  are   in  satisfactory  agreement  with  the contour
values for this complicated flow process.
                            156

-------
  a)
     z/D
                              10
                  Viollet, 1977 Centerline
                  Isoconcentration c/c0
                  CORMIX1  Centerline
                  Width b
                               20    x/D
  b)
     z/D
                                      F0=0.8   R = 0.33
                              0.045
                                 -0.03
                        -^ V   10
                  Wake     XLift-off
                recircuiation
                               20    x/D
Figure  6.17
Strongly  Buoyant Plume  in Crossflow,  a)  Weak
crossflow  without   attachment,   b)   strong
crossflow with wake attachment.
                            157

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6.2.4 Negatively Buoyant Flows With Upstream Spreading Along
Bottom

    The CORMIX1 prediction  for the bottom  interaction of
negatively  buoyant  flows  is  shown  in  Figure  6.18  in
comparison with the laboratory data of Tong and Stolzenbach
(1979). This implies a flow class NV2, and CORMIX1 predicts
bottom contact at  x =  0.45 m,  an upstream intrusion of 0.02
m and an intrusion thickness of 0.10 m,  which is less than
the  visual  data  indicate.    The  predicted  trajectory
prediction tends to deflect somewhat less in the direction
of  the crossflow  than  the  visual  data  indicate.    The
experiments conducted  in a laboratory flume of limited width
may exaggerate the extent of the bottom upstream intrusion
for two reasons:  First,  due to the sidewalls there is less
freedom for lateral spreading and therefore more upstream
intrusion.  Secondly,  due to the viscous boundary layer in
the   ambient   approach-flow  there  is   less   resistance
(stagnation  pressure)  to  the  intrusion  flow.   For  the
analysis the  ambient velocity was adjusted  upward to 0.08
m/s from the reported mean velocity of 0.07 m/s to account
for  the contraction  of   the  ambient flow  caused by  the
presence of the density current in the laboratory channel.
The  important  conclusion is  that  CORMIX1  recognizes this
complicated interaction process  with  a  negatively buoyant
plume and upstream bottom buoyant spreading.


6.3 Summary and Appraisal

    Seen as  a  whole,  the preceding data/model comparisons
indicate that CORMIX1  is  a satisfactory modeling system for
the mixing prediction of aqueous single port discharges in
diverse conditions.  CORMIX1  appears to be i)  reliable and
ii) accurate.

    i) The system's reliability seems rooted in its robust
classification   scheme   that   determines   which   flow
configuration  (class)  will occur for a  given discharge/
environmental  situation  before the appropriate simulation
model is executed.

    ii) The overall accuracy  of the system is of the order
of ±50% for the spatial definition of the flow zones (e.g.
trajectories,  width,   etc.)  and  for  tracer  (pollutant)
concentration.  Given the broad  range  of flow conditions
this  accuracy level for  a  comprehensive,  non-specialized
model   appears  fully  acceptable   from   an   engineering
standpoint.    As   usual,  any lack  of   accuracy  in  such
comparisons has to viewed in  the perspective  of turbulent
mixing  processes   with  their intrinsic  fluctuations  and
unsteadiness.  Variations can also be caused by disturbing
influences in experiments or field conditions;  e.g. a shear


                            158

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 z (cm)'

    60
    40
    20
     0
           U0-6.93 cm/sec
                                          F0=I77
                                          R = 144
                    CORMIX1 Centerline
                    Width b
                    long S  Stolzenbach, 1979
                    Visual Boundary
20          40
      x (cm)
                                              60
Figure  6.18   Interaction  of Negatively  Buoyant  Jet  with
               Bottom Boundary
                             159

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flow instead of a uniform mean flow, and by different data
interpretation   and   analysis   techniques  employed   by
researchers.

    Emphasis has been placed  in  the data/model comparison
on the  near-field  mixing characteristics  of the effluent
discharge, with comparatively  less attention to the passive
far-field mixing.  This emphasis is of course motivated by
the intended primary use of CORMIX1 as a predictive tool for
mixing zone analysis.  Another reason, however, is the fact
that  far-field  mixing   processes   are   reasonably  well
understood.  The CORMIX1  far-field modules  rely on standard
plume models of the passive ambient diffusions processes (as
discussed in Section  2.3)  and  the numerical values are well
established  (see Fischer,  et  al.,  1979, Holley  and Jirka
1986).

    For many of the flow  classes  that can  be predicted by
CORMIX1, actual field  or  laboratory  data are quite limited.
One  of  the  continuing  goals of  CORMIX1  is  to  update,
enhance,  and validate the  knowledge base  and predictive
capability  of  the system as  more  information  becomes
available.
                            160

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                        Chapter VII

                  Applications of  CORMIX1
    The purpose of this  chapter  is  twofold:  i)  to give an
overview  of  the  typical  steps  of CORMIX1  application,
including data input,  in discharge  design and mixing zone
evaluation, and ii) to illustrate the flexibility of CORMIX1
using three hypothetical  examples of highly divergent design
or  environmental  conditions.     The   first  case  study
represents a small toxic industrial discharge into a river
(Section 7.1), the second is  a toxic discharge into coastal
waters illustrating the  effects  of density stratification
(Section 7.2), and the third is  a cooling water discharge
into the  ocean under different  ambient  currents  (Section
7.3) .
7.1 AB Chemical Company

    This  example  illustrates  a  buoyant  discharge  in  a
bounded riverine section.  The discharge flow represents a
complex three-dimensional trajectory subject to three legal
mixing  criteria;  a  toxic  dilution zone,  a  plume width
criterion on a legal mixing zone defined by  existing channel
width, and  a downstream region of  interest.   The analyst
seeks pollutant  concentrations at  these  locations.   The
analyst will  use CORMIX1 to potentially improve dilution
characteristics of the discharge by altering the discharge
angles of the outfall design.
7.1.1 The Problem Statement

    AB  Chemical Company  discharges  a heated  industrial
effluent  into  the  Ohio  River  through  a  submerged  pipe
outfall. The discharge flow is 0.053 m3/s and contains 500
Mg/1 of  a  toxic substance.   The material  has a criterion
maximum concentration  (CMC) value  of  25  M
-------
    The outfall is located 55 m from the berm line near the
left bank. The right bank is under the jurisdiction of the
State  of Ohio.    The  initial  design proposed for  this
discharge is  as  follows:  The port  is pointing  directly
offshore  (normal  to  the  ambient  flow)   and is  directed
horizontally along the  bottom  (00 = 0°) .  The round port has
a diameter  of  15  cm and  its  center  lies 0.4 m above the
river bottom (see Figure 7.1).

    The  mixing zone  limitations  of  the State  of  West
Virginia have to be considered.  For  this case  the mixing
zone will be assumed to have a maximum width value equal to
10%  of  the  river  width,  and the  dilution values  3000  m
downstream from the discharge point are of interest because
of an intake to a public water supply on the Ohio shore.
This will be labeled design case No.  1.
7.1.2 CORMIXl Analysis

Design Case No. 1:

    The  first  step in the  analysis  is to  schematize the
bounded cross-section as shown in Figure 7.1.  Stream cross-
sections  are  usually  highly  irregular;  the  trapezoidal
cross-section  represents  an initial approximation  of the
actual stream cross-section. CORMIXl assumes an equivalent
rectangular cross-section as shown  in Figure 7.1, which the
analyst would approximate.  Using DATIN,  the site parameters
are specified.

    An advantage to logic  programming is in error handling.
It is simple to write rules  that reject contradictory data.
For  example,  when schematized  as a  rectangular  cross-
section, the schematized  stream width  is  262.75 m and the
distance to  the  nearest  bank (W.  Va.)  is 37.5  m.   If the
user made an error and responded that  the distance to the
nearest  bank  (West  Virginia)  was  225.25  m,  i.e.  the
complement value, DATIN would respond:

    The distance to nearest bank is in error.
    The  value  must  be  less than  half the  stream width.
    Recheck and re-enter a value less than or equal
    to 131.375  (m).                                   [1]

and the  user  is  given another  chance  to enter the correct
value of 37.5 m.

    After  completing DATIN,  the  system executes  PARAM,
followed by  CLASS.  In CLASS the  analyst is  advised of the
intermediate  conclusions  reached;   i.e.  the  discharge  is
positively buoyant.  CORMIXl assigns a flow class  H1A3 to


                            162

-------
        Cross-section View

           55m
W.Vo.
                                                    Ohio
                           230m
        Plan  View
262.

37.5m
t
ua=0
t t t
75m
.3m/s
t f

1
                          0=0.15
                                 0.4m
                   Detail  of  Discharge
            Schematization  of  Cross-section
Figure  7.1
             AB Chemical Company: Schematization of Cross-
             Section at the Discharge site
                              163

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the discharge indicating a Coanda attached jet with buoyant
lift-off  (attached wall  jet,  lift-off,  strongly deflected
plume (bdff), surface approach, buoyant surface spreading,
passive diffusion).

    After the program element  HYDRO  executes,  the program
element SUM summarizes  the  hydrodynamic simulation output
for the design case.   The results are shown in Figure 7.2.
Figure 7.2a gives  a longitudinal side view of the near-field
and surface interaction.  Figure 7.2b  gives  the detail of
the near-field  attachment  looking  downstream in  the z-y
plane.  The buoyancy of the discharge causes lift-off at x
= 2.5 m downstream.   SUM  notifies the  user  that surface
interaction and thus the limit of  the  hydrodynamic mixing
zone  (HMZ),  a  region of strong  initial discharge induced
mixing  (but of no legal significance),  occur at  x = 117 m
downstream from the discharge point where the dilution value
is  S  =  620  and the   plume  half-width  bh  and  vertical
thickness b%,  are both =  7.4  m.
           V
    The  toxic  dilution  zone  (TDZ),   where  the  tracer
concentration falls below the CMC  value,  occurs  at x & 13
m in the submerged plume  region  (bdff).  SUM concludes that
the  criterion  maximum concentration  (CMC)  value  for the
toxic discharge does not meet all legal restrictions.  SUM
notifies the user on the  criteria checked  for a TDZ; i) the
discharge velocity was equal to  or  greater than the minimum
value of 3.0 m/s,  ii) the downstream distance of the TDZ (13
m) exceeded the maximum distance of 50 times the discharge
length scale 1^ = 0.13 m, i.e.  6.5  m,  iii)  the downstream
distance of  the  TDZ was  less than  the  maximum distance of
5  times  the  water depth  of 12 m, and  finally  iv)  the
downstream distance of the TDZ was  less than the maximum of
10% of the distance to the LMZ.  Thus SUM  notifies the user
that the discharge did not meet criterion (ii)  for the toxic
dilution zone.  For this reason an alternative design case
No. 2 will be evaluated.

Design Case No. 2:

     Using the expert advice given by SUM an  attempt is made
to  avoid  the  Coanda  attachment  of  the  discharge  by
increasing  the  vertical  angle of the  discharge.    If
attachment is averted, improvements in dilution within the
near-field  - and thus the  TDZ  -  may be  possible.   These
design changes will also illustrate the sensitivity of the
model and  flow  classification wheno the vertical discharge
angle is changed  from 9Q  = 0° to 30° (aQ =  270°) .

    Using  the  new discharge  orientation  CORMIX1  indeed
assigns an unattached flow class HI to the discharge  (mdnf,
mdff, bdff,  surface approach,  buoyant  surface spreading,
passive mixing)   indicating  the   increase   in   vertical


                            164

-------
    z(m)
                                                           HMZ.
                                                           Limit
                                               Surface approach  |
                                                  Begining of
                                                  buoyant
                                                  spreading—

         "Lift-off
                             50
00
x(m)
            a) Longitudinal  Side  View  (distorted scale)
   z(m)
\ (-»-TDZ Limit
        x
            b) Vertical  View  Looking Downstream (undistorted)
Figure 7.2     AB Chemical Co. Design Case No. 1:  Predictions
                 (bottom attached jet)
                              165

-------
discharge angle to 30° avoids Coanda attachment.   A close-
up of the near field of the discharge appears in Figure 7.3.
This should be  compared  to the attached case  as  shown in
Figure 7.2b.

    SUM  indicates  the hydrodynamic  mixing zone  (HMZ)  is
limited to the surface contact at  x a 108 m downstream from
the discharge point with  dilution  value S a 594.  The plume
half-width  bh  and  thickness  b  are  both  a   7.2  m,
demonstrating that  altering  the discharge angles  did not
significantly improve  mixing characteristics  in  the HMZ.
In this case, only a small decrease in HMZ size and dilution
is apparent.

    The  TDZ,  however,  shows  a marked improvement  of the
unattached  case.   The CMC value  of 25  ^g/l  is met  at a
downstream distance x =  6.1  m from  the  discharge point in
the mdff  region.  Thus a shorter  downstream  distance than
for the previous attached  case is required to achieve the
CMC  value.    Because  of  this,  SUM concludes  that  the
criterion maximum concentration  (CMC) value  for  the toxic
discharge now does meet all legal restrictions.

    The overall plume shape,  extending into the far-field,
for this design  case is shown in Figure 7.4.  The transition
from  buoyant  surface  spreading  plume  to passive  mixing
occurs at x a 835 m.   The  plume contacts the left bank in
the passive mixing region at  x a 1211 m downstream from the
discharge point,  where the plume also  becomes vertically
fully mixed over the water depth  (bv = 12  m)  m.

    At the  position of the public water supply located on
the Ohio  shore 3000 m downstream  from the discharge point,
the dilution value in the surface buoyant spreading region
is S  a  6763,  and the plume half-width  is  bh  =  97  m  (bank
attached to left shoreline).   The  plume is vertically fully
mixed (bv =  12 m) .   Therefore,  the plume does not influence
the water supply intake.

    The plume meets the legal mixing zone  (LMZ) criteria of
10%  of  the  stream  width at  x  =  199 m downstream  of the
discharge in the buoyant surface  spreading region, where S
= 582.  At this point the plume thickness is  bv = 4.5m and
the plume half-width is bh =  14 m.

    In summary,  this example  illustrates  that  the effect of
altering discharge angles on  mixing is often limited to the
immediate near-field  of  the  discharge.   Plume attachments
to the bottom should  be  avoided to insure rapid mixing in
the  near-field  of the  discharge.   This is  especially
important  for  toxic  dilution  zones.    However,  altering
discharge angles may have a limited  effect  on overall plume
                            166

-------
                                  00=30°  cr0=270°
                                              -10  y(m)
                 mdnf  mdff \
                 region  region  \-TDZ  limit
Figure 7.3    AB Chemical  Co.  Design Case No.  2:  Close-up
              View of Unattached Buoyant Jet Near Discharge
                           167

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           0
          IGOOV      2000        3000
                 Bottom Attachment

   a) Longitudinal  Side View  (distorted)
                                          .(m)
       y (m) /


        100

       —*»•
       Ja  0


        -100


       -200
'LMZ Limit1
               Bonk Attachment
               /        W Va.
-I Region
                                 Ohio
                b)  Plan  View (distorted)
                                   X   ww'"
                                Water Supply
                                  Intake
Figure 7.4     AB  Chemical  Co.  Design Case No.   2:  Overall
                Appearance of Discharge Plume
                              168

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mixing  behavior,  especially  in  the  far-field at  large
downstream distances from the source.
7.2 MM Municipal Treatment Plant

    In this  hypothetical example a  mid-size municipality
(about  100,000  inhabitants)  is  discharging  its  treated
effluent  into  adjacent  costal  waters.    A  local  metal
processing plant  is  proposing to dispose  its  brine waste
water containing toxic materials combined with the municipal
effluent.  This buoyant discharge is subject to  three mixing
criteria: a toxic dilution  zone,  a plume width  criterion on
the legal mixing zone, and  a downstream region  of interest.
The analyst will use  CORMIX1 to study the effect of typical
winter and  summer ambient  density profiles  on the mixing
behavior of the discharge.
7.2.1 The Problem Statement

    Typical winter and  summer  profiles  have been measured
in the discharge  area  and are shown in  Figure  7.5a.   The
discharge is  to be located  2000  m from shore  at  a local
water  depth   of   24.4  m.  The   bathymetry  is  sloping
approximately linearly from the shoreline.

    The discharge port  is round with a  diameter of 0.5 m
and extends about 0.5  m above  the surrounding bottom with
the  vertical   angle  6Q  =  30°  in  the   direction  of  the
prevailing ambient current (co-flow, a0 =  0°) which is of the
order of  0.25  m/s.   The  design discharge  flowrate is 0.6
m3/s  and contains 100  ^9/1  of a  toxic  metallic substance
with  a  CMC of  10 ^g/1-   The  discharge density  for the
mixture of municipal effluent and industrial brine is 1015
kg/m3.   A public beach is located 2000 m down-current from
the discharge point, so that plume characteristics at this
distance are of interest.
7.2.2 CORMIX1 Analysis

    The first step in the  analysis  would be to choose one
of the four ambient stratification types as seen in Figure
5.3 to represent the actual density profiles .   An ambient
profile of  (Stratification Type  C,  Figure 7.5b)  is chosen
to represent  the August data,  with surface density ps  =
1022.6 kg/m5,  bottom  density  pb = 1024.4  kg/m3,  and ambient
density jump Ap  =0.83  kg/m at the stratified layer height
Hs =  12.61 m.  The schematized cross-section in this case of
a  linearly  sloping  bottom would assume would  place the
discharge 1000 m from "shore" in 24.4  m of water.   A weak
linear ambient density stratification  (Stratification Type


                           169

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^^^
£

IM
j£
"5.

\
b
V
\
o
\_
^
i i i
o
1
i
0
i
i
H
o
I
i
o
i
i
0
I
i
O
i
n
Figure 7.5
               1,022     1,024     1,026

                   Density (kg/m3)

                 b) CORMIX1  Representation
MN Treatment Plant:  Typical Density Profiles
for Summer and Winter  Conditions
                            170

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A, Figure 7.5b) is chosen to represent the March data, with
surface density ps = 1025.6 kg/m , bottom density pb = 1025.7
kg/m3,  and the stratified layer height Hs equal to the full
discharge depth of 24.4 m.

Summer Design Case;

    For the August design conditions, CORMIX1 concludes the
flow will  be confined to  the lower density layer  by the
ambient density jump  at  the pycnocline  and assigns a flow
class H2  (mdnf, mdff, surface approach,  buoyant spreading,
passive diffusion).   The simulation results are  shown in
Figures  7.6  and  7.7.   SUM  notifies  the  user that the
hydrodynamic mixing zone  (HMZ)  occurs at x a  54 m downstream
from the discharge point with plume centerline height z a
12.6m (indicating a submerged plume trapped by the
pycnocline density jump), the dilution value is S s 39, and
the plume half-width bh and thickness bv are both % 5.8 m.

    The CMC (Figure 7.6)  value occurs at x s  16.4 m from the
discharge point in the mdff.  SUM notifies the user that all
criteria checked for the TDZ are satisfied.

    The far-field behavior of the internally trapped plume
is shown in Figure 7.7.   The plume is still  in the internal
buoyant spreading regime.  A very thin,  but wide,  layer of
mixed effluent flow arises.

    The legal mixing zone  (LMZ, Figure 7.7)  width of 200 m
occurs in the subsurface  buoyant spreading region at x a 784
m from the discharge point with a dilution S =  76.   At the
LMZ the flow is at the pycnocline height  z =  12.6 m and not
bank attached, with plume  half-width bh =  100  m and plume
depth bv  «  0.9 m.

    At 2000 m from the outfall,  the plume dilution is S ^
910, and the  flow half-width  bh and thickness bv are a 196
m and 0.55 m, respectively.  This indicates the subsurface
buoyant  spreading  region  still  does  not  contact  the
shoreline near the public beach.

Winter Design Case:

    For the March design conditions, CORMIX1 concludes the
linear ambient density stratification is  too weak  to trap
the flow,  and a uniform ambient density is set equal to the
depth average value of 1025.6  kg/m3.  CLASS assigns a flow
class  HI   (mdnf,  mdff,  bdff,  surface  approach,  buoyant
spreading, passive diffusion)  for the full water depth.  It
should be noted that the flow is classified as HI (instead
of H2 as  in the previous  example) because within the deeper
layer the  flow will  develop a bdff  region  before  surface
contact.   The simulation results  for the near  field  are
                            171

-------
                     z(m)
                              ix
JDZ Limit  ,  HMZ Limit
                                Pycnocline Interaction


                                          Buoyant Spreodingj
                    a)  Side  View (distorted)
                     y(m)
       ua=0.25m/s
                      -20-
                    b) Plan  View  (undistorted)
Figure 7.6     MN  Treatment  Plant  Summer   Design   Case:
                Internal Flow Trapping Caused  by Pycnocline
                Density Jump
                              172

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z(m>4  ^xHMZ Limit
                               LMZ Limit
       20r[—*• Buoyant Ambient  Spreading
                                 '
500 ' ~^   1000  	   1500

  a)  Side View (distorted)
         0
                                                 2000   x(m)
     1000
        0
    -1000
               Buoyant Ambient Spreading
                     b)  Plan View (distorted)
                                                      Public Beach
                                                      2000  x(m)
Figure  7.7     MN Treatment  Plant Summer Design Case:  Far-
                Field Behavior of  Internally Trapped Flow
                              173

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shown in Figure 7.8.

    The hydrodynamic  mixing  zone (HMZ) occurs  at surface
contact at x * 81 m downstream from the  discharge point with
plume centerline height z = 24.4 m,   dilution S as 149, and
plume  half-width  bh  and  thickness  by  both  a  13.3  m,
indicating slightly greater  HMZ  dimensions  and associated
dilutions than the strongly stratified August design.

    For the March design the legal mixing zone (LMZ) width
of 200 m occurs in the surface buoyant spreading region at
x a 753 m  from  the discharge point  with  a larger dilution
S = 248.  At the LMZ the surface flow does not contact the
shoreline, with plume half-width bh & 102 m and plume depth
bv = 2.9 m.

    The CMC value  occurs at  x  = 16 m from  the discharge
point, again indicating that  all criteria  for  the TDZ are
met for this discharge design condition.

    In summary,  this example  illustrates the flexibility of
CORMIX1 in predicting  flow behavior in density stratified
environments,  where  plume  trapping by the  pycnocline may
inhibit dilution.
7.3 PQ Power Company

    This design example  represents  an ocean cooling water
outfall  from  a   small   steam-electric  power  plant  in
relatively shallow water and varying ambient tidal currents
with weak ambient  density stratification.  There is no legal
mixing zone  under consideration for  this  discharge.   But
because the  cooling water intake structure  for the power
plant is located on the shoreline  1000 m from the discharge
point, the behavior of the heated  effluent  over  this region
is sought.
7.3.1 The Problem Statement

    The outfall is located 300 m offshore at a local water
depth  of   5.0  m.   The   bathymetry  is  given  by  a  an
approximately  flat  shelf region.    Available  site  data
indicate a  linear ambient density  profile  with  a osurface
temperature of 18° C and  a bottom temperature of  15° C.

    The outfall port is round with a diameter of 1.0 m which
extends  about 0.5  m above the  surrounding bottom.   The
cooling water is discharged vertically at a  flowrate of 3.0
m3/s.    The design  discharge  temperature is  30° C.   The
discharge site  is characterized  by varying tidal currents
between 0.2 m/s and  0.8 m/s.
                            174

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            z(m)
             Surface Interaction Region
      _2	.	_*_
                                               Buoyant Sui face Spreading
            y(m)1


             20



              0



            -20
                    a)  Side  View (distorted)
        -TDZ  Limit


        Surface Plume
I    I
                   b)  Plan  View (undistorted)
Figure 7.8
MN Treatment Plant Winter Design  Case:  Plume
Surface Interaction
                                 175

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7.3.2 CORHIXl Analysis

Low Current Case:

    For the minimum ambient current speed of ua = 0.2 m/s,
CORMIX1  concludes linear  ambient density  stratification
resulting  from  the  difference  in  surface  and  bottom
temperatures is  weak and dynamically unimportant.   CLASS
assigns a  flow class V5 (mdnf, bdnf,  surface  impingement
with  upstream  spreading, buoyant surface  spreading,  and
passive mixing).   The simulation results are  shown in Figure
7.9.

    CORMIX1 indicates an upstream intrusion length of x =
66 m with  the  intrusion  layer  maximum thickness of 4.34 m
at  the leading  front  (stagnation point).     The  buoyant
intrusion rapidly collapses  into a wide and shallow density
current.  At the edge of the HMZ the density current has a
half-width bh of  173  m and a thickness bv of only 0.15 m.

    Farther downstream  in  the  far-field, the  dilution is
still limited to S =  3.5  at  x a  lOOO m  (not shown in Figure
7.9) from  the  outfall where the buoyant surface spreading
plume  half-width  bh  and  thickness by =  189  m  and  0.14 m,
respectively,   indicating  very  little  mixing under  a low
ambient  crossflow.    The plume would  not   influence the
cooling water  intake under these conditions.

    Note that  CORMIX1 does not  include any decay processes
in the effluent.  In practice, the heated effluent in this
design case would undergo surface heat exchange processes
which  would be reasonably  strong due the small degree of
mixing.   A discussion  of  the adaptation  of  CORMIX1  to
include such decay is given in Section 7.4.4.

High Current Case;

    For the maximum ambient current speed of ua = 0.8 m/s,
CORMIX1 concludes that the weak linear ambient density
stratification is again unimportant.  CLASS assigns a flow
class  V4   (mdnf,  boundary  impingement with  full  vertical
mixing; buoyant surface spreading, and passive mixing). The
simulation results are shown for  the near-field in Figure
7.10, indicating that the stronger ambient current prevents
buoyant  upstream intrusion, and  an unstable  mixing zone
occurs around  the discharge.  The plume makes a transition
from buoyant surface spreading to  passive mixing at x  = 703
m from the outfall (not shown in Figure 7.10).   However, the
stratified passively mixing  plume only slowly approaches the
shoreline.   At  1000  m downstream from the  outfall, the
dilution is still limited to S = 34 and the plume half-width
bh a 40.5 m and the thickness bv *  1.5 m.    Thus,  one can
                            176

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              50
0
                      a)  Side View (distorted)
                         y (m),
                         200-
                          100
                Buoyant Upstream
                   Spreading \
                            x
          'Stagnation
           Point
                        -200
                     b) Plan  View (distorted)
Figure 7.9     PQ Cooling Water Outfall in Low Current Design
                Case: Near-Field Plume Behavior
                                177

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     Unstable Recirculation
           Zone
                                                       150   x(m)
                       a)  Side  View (distorted)
                       b)  Plan  View (undistorted)
Figure 7.10    PQ Cooling Water Outfall High Current Design
                Case: Near-Field Plume Behavior
                               178

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conclude the  cooling water intake would  not experience a
temperature rise due to heated discharge re-entrainment.

    In conclusion,  this example  illustrates that ambient
current can have a  significant  effect on discharge mixing
and plume  behavior,  especially on discharges  with strong
buoyancy  dominated  boundary  interaction and  subsequent
buoyant  spreading.    Because  of  the  normal variation in
natural   systems,    the   analyst  should   study   plume
characteristics  under  a  range  of ambient  environmental
conditions.

    In all three  of the  previous examples,  the buoyant
spreading region extends to large  distances downstream  from
the outfall.  Discharge buoyancy tends to stabilize the
plume  in  the  far-field  and  prevents  the  transition to
passive  ambient  mixing,   which  in   general,   is  a  more
efficient  mixing mechanism.   Toxic dilution zone criteria
may be most restrictive and occur in the near-field in the
vicinity of the discharge.  The legal mixing zone commonly
occurs in  the far-field in either the buoyant spreading or
passive mixing region.
7.4 Comments on the Application of CORMIX1

    As mentioned in Chapter IV it is expected that CORMIX1
will  be a  general  predictive  system  applicable to  the
majority  (better  than  95%)  of  submerged  single  port
discharge/environmental  conditions.     It  is  impossible,
however,  to  devise   a   system   that  will   analyze  all
conceivable submerged discharges.  For this reason, CORMIX1
intentionally    contains    several    internal    criteria
(limitations)  designed to  avoid  system  misuse  for such
extreme conditions.   These limitations are  summarized in
Section 7.4.1.   However, an experienced  user can modify the
data  input  to  allow  for  CORMIX1  analysis  for  conditions
(e.g. near-surface discharges) that  are seemingly outside
the normal range of  system applicability.   Hints for such
system application are given in Section 7.4.2
7.4.1  Limitations of CORMIX1

    CORMIX1 is devised for submerged single port discharges
in water of variable depth H (see Figure 7.11).  Thus the
discharge is assumed to be located  near the bottom of the
water body.  CORMIX1  uses the  applicability criterion for
the height of the discharge port hQ

    h0 <  0.33H                                         (7.1)
Eg. (7.1) is needed to assure a valid test for deep/shallow
discharge stability in the flow classification scheme.


                            179

-------
               z=h. -
                 mt
             H
                                             inl
Density profile
example
                             ------ hint=0.4H
                                            h0=0.33H
Range
                                                          mt
                                                       Range
                                                       of  h0
                                     00 > 45°   D ^ H
                                      90 < 45°   D< H/3
                        Range
                        of D
Figure 7.11    Parameter Range of  CORMIX1  Applicability
                           180

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    Also  the  discharge  port  diameter  D must  not exceed
practically  unrealistic  (yet  theoretically  conceivable)
values  of the order  of the water  depth,  thus  for near-
vertical discharges

    D < H                                              (7.2)
and for near-horizontal discharges

    D < 0.5H                                           (7.3)

    Finally, the height of  the pycnocline  (i.e. thickness
of the lower layer)  h1nt must be more that 40% but less than
90% of the water depth

    0.9H > h,nt >  0.4H                                  (7.4)


7.4.2  Hints for CORMIX1 Use in Extreme Conditions
7.4.2.1   (Near-)Surface Discharges

    As  an  example,  assume  that  a  positively  buoyant
discharge is located at a small submergence  - perhaps at 10%
of the  depth  - below the free  surface  of  an unstratified
water body.  Clearly, the condition of Eq.  7.1 is violated
so CORMIX1 cannot be used with  such input data  (in  fact the
system will reject  this input, and ask  the  user to check
the data!).

    Yet   a  valid   application  of   CORMIX1   for  buoyant
discharges is still  possible if the reverse  situation - i.e.
a "mirror image"  -  of the ambient/discharge configuration
is  considered using  the water  surface as  the plane of
symmetry.   In  this  situation the discharge jet - now with
reversed "negative"  buoyancy - is located near the "bottom".
After  appropriate  data input,  CORMIX1  would  conclude   a
negatively  buoyant  flow  class  (NH)  and   all   system
predictions have to  be interpreted in the coordinate system
of the mirror image.

    Even more complicated ambient stratification conditions,
can be handled in this  mirror image interpretation as long
as careful  attention is paid to  the  specification of the
reverse stable profile.

    However,  CORMIX1  is not applicable  to (near-)surface
discharge conditions  that  i)   experience strong shoreline
interaction, or ii)  have a highly non-uniform  cross-section
(aspect ratio) as in a  channel inflow.

    i) The  near-field  processes  considered in  CORMIX1 are
valid only  for offshore conditions and  do  not  include any
shoreline (bank)   interaction  (Such  interaction is  allowed
only  in the far-field  in CORMIX1).   Shoreline  interaction
                            181

-------
processes may sometimes  dominate surface discharge dynamics
as discussed in detail by Chu and Jirka (1986).

    ii) Surface  discharges  may often have a  large cross-
sectional aspect ratio (e.g. width/depth ratio of a channel
inflow).   Since  CORMIX1  neglects  the geometric  details of
the zone of  flow establishment it is valid only for round
or  near-square  cross-sections with  maximum  aspect  ratio
values of about 3:1.
7.4.2.2  Elevated Discharges

    If  a  discharge is  still  well submerged  but elevated
above one third of the water depth as specified by Eq. 7.1,
then CORMIX1 can  still  be  used  in the  following iterative
fashion:

    Case  i) :  For  a  strongly  buoyant  jet  that tends  to
quickly rise to the surface,  assume  the  water bottom lies
higher  so that the  port elevation relative  to the reduced
depth is  within the 33% limit expressed in Eq.  7.1.   The
CORMIX1 predictions will be valid if they indicate a stable
flow class  for this  reduced  depth condition  without any
unstable recirculation.

    Case  ii) :  For a strongly negatively buoyant jet that
would rapidly  sink towards the  bottom,  assume  the water
surface  is  sufficiently higher  so that Eq.  7.1  is met.
Evaluate  the  CORMIX1  predictions  to  check  for  stable
discharge configurations that wouJd  not  interact with the
actual water surface.

    Case iii):  If unstable discharge conditions are expected
(this  would be  indicated  if the  above assumptions are
violated) then the  actual  port  elevation is frequently of
secondary importance,  while the water depth is the primary
parameter.  In this case,  a reduced port elevation - within
the limits of Eq.  7.1 - can be specified.

    Clearly the experienced user will proceed with a careful
iterative evaluation  of such complex, and perhaps unusual,
cases that  fall outside the normal  CORMIX1  problem domain
of deeply submerged single port discharges.


7.4.3   Applications to  Non-Dimensional Coordinate systems

    Available  data on  buoyant  jet  mixing processes are
usually presented in  non-dimensional form.   Often the port
diameter  D  is  used for length normalization  and the non-
dimensional parameters F0/  R, and T (Eqs.  6.1,  6.2, and 6.3,
                            182

-------
respectively)  are  given.   Also the coordinate  system is
frequently put at the discharge orifice.

    Since COKMIX1 uses the SI System of units  (e.g. length
expressed  in  meters)  a  simple  numerical  comparison is
achieved by preparing the buoyant jet input data as  follows:
D = 1 m, pa  ~ 1000  kg/m3, pQ = 990 kg/m3, UQ = 0.3132F0,  ua =
Ug/R,  h0 = 0 m, and H^ =  1000 m (unless the actual normalized
water depth  H/D  =  H* is  known in the experiment,   in which
case H = H* m) .  Furthermore, for linearly stratified cases,
the ambient density pa(H) at the water surface  is specified
t>Y  P^(H)   =   1000(1   -   10/T)   kg/m3,  where   T  is  the
stratification parameter given by Eq. (6.3), and the ambient
bottom density pb = 1000 kg/m3.  If this  convention  is made,
all lengths  (m)  predictions by  provided by CORMIX1 can be
conveniently  interpreted as predictions normalized by the
diameter D,  i.e. they are numerically the same.

    Since the port height h0 is  zero for these  simulations,
CORMIX1 assumes a bottom at z =  0,  and hence  for many cases
an attachment process  is indicated.  However, in program
element  CLASS the user  can override this  attachment and
CORMIX1  will provide  predictions  for the  unconfined and
unattached flow.
7.4.4 Adaptation to First-Order Reaction Processes

    CORMIX1 assumes a  conservative pollutant or tracer  in
the  effluent.    This  assumption  is reasonable  since the
emphasis of  CORMIX1  is on  initial mixing  mechanisms that
have very  short  time  scales  (order  of  minutes)  much less
than the typical  reaction times for growth or decay of most,
though not all, discharged substances.

    If the physical,  chemical,  and/or biological reaction
mechanism can be represented as a  first-order process with
reaction time  constant  Kr  [s~1],  then the user can convert
the  conservative pollutant  concentration  c  predicted  by
CORMIX1  in the far-field,  i.e.  the  buoyant spreading and
ambient  diffusion regimes.   The  conversion  to reacting
substances yields a non-conservative concentration cn

    cn  = c  exp (-Krx/ua)                                (7.5)

in which x/ua represents the travel time in the  far-field.
This simple adaptation  is  acceptable if the reaction time
scale,  l/Kr,  is sufficiently larger than the travel time  to
the  end  of the  near-field  (i.e.  the  hydrodynamic mixing
zone) ,  *HMZ/ua.   For substances with faster reactions more
detailed analyses  which consider  the actual  travel time
within the near-field have to be performed.
                            183

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                       Chapter VIII

              Conclusions  and  Recommendations
    U.S. water quality policy allows  for  a  mixing zone as
a limited area or volume of water where the initial dilution
of a discharge  occurs.   Water quality  standards  apply at
the edge and outside of the mixing zone.  Toxic discharges
have  additional  regulatory  restrictions,  which  require
additional dilution analyses.   The  implementation of this
policy  in the  National  Pollution  Discharge  Elimination
System  (NPDES)  permitting  process  places  the burden of
prediction  of   initial  dilution  on  both regulators  and
dischargers.    Given  a   myriad  of   possible  discharge
configurations,   ambient  environments,   and  mixing  zone
definitions, the  analyst  needs considerable  training and
expertise  to conduct  accurate  and  reliable  mixing  zone
analysis.  Against this background,  a micro-computer based
expert  system,   the  Cornell  Mixing  Zone  Expert  System
(CORMIX),  was   developed   as  a  tool   for  effluent  flow
prediction and mixing zone analysis.

    Subsystem CORMIX1 predicts the dilution and trajectory
of  a  single port  buoyant   (positively,  negatively,  or
neutrally) discharge  into  a uniform or  stratified density
environment  with  or   without   crossflow.    CORMIX1  uses
knowledge  and  inference  rules obtained from hydrodynamic
expertise to classify  and predict mixing  processes.  CORMIX1
gathers the  necessary data,  checks for data consistency,
assembles  and   executes   the  appropriate   hydrodynamic
simulation models, interprets  the results  of the simulation
in terms of the legal requirements including toxic discharge
criteria,  and   suggests   design alternatives  to  improve
dilution characteristics.

    CORMIX1, with its emphasis on  rapid  initial mixing,
assumes a  conservative pollutant discharge  neglecting any
physical, chemical,  or biological reaction or decay process.
However, the predictive results  can  oe readily converted to
adjust for first-order reaction processes.

    The results of the hydrodynamic simulation are in good
to excellent agreement with field and laboratory data and
other available simulation models.   In particular, CORMIX1
correctly predicts a wide  range  of highly complex discharge
situations  involving  boundary  interactions,  stratified
terminal layers, buoyant intrusions,  and  bottom attachments,
all  features which are not  predicted  by  other currently
                            184

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available initial mixing models.   Overall CORMIX1 appears
to be an excellent first cut tool for the analyst.

    As more data become available and experience with using
the  expert  system  is obtained,  the  hydrodynamic  flow
protocols  in  the  flow  classification  system should  be
further analyzed along  with  verification of the constants
used   within  the   model.      For  some   possible   flow
configurations,  the   existing  data  base  is  limited  for
conducting rigorous validation studies indicating a need for
additional   field   and   laboratory  data.     Also   the
implementation  of  computer  graphics should  be pursued in
order to display the results of CORMIX1 predictions.
                            185

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2. Abraham, G.  (1963),  "Jet Diffusion in Stagnant Ambient
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                            187

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38. Liseth,  P. (1970),  " Mixing of  Merging Buoyant Jets from
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39.  List,  E.  J.  and  J.   Imberger   (1973),  "Turbulent
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41. Margason, R. J. (1968),  "The Path of a Jet Directed at
Large Angles  to  a  Subsonic  Stream".  N.A.S.A., TN.D.-4919,
Langley Research Center, Hampton,  Virginia.

42. Monin, A.  S.  and A.  M. Yaglom  (1971), Statistical Fluid
Mechanics;  Mechanics  of  Turbulence, Vol.  1, MIT Press,
Cambridge, Mass, p.485.

43. Morton,  B. R.,  G.  I.  Taylor,  and J. S. Turner (1956),
"Turbulent  Gravitational Convection  form Maintained  and
Instantaneous  Sources."    Proceedings   Royal  Society  of
London, A234, pp. 1 -23.

44. Morton,  R. B. (1959),  "Forced  Plumes."  Journal of Fluid
Mechanics, Vol. 5, pp 151-163.

45.  Muellenhoff,  W. P.,  et  al.   (1985),  "Initial Mixing
Characteristics of Municipal Ocean Discharges (Vol. l&2)"f
U.S.E.P.A, Environmental Research  Laboratory, Narragansett,
R.I.
                            189

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46. Munk, W. and E. R. Anderson (1948), "Notes on a Theory
of the Thermocline." J.Mar. Res. 7, 276-295

47. Naib, S. K.  A.  (1974),  "Deflection  of a Submerged Round
Jet to Increase  Lateral Spreading". La Houille Blanche, Vol.
29, No. 6.

48.  National Academy  of  Science  (1968),   "Water  Quality
Criteria  (1968)",   (Green  book),   Report  of the  National
Technical  Advisory  Committee  to the Secretary  of  the
Interior, Federal  Water  Pollution Control  Administration,
U.S. Dept. of the Interior, Washington, D.C.

49. Ortolano, L.  (1984), Environmental Planning and Decision
Making. John Wiley & Sons.

50.  Flatten,  J. L.  and J.  F.  Keffer  (1971),  "Deflected
Turbulent Jet Flows". Transactions of the American Society
of Mechanical Engineers, Vol. 38,  Dec.  1971, pp. 756-758.

51. Rajaratnam,  N.   (1976), Turbulent Jets.  Elsevier.

52.  Roberts, P.   J.  W.  (1977),   "Dispersion  of  Buoyant
Wastevater  Discharge  From  Outfall  Diffusers  of  Finite
Length".   Report No.  KH-R-35,  W.  M.  Keck  Laboratory  of
Hydraulics and Water Resources,  Division of Engineering and
Applied  Sciences,   California  Institute  of  Technolngy,
Pasadena, Cal.

53. Roberts, P.  J.  W.  (1979),  "Line Plume and Ocean Outfall
Dispersion". Journal  of  the  Hydraulics Division,  Proc.  of
the Amer. Soc. of Civil Engineers,  Vol.  105,  No. HY4, April,
pp. 313-331.

54. Rodi, W. ed. (1982),  Turbulent Buoyant Jets and Plumes,
Pergamon Press,  New York.

55. Scorer, R.  S. (1954),  "The Behavior of Chimney Plumes."
International Journal of Air  Pollution, Vol.  I, pp 198-220.

56. Sharp, J. J. and B. D. Vyas,  (1977), "The Buoyant Wall
Jet".  (1977),   Proceeding of  the  Institution  of  Civil
Engineers, Part 2,  No. 63, September.

57. Shwartz, J.  and M. P. Tulin (1972), "Chimney Plumes in
Neutral and  Stable Surroundings".  Atmospheric Environment,
Vol. 6 pp. 19-36.

58. Sobey,  R. J.,  A.  J.  Johnston,  and  R.  D. Keane  (1988),
"Horizontal Round Buoyant Jet in Shallow Water", Journal of
Hydraulic Engineering, ASCE,  Vol.   114,  No.  8., August.
                            190

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59. Tait, H. (1984), "Section 402 Guidelines for Reviewing
National Pollutant Discharge  Elimination Permits", National
Coastal Ecosystems Team, Rept. No. FWS/OBS-84/05, U.S. Dept.
of the Interior, Washington,  D.C., September.

60. Tennekes, H. and J.  L.  Lumley (1972), A First Course in
Turbulence. MIT Press, Cambridge, Mass, p.  99.

61. Tong,  S.  S. and K. D. Stolzenbach (1979),  "Submerged
Discharges of  Dense Effluent".  Tech.  Rept.  243,  Ralph M.
Parson  Laboratory  for Water Resources and Hydrodynamics,
Massachusetts   Institute    of    Technology,   Cambridge,
Massachusetts.

62. USEPA (1972),  "Water Quality  Criteria 1972". EPA-R3-73-
003, Environmental Studies  Board, Committee on Water Quality
Criteria, Washington, D.C.

63. USEPA  (1976),  "Quality Criteria for Water  1976"  (Red
Book),  Guidelines  for State and Area Wide  Water Quality
Management Program, Washington,  D.C. (Chapter 5).

64. USEPA (1984),  Water Quality Standards Handbook.  Office
of Water Regulations and Standards, Washington, D.C.

65.  USEPA  (1984),  "Technical   Guidance  Manual  for  the
Regulations Promulgated Pursuant to Section 301 (g)  of the
Clean Water Act of 1977 (Draft) ", Washington D.C., August.

66.  USEPA  (1985),  "Technical Support Document  for Water
Quality-based Toxics Control". Office of Water, Washington,
D.C., September.

67.  Viollet,  P.-L.  (1977)  "Study  of  Jets  in  Transverse
Currents in Stratified Environments". Doctoral Dissertation,
Curie University,  Paris, France,  February, 1977.  (in French)

68. Wright,  S.  J.  (1977),  "Effects  of Ambient Crossflovs
and Density  Stratification on the Characteristic Behavior
of Round Turbulent Buoyant Jets".  Rep. KH-R-36,  W.M. Keck
Laboratory of  Hydraulics  and Water  Resources,  California
Institute of Technology, Pasadena, Calif.

69.  Wong,   D.   R.   (1984),   "Buoyant  Jet  Entrainment  in
Stratified Fluids". Ph.D.  Thesis, Civil Engineering Dept.,
The University of Michigan, Ann Arbor Mich.
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                        Appendix A

        Stability of Stratified Ambient Shear Plows
    Within  the context  of this  study there  are  several
possibilities for stratification effects superimposed on the
ambient shear  flow.  The stratification may be present due
to existing environmental conditions, or it may be  induced
by the buoyancy of the effluent discharge  (i.e. within the
buoyant spreading phase).  In either case, a determination
can be made as to whether such stratification  (i.e.  density
gradient) can  in  fact  be maintained or whether it  will  be
rapidly eroded by the ambient turbulence.

    The flux Richardson number, Rfc, is defined as  the ratio
of the buoyant energy  flux to  the shear energy production
(Tennekes  and  Lumley,  1972).     In  terms   of   the  eddy
diffusivitiy convention  (Turner,   1973) this can be  written
as

    Rf= -gkH(dp/dz)/(PkM(du/dz)2)                       (A.I)

in which  k,,, kH = eddy  diffusivity for momentum and  for a
scalar (heat) , respectively,  p = local density, and u is the
local velocity.  A critical value  of Rfc =  0.10 to 0.20 has
been suggested (Monin  and  Yaglom, 1971 and Turner,  1973) .
Above  this  value,   turbulence  is  damped and   a   stable
stratified  profile  can  be maintained; below this  value,
turbulence  erodes  the  density  profile  and  the  ambient
environment will become  fully mixed.

    Jirka (1980) has proposed an adaptation of Eq.  (A.I) for
the  present  shear  flow  conditions.    In  the  limit  of
marginally stable conditions, the eddy diffusivities are of
the same  order,  k^ ^ ^ (Reynolds  analogy).  Hence  if  s  is
the  existing  or  the  imposed  buoyancy gradient,  and  the
velocity gradient is given  by the  logarithmic  law  argument,
(du/dz) = U»/(KHS)  in which u*  =  shear velocity, «  =  0.4 =
von Karman  constant,  and Hs  =  layer height of the  ambient
flow.  This leads to

    Rf = e/c2Hs2/U«2                                      (A. 2)

With the  Darcy-Weisbach  friction  law, u* = (f/8)1/2ua,  where
f  =  friction  factor,  the  critical value  of  the buoyancy
gradient  is derived as

    ec = cf(ua/Hs)2                                    (A. 3)


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where c =  Rfc/(8«;)2  a  o.02.   If the actual  e  < ee  then the
stratified  shear flow will  be unstable  and  will  tend to
rapid mixing.
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                        APPENDIX B

                   CORMIX1  SYSTEM ADVICE


B.I Introductory Advice

CORNELL MIXING ZONE EXPERT SYSTEM:  GENERAL INFORMATION

The Cornell Mixing Zone Expert System (CORMIX) is a series
of  software  subsystems for  the analysis,  prediction and
design  of  aqueous  discharges  into  watercourses,  with
emphasis on the geometry and dilution characteristics of the
initial mixing zone.  Subsystem CORMIX1 deals with buoyant
submerged single port discharges into flowing unstratified
or  stratified  water environments,  such as  rivers,  lake,
estuaries, and coastal waters.  It  includes  the limiting
cases of non-buoyant and negatively buoyant discharges and
of stagnant ambient conditions.  Please note that the time
for loading of individual  program  elements will depend on
the speed of  your  computer and the size of  the program
element. The time for these file operations may range from
a few seconds (IBM PS/2 Model  70, 80386-based) to more than
a  minute   (IBM   PC/XT,   8088-based).     Also   DOS  file
manipulation information is displayed by the system during
program execution and may be neglected by the user.

PROGRAM  ELEMENTS:    The  program elements  of  CORMIX1 are
listed below.  During system use the program elements are
loaded sequentially  and  automatically in  the order given
below.

    1) DATIN This  is a knowledge base program for the entry
    of relevant data  about the discharge situation and for
    the initialization of the  other program elements. DATIN
    consist of four subprograms that execute automatically;
    each  subprogram  assembles  a   data  group.  You  are
    presently using DATIN.  The four data groups DATIN seeks
    are: general identifier information, ambient conditions
    (geometry  and  hydrography),    discharge  conditions
    (geometry  and fluxes), and output  information desired
    including  legal  mixing zone definitions.   After each
    subprogam  executes,  the  values  for  data  entered  or
    concluded  are  displayed.   DATIN is a detailed program
    with  complete   explanations   on  data  preparations,
    assumptions and  schematizations. DATIN along with the
    programs PARAM and CLASS (described below) automatically
    creates the files  fn.CXD,  and  HYDRO.CXE where fn is  a
    user  supplied  file  name.  The  fn.CXD   contains  all


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    necessary  input  data for the  hydrodynamic simulation
    model  HYDRO  described   below.   The  HYDRO.CXE  file
    instructs HYDRO which fn.CXD file to load as input for
    the current session.

    2) PARAM  This is a knowledge base program that computes
    the relevant physical parameters for the given discharge
    situation.  Output from PARAM is  included in the fn.CXD
    file.

     3)  CLASS   This  is  a  knowledge  base  program  that
    classifies the given discharge into one of many possible
    hydrodynamic configurations,  e.g. a boundary attached
    discharge, an unstable vertically mixed case, or mixing
    controlled by the ambient crossflow.  Each separate flow
    configuration has a unique alphanumeric  label (Example
    VI,S5,..). A detailed hydrodynamic description for each
    flow configuration  is  available.  Output  from CLASS is
    contained in the fn.CXD file.

    4) HYDRO  This is a knowledge base program that executes
    the external FORTRAN hydrodynamic program consisting of
    a  number  of  simulations  subroutines (modules)  each
    corresponding  to  a  particular  hydrodynamic  mixing
    process.  For  each  flow  configuration  (Examples:  VI,
    S5)identified in CLASS,  the appropriate  modules  are
    executed sequentially according to a  specific protocol.
    The  program outputs  data on  geometry  (trajectory   ,
    width,   etc.)    and   associated  mixing   (dilution,
    concentration)  following  the path   of  the  effluent
    discharge. CLASS automatically creates the  files fn.CXO
    and fn.CXS where fn is the user supplied  file name. The
    fn.CXO contains  the output file data  for  the HYDRO. The
    fn.CXS  file is  used  as  input  by the  final  program
    segment SUM.

    5) SUM This is a knowledge base program that summarizes
    the   given   situation,    comments   on    the   mixing
    characteristics,   evaluates  how   applicable   legal
    requirements  are  satisfied,  and  suggests  possible
    design alternatives and improvements.

UNITS  OF  MEASUREMENT:  CORMIX  uses  the  SI  system  of
measurement, specifically: length in  m, mass  in kg, time in
s,  and temperature  in  deg C. Furthermore,  all  pollutant
concentrations are considered without units,  i.e.  the user
can specify these  in any units he/she  desires  and all output
data must be interpreted accordingly in these same units.

COORDINATE SYSTEM: All  predictions in CORMIX1 are displayed
using  the  following three-dimensional  coordinate  system:
    -The origin is located at the bottom of the water body
    vertically below the center of the discharge port.


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    -The x-axis  is  located  at the bottom  and  directed in
    the downstream direction following the ambient flow.
    -The y-axis is located at the bottom and points to the
    left normal to the ambient  flow  direction  (x-axis).
    -The z-axis points vertically upward.
B.2 Ambient advice

  DATA  REQUIREMENTS  FOR  AMBIENT  CONDITIONS:    Ambient
conditions are defined by the hydrographic and the geometric
conditions  in the  vicinity  of  the  discharge.  For  this
purpose typical cross-sections normal  to the  ambient flow
direction at the discharge  site and further downstream need
to be considered:

A) Bounded cross-section:  If  the  cross-section is  bounded
on both  sides by  banks  -  as  in  rivers,  streams,  narrow
estuaries,  and other  narrow watercourses  -,  then  the
cross-section is considered "bounded".

B) Unbounded cross-section: In some cases the discharge is
located close to one boundary while  the other boundary is
for practical  purposes very far away.  This  would  include
discharges into wide  lakes, estuaries  and  coastal  areas.
These situations are defined as "unbounded".

A) BOUNDED CROSS-SECTION:  Hydrographic information:  Data
on the design ambient flow condition - such as average river
discharge or low flow discharge - needs to be available. The
user has  the  option of entering such data directly as the
discharge or  as  an average velocity.  The ambient  density
profile (i.e. the vertical distribution of the ambient water
density)  must be approximated. It may be specified as either
uniform (within given limits) or approximated as one of four
simplified  profiles.  An  opportunity  for obtaining  more
detailed  information on these profiles is given later.  The
ambient density can be specified  directly,  or -in  case of
freshwater- is computed after specification of the ambient
temperature.   Geometric  information:   CORMIX will  conduct
its analysis  assuming  a  rectangular  cross-section  that is
given by  a width and a depth both of which are constant in
the downstream direction following the ambient flow.  This
schematization may be quite evident for well-channeled and
regular rivers or  artificial channels.  For highly irregular
cross-sections, it may require more judgement and experience
- perhaps combined with  a  repeated use of CORMIX to get a
better feeling on  the  sensitivity of  the results.  In any
case, the user is advised to consider the following steps:

1) Be  aware that  a particular  flow condition  (such  as a
river discharge)  is usually associated with a certain water
surface  elevation  ("stage"). Data  for  a stage-discharge
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relationship is normally available from a separate hydraulic
analysis or from field measurements.

2) For  the given stage-discharge  combination  display the
cross-section   at  the  discharge   location  and  several
downstream cross-sections.  Look over  these.  Determine an
"equivalent rectangular cross-sectional area". Very shallow
bank areas or shallow floodways  may be  neglected. Also more
weight should be given to the cross-sections at, arid close
to, the discharge location.

3) Determine the surface width and depth of the equivalent
rectangular area.  In  case that ambient discharge  and ambient
velocity  data  are   available,  note  that   the  continuity
relation   specifies   that   discharge  =   (velocity   *
cross-sectional  area).  The  width  and depth values  thus
chosen need to be specified to CORMIX which will check for
any inconsistencies.  Note On Stagnant Conditions: If zero
(or a very small value) for  ambient  velocity  is entered,
CORMIX will label the discharge  environment  as stagnant. In
this case  CORMIX  will predict only the near  field  of the
discharge. Although stagnant conditions represent an extreme
limiting  case for dilution  prediction,  a  more realistic
assumption for natural water bodies would be to consider a
finite  ambient  crossflow,  no  matter  how  small.  It  is
therefore  recommended to conduct  subsequent analysis with
a small crossflow.

4) As a  measure  of geometric non-uniformity  also  specify the
actual maximum depth of  the cross-sections  (again with more
weight given to the near-discharge cross-sections).

5) As  a measure  of  the roughness  characteristics  in the
channel the value of the Manning  "n",  or  alternatively of
the Darcy-Weisbach friction factor "f", must be specified.
These parameters  influence the  mixing  process  only  in the
final stage considered by CORMIX and are not very sensitive
to the predictions.  Generally, if these values are assumed
known within +-30% the predictions will vary by +-10% at the
most.

B)UNBOUNDED CROSS-SECTIONS:  Both hydrographic and geometric
information are closely linked in this case:

1) Determine the water elevation (given by lake or reservoir
elevation or tidal stage etc.) for  which the  analysis should
be conducted.

2) Assemble cross-sectional profiles that plot water depth
as a function of distance from the shore for the discharge
location and for several positions  downstream following the
ambient current direction.
                            197

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3) a) If detailed hydrographic data (from field surveys or
from  some  hydraulic numerical  model  calculations)  are
available, determine the cumulative ambient discharge from
the  shore to  the  discharge  location  for the  discharge
cross-section.  For  each  of  the  subsequent  downstream
cross-sections determine  the distance  from the  shore  at
which  the  same   cumulative  ambient  discharge  has  been
attained.Mark this position on all cross-sectional profiles.
Now  consider  the velocity  (vertically  averaged)  and  the
depth  at these  positions.  Specify  to  CORMIX  a  typical
ambient  velocity  and a typical depth  from these  data  by
giving most weight to the conditions at, and close to,  the
discharge location.  Specify a  typical  distance  from  the
shore  by dividing  the  cumulative ambient discharge  by
(ambient velocity * depth).

3b) If detailed hydrographic data  is not available - but at
least  data,    or estimates,  on  the  vertically averaged
velocity  at the  discharge  location must  be  available!  -
then determine the  cumulative cross-   sectional  area from
the  shore to the  discharge location  for  the   discharge
cross-section.For   each   of  the   subsequent   downstream
cross-sections, mark  the   position where  the cumulative
cross-sectional area has the same value  as  at the discharge
cross-section. Determine the typical ambient  velocity and
the  typical  ambient  depth  at  these  positions  with  most
weight given to conditions  at,  or close to, the discharge
location.  Specify  the typical  distance from  the shore by
dividing the cumulative  cross-sectional area by the ambient
depth.

4) In  summary,  CORMIX will  conduct its analysis  for  the
unbounded case by    assuming  an   "equivalent  rectangular
cross-sectional area" defined by   depth,  by distance from
one  bank to  the  discharge  position,   and by    ambient
velocity.  Note  the  similarities  to  the  bounded  case
discussed   above.  As  for the bounded  cross-section,  the
ambient density profile  (i.e. the vertical distribution of
the ambient water density) must  be  approximated. It may be
specified  as  either  uniform  (within  given   limits)  or
approximated  as  one  of  four  simplified  profiles.   An
opportunity for obtaining  more detailed information on these
profiles    is  given  later.The  ambient   density  can  be
specified directly,  or -in case of a  freshwater ambient -
is computed by specification of the ambient  temperature.

5) As a measure of the roughness characteristics of the flow
area the  value of the Manning  "n", or alternatively of the
Darcy-Weisbach   friction factor  "f",  must be specified.
These parameters influence the  mixing process only in the
final stage considered by  CORMIX and are not very sensitive
to the predictions.  Generally,  if  these  values  are  assumed
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known within +-30% the predictions will vary by +-10% at the
most.


B.3 Density Profile Advice

SPECIFICATION OF AMBIENT DENSITY STRATIFICATION:

Since  the  ambient density  is  not uniform  over the  water
column,  the  actual  vertical  density  distribution  -  as
determined by field data  -  must be approximated by  one of
the schematic stratification types. These are:

Type A: Linear Density Profile

Type B: Two-Layer System With Constant Densities and Density
Jump

Type C: Constant Density Surface Layer with Linear Density
Profile in Bottom  Layer Separated by a Density  Jump

Type D: Constant Density Surface Layer With Linear Density
Profile in Bottom  Layer Without a Density Jump

Brief  sketches  for these  four stratification types  follow
below. Note that a dynamically correct approximation of the
actual distribution should keep a balance between over - and
under - estimation of the  actual data similar  to a  best-fit
in  regression analysis.  It  is desirable to  test through
repeated use of CORMIX different approximations (i.e.  with
different stratification types and/or parameter values)  in
order  to  evaluate the sensitivity of  the resulting  model
predictions.


B.4  Discharge Advice

ADVICE  FOR SPECIFYING DISCHARGE CHARACTERISTICS
SINGLE  PORT DISCHARGE DISCHARGE GEOMETRY:

1) In most cases, the port or nozzle geometry  will  be round
so that the  radius or  diameter must  be specified. If  not,
then the cross-sectional area must be specified.

2) Specify the height of the port center above  the bottom.

3) The vertical angle of discharge is the  angle  between the
port  centerline and a horizontal plane, in  CORMIX1  this
angle  may range between -45 deg and 90.0 deg. As examples,
the  vertical angle  is 90  deg  for  a discharge  pointing
vertically  upward,  and   it  is  0  deg  for  a   horizontal
discharge.
                            199

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4) Consider a plan view of the discharge situation as seen
from above. The horizontal angle of discharge is the angle
measured counterclockwise from the ambient current direction
(x-axis) to the plan projection of the port centerline. In
CORMIX1 this angle may range between 0 deg and 360 deg. As
examples, the horizontal angle is 0 deg if the port points
downstream with the ambient flow,  it  is  90 deg if it points
to the left of the ambient flow,  it is 180 deg if it points
upstream opposing the ambient flow, and  it is 270 deg if it
points to the right of the ambient flow, respectively.

DISCHARGE FLOW VARIABLES:

1) The discharge flow rate or the discharge velocity should
be  specified.  Note that  these  two variables  are related
through the port diameter or cross-sectional area.

2) The discharge density can be specified directly, or -in
case of  an essentially freshwater discharge  in which the
addition of any pollutant or tracer  has negligible effect
on  density -  it  is  computed  after  specification  of the
discharge temperature.

3) The discharge concentration of the material of interest
(pollutant, tracer, or temperature) is defined as the excess
concentration above any ambient  concentration. The user can
specify this quantity  in any units and the CORMIX1 results
for   computed  excess   concentrations   should   then  be
interpreted in these same units.
B.5 Mixing Zone Advice

SPECIFICATION OF DESIRED MIXING ZONE INFORMATION:
The user must specify data that indicates over which spatial
region  information  will be  desired,  and  in what detail.
Legal mixing zone (LMZ)  requirements may exist  or not.  The
user has several options for this specification:

1) LEGAL MIXING ZONE (LMZ): Options exist for specifying the
legal mixing zone as a maximum distance  from the  discharge
location, or as a maximum cross-sectional  area occupied by
the plume, or  as  the  maximum width of the  effluent plume.

2)  REGION  OF  INTEREST  (ROI):   When  legal  mixing  zone
restrictions do not exist or when the user is interested in
information  over  a  larger  area,  then a  region of interest
must be specified as the maximum distance  in the direction
of mixed effluent flow.

3) HYDRODYNAMIC MIXING ZONE  (HMZ) : In all cases, CORMIX will
label   a  usually   smaller   initial   region   in   which
discharge-induced mixing takes  place as the "hydrodynamic


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mixing zone". The dilution conditions in the HMZ may be  a
useful measure for the outfall designer when attempting to
optimally design the discharge conditions.

4) TOXIC DILUTION ZONE (TDZ): For all discharges that have
been  designated  as  toxic  by  USEPA  standards  (Technical
Support Document for Water  Quality- Based Toxics Control,
USEPA,   1985)   CORMIX   will   automatically   define  the
concentration values at the  edge  of  the toxic dilution zone
as defined  in  that document. CORMIX  will  indicate if the
criterion maximum concentration (CMC) standard has been met.
After  all  applicable  data  have  been specified  on these
zones, CORMIX also needs information on the  level of detail
for the output data within these  zones and, simultaneously,
within  all  the hydrodynamic  elements (modules)  that  may
occupy these zones.
B.6 Design Advice

A reliable environmental analysis and mixing zone prediction
is possible only  if  each  design case is evaluated through
several iterations of CORMIX1.   Small changes  in ambient or
discharge  design  conditions can sometimes cause drastic
shifts in the applicable flow configuration (flow class) and
the size or appearance of mixing zones.   Iterative use of
CORMIX1  will  give  information  on  the  sensitivity  of
predicted  results  on design and  ambient   conditions.Each
predictive case should be  carefully assessed as to:  - size
and shape  of LMZ  -  conditions  in the TDZ  (if  present)-
bottom  impact  of  the  discharge  flow    - water surface
exposure- bank attachment, and other factors.   In general,
iteration should be conducted in the following order:

A) Discharge design changes (geometry variations)

B) Sensitivity to ambient conditions

C) Discharge flow changes  (process variations)

When investigating these  variations the CORMIX1  user will
quickly appreciate the fact that mixing conditions at short
distances  (near-field)  are  usually  quite sensitive  and
controllable.    In contrast, mixing  conditions  at large
distances  (far-field) often show little sensitivity unless
the ambient  conditions  change  substantially or drastic
process variations are introduced.

A) DISCHARGE DESIGN CHANGES (GEOMETRY VARIATIONS): Most of
the following recommendations are motivated by the desire
of improving conditions in the applicable mixing zones  (i.e.
minimizing concentrations and/or areal extent).
                            201

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1)  Outfall location:  Consider  moving the  discharge
farther offshore to  a  larger water depth  in order to
delay flow interaction with the bank and/or surface, and
to improve near-field mixing.

2) Height of discharge port: For positively buoyant or
neutral discharges it is usually desirable to minimize
the port  height in  order  to provide  a  low submerged
jet/plume trajectory.  However,  if the port height is
too small  undesirable flow bottom attachment may result.
A typical  range for port  heights  is  from two  to ten
diameters.  For negatively buoyant discharges,  on the
other hand, it  may be desirable to  maximize the port
height. Navigational  requirements may put further limits
on large port heights.

3) Vertical angle  of  discharge: Near-field dilution for
positively  or  neutrally  buoyant discharges  is  often
improved by providing  a  near-horizontal discharge. In
order to  prevent bottom  interference a slight  upward
orientation (in the range of +15  to +30 degrees) may be
advisable.  In  contrast,  a  vertical  or near-vertical
angle  may  be  favorable   for    negatively  buoyant
discharges.

4) Horizontal angle  of discharge:  This angle provides
the  discharge  orientation  relative  to  the  ambient
current.  A co-flow design  (angle  of  about 0 degrees)
or  a  cross-flow   design   (about  90  or 270  degrees,
respectively)  are preferable.  A  counter-flow  design
(about 180 degrees)  is  undesirable from the viewpoint
of  mixing  zone  predictability and   bottom  impacts.
Cross-flow  designs may  be particularly  effective in
optimizing near-field  mixing,  and  if they are chosen,
the port should point  in the offshore  direction.

5)  Port  diameter/area  (discharge  velocity): Remember
that for a given discharge  flow rate the port area and
discharge  velocity  are  inversely   related:  a  small
discharge port  implies a high discharge velocity, and
a consequently high discharge momentum  flux. Typically,
a  high velocity   discharge  will  maximize  near-field
mixing.   Note,  however,  that high velocity discharges
a) may lead to  unstable near-field flow configurations
perhaps involving  undesirable mixing patterns,  and b)
usually have  little,  if  any, effect on dilutions over
the far-field where a LMZ may apply.Discharge velocities
in typical engineering designs may range from 3 m/s  to
8  m/s. Very  high  velocities may lead  to excessive
pumping energy  requirements.  Very low velocities  (less
than   0.5   m/s)  may  lead  to  undesirable  sediment
accumulation within  the discharge  pipe.
                        202

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B) SENSITIVITY  TO  AMBIENT CONDITIONS:Variations  -  of the
order  of  10  percent -  of the  following  ambient  design
conditions  should  be  considered:-  ambient velocity  (or
ambient flowrate)  - ambient  depth (or river/tidal stage)
     ambient    density     structure     (notably    density
differences)Such variability is important for two reasons:

    1) the usual uncertainty in ambient environmental data,

    2) the schematization employed by CORMIX1 Please refer
    to  the   detailed  advice  on  the  specification  of
    environmental data,  including the  density  structure,
    that  is  available   in   program  element   DATIN.  In
    particular,   note the  advisory  comments on  stagnant
    ambient  conditions.

C)  DISCHARGE FLOW  CHANGES  (PROCESS VARIATIONS):  Actual
process changes can result in variations of one or more of
three  parameters associated with  the discharge:  flowrate,
density, or  pollutant  concentration. In  some  cases,  such
process changes may be difficult to achieve or too costly.
Note,  that  "off-design"  conditions  in which a  discharge
operates  below   its  full  capacity  also  fall  into  this
category.

    1) Pollutant mass flux: The total  pollutant  mass flux
    is  the  product of discharge  flow  (m**3/s)  times the
    discharge pollutant concentration (in arbitrary units).
    Thus,   decreasing the  pollutant  mass  flux  will,  in
    general, decrease the resulting pollutant concentration
    in  the  near-field    and  far-field.  This  occurs,  of
    course,  during off-design conditions.

    2) Discharge flow:  For a given pollutant mass flux, an
    increase  in discharge flow  implies  an increase  in
    discharge pollutant  concentration,and  vice versa.  For
    the variety of flow classes contained in CORMIX1 there
    is  no  universal rule whether  high  or  low  volume
    discharges  are  preferable  for  optimizing  near-field
    mixing.  Mostly, the sensitivity is small, and even more
    so  for  far-field  effects.   Note  that  a  change  in
    discharge flow will  influence  in  turn  the  discharge
    velocity and hence momentum flux.

    3)  Discharge  density:  The  actual  density  of  the
    discharge flow controls the buoyancy effects relative
    to  the  ambient  water.  Occasionally,  the  discharge
    density is controllable through  the  amount  of process
    heating  or  cooling  occurring  prior  to  discharge.
    Usually, near-field mixing is   enhanced by  maximizing
    the total density difference  (positive or  negative)
    between discharge flow  and ambient water.  In most cases,
    however, this  effect is minor.
                           203

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                        APPENDIX C

             Flow  Classification Descriptions

C.I V-Flow Classes

FLOW CLASS VI

A   submerged  buoyant   effluent   issues  vertically   or
near-vertically from the discharge port.

The discharge  configuration  is  hydrodynamically "stable",
that is  the  discharge strength (measured  by  its momentum
flux)  is weak in relation to the layer depth and in relation
to  the  stabilizing  effect  of  the  discharge  buoyancy
(measured by its buoyancy flux).

The following flow zones exist:

I) Momentum-dominated near-field jet:  The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.

2) Buoyancy-dominated near-field plume:  After some distance
the  discharge  buoyancy  becomes  the  dominating  factor
(plume-like).  The plume deflection by the ambient current
is still weak.

Alternate possibility: Depending on the  ratio of the jet to
crossflow  length  scale to the  plume to  crossflow length
scale the above zone may be replaced by a momentum-dominated
far-field jet:

2)  Momentum-dominated far-field  jet:  The jet  has become
strongly deflected by the ambient current.

3) Buoyancy-dominated  far-field plume:  The plume has been
strongly   deflected by  the  current and  is  slowly rising
toward the surface.

4)  Layer  boundary   approach:   The  bent-over  submerged
jet/plume approaches  the  layer  boundary (water surface or
pycnocline) .   Within  a  short distance  the concentration
distribution becomes  relatively   uniform across the plume
width and thickness.

*** The zones  listed above constitute  the  HYDRODYNAMIC
MIXING ZONE  in which strong  initial mixing takes place.***
                            204

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5) Buoyant spreading at  layer  boundary:  The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it  is  being advected  by the ambient  current.   The
plume thickness may decrease during this phase.  The mixing
rate is relatively  small.   The plume may  interact with a
nearby bank or shoreline.

6)  Passive  ambient  mixing:   After   some  distance  the
background turbulence in the ambient shear  flow becomes the
dominating mixing  mechanism.  The  passive  plume is growing
in depth  and  in width.   The   plume may  interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated  in  zone  5  or 6 depending
on the definitions of the  LEGAL MIXING  ZONE or the REGION
OF INTEREST.  ***
FLOW CLASS V2

A   submerged  buoyant   effluent   issues   vertically   or
near-vertically  from  the discharge  port.    The  discharge
configuration  is hydrodynamically  "stable",  that  is  the
discharge strength (measured by its momentum flux) is weak
in  relation  to the layer  depth.   The  discharge buoyancy
plays a minor role in this case.  The following flow zones
exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected by the ambient current.

2)  Momentum-dominated  far-field jet:  The   jet has  become
strongly deflected  by the  ambient current and  is  slowly
rising toward the surface.

3)  Layer  boundary   approach:  The  bent-over  submerged
jet/plume approaches the layer  boundary (water surface or
pycnocline).  Within a  short  distance the concentration
distribution becomes  relatively uniform across  the plume
width and thickness.

*** The  zones  listed above  constitute the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4)  Buoyant spreading at  layer  boundary:  The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it  is being advected by the ambient current. The plume
thickness may decrease during  this phase.  The mixing rate
is  relatively small. The plume  may interact with a nearby
bank or shoreline.
                            205

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5)  Passive  ambient  mixing:  After   some  distance  the
background  turbulence in the ambient shear flow becomes the
dominating mixing mechanism. The  passive  plume  is growing
in depth  and in  width.  The plume  may interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated in  zone  4 or 5 depending
on the definitions  of the  LEGAL MIXING ZONE or  the REGION
OF INTEREST.***

SPECIAL CASE: If  discharge is  non-buoyant, then the layer
boundary buoyant spreading regime (zone 4) is absent.
PLOW CLASS V3

A   submerged   buoyant   effluent   issues  vertically  or
near-vertically  from  the discharge  port.    The discharge
configuration  is hydrodynamically  "stable",  that  is the
discharge strength (measured by its momentum flux) is weak
in  relation  to  the  layer  depth  and  in  relation  to the
stabilizing effect of  the discharge buoyancy (measured by
its buoyancy flux). The  buoyancy  effect  is very strong in
the present case.  The following flow zones exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.

2) Buoyancy-dominated near-field plume: After some distance
the  discharge  buoyancy  becomes  the  dominating  factor
(plume-like). The  plume  deflection  by  the  ambient current
is still weak.

3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary  (water surface
or pycnocline) at a near-vertical angle.  After  impingement
the  flow  spreads  more or  less  radially along the layer
boundary.  In  particular, the  flow spreads  some  distance
upstream against the  ambient flow, and laterally across the
ambient  flow.  This spreading  is  dominated by  the  strong
buoyancy of the discharge.

***  The zones  listed above  constitute  the  HYDRODYNAMIC
MIXING ZONE in which  strong  initial  mixing takes place. ***

4) Buoyant spreading  at  layer  boundary:  The plume spreads
laterally along the layer boundary  (surface or pycnocline)
while it is being advected by the ambient  current. The plume
thickness may decrease during  this  phase.  The mixing rate
is relatively small.  The plume may  interact with  a nearby
bank or shoreline.
                            206

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5)  Passive  ambient  mixing:  After   some  distance  the
background turbulence in the  ambient shear  flow becomes the
dominating mixing mechanism. The  passive  plume is growing
in depth  and in  width.  The plume  may interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated in  zone  4 or 5 depending
on the definitions  of the  LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
PLOW CLASS V4

A   submerged  buoyant   effluent   issues  vertically   or
near-vertically from the discharge opening.  The discharge
configuration is hydrodynamically  "unstable",  that is the
discharge strength (measured by its momentum flux) dominates
the flow in  relation to  the  limited  layer depth.  The role
of buoyancy is secondary.  The following flow zones exist:

1) Momentum-dominated near-field jet: The  flow is dominated
by the effluent momentum  (jet-like) and is weakly deflected
by the ambient current.

2)  Layer  boundary  impingement/full  vertical mixing:  The
weakly  bent  jet  impinges on  the  layer  boundary (water
surface or pycnocline)  at a near-vertical angle. Given the
shallow layer depth and the weak buoyancy of the discharge,
the flow becomes unstable  after impingement. This results
in  a  recirculating region  immediately  downstream  that
extends over the full layer depth.

3) Passive ambient mixing: The vertically fully mixed plume
is  further  advected  by the  ambient  flow  and  spreads
laterally through ambient diffusion. The plume may  interact
with a nearby bank or shoreline.

***The  ambient  flow plays an important role  in this flow
configuration. Hence, all the zones listed above constitute
the HYDRODYNAMIC  MIXING  ZONE with strong  initial mixing.
Predictions will be  terminated  in  zone  3  depending on the
definitions  of  the  LEGAL MIXING  ZONE  or  the REGION  OF
INTEREST.  ***
FLOW CLASS V5

A   submerged  buoyant   effluent   issues  vertically   or
near-vertically  from  the discharge  port.    The  discharge
configuration  is hydrodynamically  "stable",  that  is  the
discharge strength (measured by its momentum flux) is weak
in  relation  to  the  layer  depth  and  in  relation  to  the
stabilizing  effect of the discharge buoyancy (measured by


                            207

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its buoyancy flux). The buoyancy  effect  is  very strong in
the present case.  The following flow zones exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.

2) Buoyancy-dominated near-field plume: After some distance
the  discharge  buoyancy  becomes  the  dominating  factor
(plume-like). The  plume deflection  by  the  ambient current
is still weak.

3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle.  After impingement
the  flow  spreads  more  or  less  radially along the  layer
boundary.   In  particular,  the  flow spreads  some  distance
upstream against the ambient  flow, and laterally across the
ambient flow.  This spreading  is  dominated by  the  strong
buoyancy of the discharge.

***  The zones  listed above  constitute  the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4) Buoyant  spreading  at layer  boundary:  The plume spreads
laterally along the layer boundary  (surface or pycnocline)
while it is being advected by the ambient  current. The plume
thickness may decrease during  this  phase.  The mixing rate
is relatively small.  The plume may interact with  a nearby
bank or shoreline.

5)  Passive  ambient  mixing:   After   some   distance  the
background turbulence in the  ambient shear flow becomes the
dominating mixing  mechanism. The passive plume is growing
in depth  and in  width.  The plume  may  interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated in zone 4 or 5 depending
on the definitions of the  LEGAL MIXING ZONE or the REGION
OF INTEREST.***

SPECIAL CASE: If the ambient is stagnant,  then advection and
diffusion  by  the ambient flow (zones  4  and  5)  cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this  stage.  Such  stagnant  water predictions  may  be a
useful  initial  mixing  indicator  for a given  site  and
discharge design. For practical final predictions, however,
the advection and diffusion of  the ambient flow  - no matter
how small in magnitude - should be considered.
                            208

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FLOW CLASS V6

A   submerged  buoyant   effluent   issues  vertically   or
near-vertically  from  the discharge  port.    The  discharge
configuration is hydrodynamically  "unstable",  that is the
discharge strength  (measured by its momentum flux) dominates
the  flow  in relation  to the limited  layer  depth  and in
relation to  the  weak  stabilizing  effect of  the  discharge
buoyancy  (measured by  its  buoyancy  flux).  However,  the
buoyancy is  generally  strong enough  to  affect  the flow at
larger  distances  downstream from  the  unstable  initial
region.  The following flow zones exist:

1) Unstable recirculation/buoyant restratification/upstream
spreading:  The  buoyant  jet  rises  near-vertically  and
impinges   on  the   layer   boundary   (water   surface   or
pycnocline). After impingement the mixed flow recirculates
over  the  limited  layer   depth   and   becomes  partially
re-entrained  into   the  discharge jet.  The  degree    of
recirculation - and hence the overall mixing in this region
- is controlled by  restratification of the  flow at the edge
of this recirculating  region. The restratified flow spreads
along the  layer  boundary. In particular,  the flow spreads
some distance  upstream  against  the  ambient current,  and
laterally across the ambient flow.

*** The region  described  above constitutes the HYDRODYNAMIC
MIXING  ZONE in which  strong  initial mixing takes place.***

2) Buoyant spreading  at  layer boundary:  The  plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase.  The  mixing rate
is relatively small.  The plume  may interact  with a nearby
bank or shoreline.

3)  Passive  ambient   mixing:   After  some  distance  the
background turbulence  in  the ambient  shear  flow becomes the
dominating mixing mechanism. The  passive  plume is growing
in  depth  and in width.  The plume may interact  with  the
channel bottom and/or banks.

*** Predictions will be terminated in zone  2 or 3 depending
on the definitions  of  the LEGAL MIXING  ZONE  or the REGION
OF INTEREST.***

SPECIAL CASE: If the ambient is  stagnant, so that advection
and diffusion by the ambient flow  (zones 2  and 3)  cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zone 1) and the predictions will be terminated at this
stage.   Such  stagnant  water predictions may  be  a  useful
initial mixing  indicator for a given site  and  discharge
design.  For practical  final   predictions,  however,  the


                            209

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advection and diffusion of the  ambient  flow - no matter how
small in magnitude - should be considered.

SPECIAL SPECIAL CASE: If, in addition,  the discharge is non-
buoyant, then no steady-state behavior is possible in this
case. The repeated recirculation in the near-field will lead
to an  unsteady concentration  build-up.  This would  be an
UNDESIRABLE discharge  design,  and no  reliable  predictive
techniques exist for this situation.

CORMIX1  WILL  NOT PROVIDE  A DETAILED  PREDICTION  FOR THIS
CASE.
C.2 H-Flow Classes

FLOW CLASS HI

A submerged buoyant  effluent  issues horizontally or near-
horizontally  from  the  discharge  port.    The  discharge
configuration is  hydrodynamically "stable",  that  is   the
discharge strength (measured by its momentum flux) is weak
in   relation to  the layer depth  and in relation  to the
stabilizing  effect of the discharge buoyancy (measured by
its buoyancy flux).  The following flow zones exist:

1) Momentum-dominated near-field jet:  The  flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.

2) Buoyancy-dominated near-field plume: After some distance
the  discharge  buoyancy  becomes  the  dominating  factor
(plume-like). The plume  deflection by the ambient current
is still weak. Alternate possibility: Depending on the ratio
of  the  jet  to  crossflow  length  scale   to  the plume  to
crossflow length  scale the  above zone may be replaced by
a momentum-dominated far-field jet:

2)  Momentum-dominated  far-field  jet:  The jet  has become
strongly deflected by the ambient current.

3)  Buoyancy-dominated  far-field  plume: The plume has been
strongly deflected by the current and is  slowly rising.

4)  Layer   boundary   approach:   The  bent-over  submerged
jet/plume approaches the layer  boundary   (water surface or
pycnocline).  Within a  short  distance the  concentration
distribution  becomes relatively uniform  across the plume
width and thickness.

***  The zones  listed above  constitute  the  HYDRODYNAMIC
MIXING  ZONE in which strong initial mixing takes place.***
                            210

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5) Buoyant spreading at  layer  boundary:  The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient  current. The plume
thickness may decrease  during this phase. The mixing rate
is relatively small. The plume  may interact with a nearby
bank or shoreline.

6)  Passive  ambient  mixing:   After   some  distance  the
background turbulence in the ambient shear  flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth  and in width.  The plume  may  interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated in zone  5 or 6 depending
on the definitions  of the  LEGAL MIXING ZONE or the REGION
OF INTEREST.  ***
FLOW CLASS H2

A submerged buoyant effluent  issues  horizontally or near-
horizontally  from the  discharge  point.    The  discharge
configuration is  hydrodynamically  "stable",  that  is   the
discharge strength (measured by its momentum flux) is weak
in   relation to  the  layer depth.  The  discharge buoyancy
plays a minor  role in this case.  The following flow zones
exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected by the ambient current.

2) Momentum-dominated far-field jet:  The  jet  has become
strongly deflected by the ambient  current and  is slowly
rising.

3)  Layer  boundary   approach:   The   bent-over  submerged
jet/plume approaches  the layer  boundary (water surface or
pycnocline).  Within   a  short  distance the  concentration
distribution  becomes  relatively uniform across  the plume
width and thickness.

***  The zones  listed above  constitute the  HYDRODYNAMIC
MIXING ZONE  in which  strong initial mixing takes place. ***

4) Buoyant spreading  at layer boundary:  The  plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being  advected by the ambient current. The plume
thickness may decrease  during this phase.  The mixing rate
is relatively small.  The plume  may interact with a nearby
bank or shoreline.
                            211

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5)  Passive  ambient  mixing:  After   some  distance  the
background turbulence in the  ambient shear  flow becomes the
dominating mixing mechanism. The  passive  plume is growing
in depth  and in  width.  The plume  may interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated in zone  4 or 5 depending
on the definitions  of the  LEGAL MIXING ZONE or the REGION
OF INTEREST. ***

SPECIAL CASE: If  discharge is  non-buoyant, then the layer
boundary buoyant spreading regime (zone 4) is absent.
FLOW CLASS H3

A submerged buoyant  effluent  issues  horizontally or near-
horizontally  from  the  discharge  port.    The  discharge
configuration is  hydrodynamically  "stable",  that  is   the
discharge strength (measured by its momentum flux) is weak
in   relation to  the layer depth  and  in relation  to the
stabilizing  effect of the discharge buoyancy (measured by
its buoyancy flux).   The buoyancy effect is very strong in
the present case.  The following flow zones exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected by the ambient current.

2) Buoyancy-dominated near-field plume: After some distance
the  discharge  buoyancy  becomes  the  dominating  factor
(plume-like). The plume  deflection by  the  ambient current
is still weak.

3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary  (water surface
or pycnocline) at a near-vertical angle. After impingement
the  flow spreads more or less  radially along  the layer
boundary. In   particular,  the  flow  spreads  some distance
upstream against the ambient  flow,  and laterally across the
ambient  flow.  This   spreading  is dominated by  the strong
buoyancy of the discharge.

***  The zones  listed above  constitute the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4) Buoyant  spreading at  layer boundary:  The plume spreads
laterally along the  layer boundary (surface or pycnocline)
while it is  being  advected by the ambient current. The plume
thickness may decrease  during this phase.  The mixing rate
is relatively small. The plume  may interact with a nearby
bank or  shoreline.
                            212

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5)  Passive  ambient  mixing:   After  some  distance  the
background turbulence in the ambient  shear  flow becomes the
dominating mixing mechanism. The  passive plume is growing
in depth  and in  width.  The plume  may  interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated in zone  4 or 5 depending
on the definitions  of the  LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
FLOW CLASS H4-0

A submerged buoyant  effluent  issues horizontally or near-
horizontally  from the  discharge port.  The  discharge  is
co-flowing  or nearly co-flowing with the ambient current.
The discharge  configuration  is  hydrodynamically "stable",
that is  the  discharge  strength (measured by its momentum
flux)   is  weak  in   relation to  the  layer  depth  and  in
relation  to  the  stabilizing    effect  of  the  discharge
buoyancy  (measured  by its buoyancy flux).    The buoyancy
effect is very  strong in  the  present case.  This discharge
configuration  is  very susceptible  to attachment of   the
jet/plume  to   the bottom  of the  receiving  water.   The
following flow zones exist:

1) Momentum-dominated near-field jet:  The flow is initially
dominated by the effluent  momentum  (jet-like)  and is weakly
advected by the ambient current.

2)  Buoyancy-dominated  near-field   plume:  After  a  short
distance the    discharge  buoyancy  becomes  the  dominating
factor  (plume-like).  The   plume  rises  upward  while  the
advection by the ambient current is still weak.

3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary  (water surface
or pycnocline) at a near-vertical angle.  After impingement
the flow  spreads  more  or less  radially along  the layer
boundary.   In  particular,   the  flow spreads  some distance
upstream against the  ambient flow,  and laterally across the
ambient flow.  This  spreading is  dominated by  the  strong
buoyancy of the discharge.

*** The zones  listed above  constitute   the  HYDRODYNAMIC
MIXING ZONE in which  strong initial  mixing takes place.***

4) Buoyant  spreading  at layer boundary:  The plume spreads
laterally along the layer boundary  (surface or pycnocline)
while  it  is being   advected  by the  ambient  current.  The
plume thickness may  decrease  during this phase. The mixing
rate is relatively  small.  The plume   may  interact  with a
nearby bank or shoreline.
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5)  Passive  ambient  mixing:  After   some  distance  the
background turbulence in the  ambient shear  flow becomes the
dominating mixing  mechanism. The passive plume is growing
in depth  and  in width.   The   plume may  interact  with the
channel bottom and/or banks.

*** Predictions will be  terminated  in zone  4 or 5 depending
on the definitions  of the  LEGAL  MIXING ZONE  or the REGION
OF INTEREST. ***

SPECIAL CASE:  If the ambient is stagnant,  then advection and
diffusion by  the  ambient  flow  (zones  4 and 5)  cannot be
considered.  The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this  stage.  Such stagnant  water  predictions may  be a
useful  initial mixing   indicator  for  a  given  site  and
discharge design.  For practical final predictions, however,
the advection and  diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS H4-90

A submerged buoyant  effluent  issues  horizontally or near-
horizontally from the discharge port. The discharge is at,
or approximately at,  a right angle with the ambient current.
The discharge  configuration  is hydrodynamically "stable",
that is  the  discharge strength  (measured by  its momentum
flux)  is weak in  relation to the layer depth and in relation
to  the  stabilizing  effect  of  the  discharge  buoyancy
(measured by its  buoyancy flux). The buoyancy effect  is very
strong in the present case. This discharge configuration is
very susceptible to  attachment  of  the  jet/plume  to  the
bottom  of  the receiving water.  The  following  flow zones
exist:

1) Momentum-dominated near-field jet:  The flow is initially
dominated by the effluent momentum (jet-like) and is weakly
advected by the ambient current.

2)  Buoyancy-dominated  near-field  plume:  After  a  short
distance  the  discharge  buoyancy  becomes  the  dominating
factor  (plume-like). The  plume  rises  upward  while  the
advection by the ambient current is still weak.

3) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline) at a near-vertical angle. After impingement
the  flow spreads more  or less  radially along  the layer
boundary.  In particular,  the  flow spreads some distance
upstream against the ambient  flow,  and laterally across the
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ambient  flow.  This spreading  is  dominated by  the strong
buoyancy of the discharge.

***  The zones  listed above  constitute  the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4) Buoyant spreading  at  layer  boundary:  The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient  current. The plume
thickness may decrease during  this phase. The mixing rate
is relatively small.  The  plume may  interact with a nearby
bank or shoreline.

5)  Passive  ambient  mixing:   After  some  distance  the
background turbulence in  the ambient  shear flow becomes the
dominating mixing mechanism. The  passive plume is growing
in depth  and in  width.  The plume  may  interact  with the
channel bottom and/or banks.

*** Predictions will be terminated in zone 4 or 5 depending
on the definitions  of the LEGAL MIXING ZONE or the REGION
OF INTEREST.  ***

SPECIAL CASE: If the ambient is stagnant,  then  advection and
diffusion by  the  ambient  flow (zones 4   and  5)  cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this  stage.  Such  stagnant  water  predictions may  be a
useful  initial mixing  indicator  for  a given  site  and
discharge design.  For practical final predictions, however,
the advection and  diffusion of  the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS H4-180

A submerged buoyant  effluent  issues  horizontally or near-
horizontally  from the  discharge port.  The  discharge  is
directly  opposed (or approximately so) to the direction of
the  ambient  current.   This is  a highly complicated  and
UNDESIRABLE  discharge     configuration.   Generally,   the
upstream  issuing jet  may  exhibit  an unsteady  pulsating
pattern with potential  attachment to the  bottom. There is
no reliable prediction methodology for this flow.

CORMIX1 WILL  NOT PROVIDE  A DETAILED PREDICTION  FOR  THIS
CASE.
FLOW CLASS H5-0

A submerged buoyant  effluent  issues  horizontally or near-
horizontally  from the  discharge port.  The discharge  is


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co-flowing, or  nearly  co-flowing,  with the  ambient flow.
The discharge configuration is hydrodynamically "unstable",
that is  the  discharge  strength (measured by  its momentum
flux) dominates the flow  in  relation  to  the  limited layer
depth.  The effect of  buoyancy is negligible and the initial
discharge is  usually  attached to the bottom.  The following
flow zones exist:

1) Momentum-dominated near-field jet (bottom-attached): The
flow is dominated by the effluent  momentum (jet-like).  The
jet attaches  to the bottom  and is weakly advected  by  the
ambient flow.

2) Layer boundary contact/full vertical mixing:  After some
distance the  jet has grown vertically over  the  full layer
depth.    From now on  the flow is vertically   mixed  and
generally ceases to be jet-like.

3) Passive ambient mixing: The vertically fully mixed plume
is   further  advected  by the  ambient  flow and  spreads
laterally  through  turbulent  diffusion.   The  plume  may
interact laterally with any  nearby bank or shoreline.

*** The ambient flow plays an  important  role in this flow
configuration. Hence,  all  the zones listed above constitute
the HYDRODYNAMIC  MIXING ZONE with strong  initial  mixing.
Predictions will be terminated  in  zone 3  depending  on  the
definitions  of  the LEGAL MIXING  ZONE or  the   REGION  OF
INTEREST. ***

SPECIAL CASE: If the ambient  is  stagnant, so that advection
and  diffusion by  the  ambient flow   (zone  3)   cannot  be
considered. The mixing is limited  to the discharge-induced
mixing zones  (zones 1  and 2) and the predictions will  be
terminated at this stage.  Such  predictions will present a
conservative  lower bound  on  the mixing   capacity as they
neglect any further mixing beyond  the stage  where  the  jet
has  grown  to the  full layer  depth.   Such stagnant water
predictions may be a useful initial mixing indicator for a
given  site and  discharge design.    For practical  final
predictions,   however,   the advection and   diffusion  of  the
ambient flow - no matter how  small  in  magnitude - should be
considered.
FLOW CLASS H5-90

A submerged buoyant  effluent  issues horizontally or near-
horizontally from the discharge port. The discharge is at,
or approximately at,  a right angle with the ambient current.
The discharge configuration is hydrodynamically "unstable",
that is  the  discharge strength  (measured by its momentum
flux) dominates  the  flow  in relation to the limited layer
                            216

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depth. The effect of buoyancy is negligible and the initial
discharge is  usually attached to  the  bottom.   This  is a
highly complicated and UNDESIRABLE discharge configuration.
The laterally  discharging  jet the tends  to  full vertical
mixing and will block the  ambient  flow.  This will cause a
recirculating eddy region downstream of the discharge. There
is no reliable prediction methodology for this flow.

CORMIX1 WILL  NOT PROVIDE  A DETAILED PREDICTION  FOR THIS
CASE.

FLOW CLASS H5-1SO

A submerged buoyant  effluent issues  horizontally or near-
horizontally  from the  discharge   port.  The  discharge  is
directly opposed, or nearly opposed, to  the direction of
the  ambient  current.    The discharge  configuration  is
hydrodynamically "unstable", that  is the discharge strength
(measured by  its momentum flux)   dominates   the  flow  in
relation to the limited  layer depth.  The effect of buoyancy
is negligible and the initial discharge is usually attached
to the bottom.  This is a highly complicated and UNDESIRABLE
discharge  configuration.  Generally,  the upstream issuing
jet may exhibit an unsteady pulsating pattern and blocking
of the ambient flow  over the full  water depth. There is no
reliable prediction methodology for this flow.

CORMIX1 WILL  NOT PROVIDE  A DETAILED PREDICTION  FOR THIS
CASE.
C.3 S-Flow Classes

FLOW CLASS SI

This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly jet-like
flow gets trapped at some terminal  (equilibrium) level. The
trapping is also affected by the reasonably strong ambient
crossflow. Following the trapping zone, the discharge flow
forms  an  internal  layer  that is  further  influenced  by
buoyant spreading and passive diffusion. The  following flow
zones exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected by the ambient current.

2) Momentum-dominated  far-field jet:  The  jet has  become
strongly deflected  by the  ambient current  and  is  slowly
rising toward the trapping level.
                            217

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3)  Terminal  layer   approach:   The  bent-over  submerged
jet/plume  approaches  the terminal  level.  Within  a  short
distance the concentration distribution becomes relatively
uniform across the plume width and thickness.

***  The zones  listed above  constitute the HYDRODYNAMIC
MIXING ZONE in which strong  initial mixing takes place.***

4) Buoyant spreading in internal layer: The discharge flow
within  the internal  layer  spreads  laterally while  it  is
being advected by the ambient current. The plume thickness
may  decrease  during  this  phase.   The  mixing  rate  is
relatively small. The  plume  may  interact with a nearby bank
or shoreline.

5)  Passive  ambient  mixing:   After  some  distance  the
background turbulence  in the ambient shear flow becomes the
dominating mixing mechanism.  The passive  plume is growing
in depth and in width. The plume may  interact  with the upper
layer boundary,  channel bottom and/or banks.

*** Predictions will be terminated in zone 4  or 5 depending
on the  definitions of the LEGAL MIXING ZONE  or the REGION
OF INTEREST. ***
FLOW CLASS 82

This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly jet-like
flow issues vertically, or near-vertically, upward and gets
trapped at some terminal (equilibrium) level. The crossflow
is weak  in  the present situation.   Following the trapping
zone, the  discharge flow forms an  internal  layer  that is
further  influenced  by buoyant   spreading  and  passive
diffusion.  The following flow zones exist:

1)    Momentum-dominated   near-field   jet    in   linear
stratification:  The flow  is  initially  dominated by  the
effluent momentum (jet-like)  and is  weakly deflected by the
ambient current and the density stratification.

2) Terminal layer impingement/upstream spreading: The weakly
bent jet/plume approaches (impinges) the terminal layer at
a near- vertical angle,  and may overshoot that level to some
extent.  After impingement the  flow spreads more  or less
radially at the  terminal  level forming  an internal layer.
In  particular, the  flow spreads  some  distance  upstream
against the ambient flow, and laterally across  the ambient
flow. This  spreading  is dominated  by the buoyant collapse
of   the   internal   layer   within   the   linear   ambient
stratification.
                            218

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***  The zones  listed above  constitute the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

3) Buoyant spreading in internal layer: The discharge flow
within  the  internal layer  spreads  laterally while  it is
being advected by the ambient current. The plume thickness
may  decrease  during  this  phase.   The  mixing  rate  is
relatively small. The plume may  interact with a nearby bank
or shoreline.

4)  Passive   ambient  mixing:   After  some  distance  the
background turbulence in the ambient  shear flow becomes the
dominating mixing mechanism. The  passive  plume  is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.

*** Predictions will be  terminated in zone 3 or 4 depending
on the definitions  of the  LEGAL MIXING ZONE  or  the REGION
OF INTEREST.***

SPECIAL CASE:  If the ambient is  stagnant,  then advection
and diffusion by the ambient flow  (zones 3 and 4) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 and 2)  and  the predictions will be terminated
at this  stage. Such stagnant  water  predictions may  be a
useful  initial  mixing   indicator  for  a  given  site  and
discharge design. For practical  final predictions, however,
the advection and diffusion of the ambient flow - no matter
how small in magnitude - should be considered.
FLOW CLASS S3

This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly jet-like
flow  issues  horizontally,  or  near-horizontally,  into the
density  stratified layer and gets trapped at  some terminal
(equilibrium) level. The crossflow  is  weak  in the present
situation.  Following the trapping zone, the discharge flow
forms  an  internal   layer that  is  further  influenced  by
buoyant spreading  and  passive  diffusion.   The  following
flow zones exist:

1)    Momentum-dominated    near-field   jet    in    linear
stratification:   The flow  is  initially  dominated by the
effluent momentum (jet-like)  and  is  weakly deflected by the
ambient current and the density  stratification.

2) Terminal layer injection/upstream spreading: The weakly
bent  jet/plume approaches (injects into) the terminal layer
at  a  near-   horizontal  angle.  After  injection  the  flow
spreads more or  less radially at the terminal  level forming
an  internal  layer.  The residual horizontal  momentum  flux
                            219

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within  the   jet  affects  that   spreading   process.   In
particular, the flow spreads some distance upstream against
the ambient  flow,  and laterally across  the  ambient flow.
This spreading is dominated by the buoyant collapse of the
internal layer  within the linear  ambient stratification.

*** The zones  listed above  constitute  the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

3) Buoyant spreading in internal layer: The discharge flow
within  the  internal  layer spreads laterally  while it is
being advected by the ambient current. The plume thickness
may  decrease  during  this    phase.  The mixing  rate  is
relatively small. The  plume may  interact  with a nearby bank
or shoreline.

4)  Passive   ambient  mixing:   After   some   distance  the
background turbulence  in  the  ambient shear flow becomes the
dominating mixing mechanism. The passive plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.

*** Predictions will be terminated  in  zone 3 or 4 depending
on  the definitions of the LEGAL MIXING  ZONE or the REGION
OF INTEREST.  ***

SPECIAL CASE:  If the  ambient is stagnant,  then advection
and diffusion by the ambient  flow (zones  3 and  4) cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 and 2) and  the  predictions  will be terminated
at this stage.  Such  stagnant  water predictions may  be a
useful  initial  mixing   indicator   for  a given site  and
discharge design. For practical final  predictions, however,
the advection and diffusion  of the ambient flow - no matter
how small  in  magnitude - should be  considered.
FLOW CLASS S4

This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly plume-like
flow gets trapped at some terminal  (equilibrium)  level. The
trapping  is also affected by the reasonably strong ambient
crossflow. Following the trapping  zone, the discharge flow
forms  an  internal  layer  that is further  influenced  by
buoyant spreading and passive diffusion.  The following flow
zones exist:

1) Momentum-dominated near-field jet:  The flow is initially
dominated by the effluent momentum (jet-like)  and is weakly
deflected by the ambient current.
                            220

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2)  Momentum-dominated  far-field jet:  The jet  has  become
strongly deflected by the ambient current.

3)  Buoyancy-dominated far-field plume: After some distance,
the plume buoyancy starts to affect the flow.  The plume is
strongly  deflected  by  the  current  and  is slowly  rising
toward the terminal level.

4)   Terminal   layer   approach:   The  bent-over  submerged
jet/plume approaches  the terminal  level.  Within a  short
distance the concentration distribution becomes relatively
uniform across the plume width and thickness.

***The zones listed above constitute the HYDRODYNAMIC MIXING
ZONE in which strong initial mixing takes place. ***

5)  Buoyant spreading in internal layer: The discharge flow
within the  internal  layer  spreads  laterally  while  it is
being advected by the ambient current. The plume thickness
may  decrease  during  this  phase.  The  mixing  rate  is
relatively small. The plume  may interact with a nearby bank
or shoreline.

6)   Passive  ambient  mixing:   After  some  distance  the
background turbulence in the ambient shear  flow becomes the
dominating mixing mechanism. The passive  plume is growing
in depth and in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.

*** Predictions will  be  terminated  in zone  5 or 6 depending
on  the definitions of the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***
PLOW CLASS S5

This flow configuration is profoundly affected by the linear
ambient density stratification. The predominantly plume-like
flow  rises vertically  upward  and  gets  trapped  at  some
terminal  equilibrium  level.  The crossflow is  weak in the
present  situation.   Following  the  trapping zone,  the
discharge  flow forms an  internal  layer  that is  further
influenced by buoyant spreading and  passive diffusion.  The
following flow zones exist:

1)    Momentum-dominated    near-field   jet    in   linear
stratification:  The flow  is  initially  dominated by the
effluent momentum (jet-like)  and is  weakly deflected by the
ambient current and the density stratification.

2)   Buoyancy-dominated   near-field   plume   in   linear
stratification:  After  some   distance,  the   flow  becomes
dominated  by  the  effluent  buoyancy  (plume-like)  and  is


                           221

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weakly  affected  by  the  ambient current  and the  density
stratification.

3) Terminal layer impingement/upstream spreading: The weakly
bent jet/plume approaches (impinges)  the terminal layer at
a near- vertical angle, and may overshoot that level to some
extent. After  impingement the  flow  spreads more  or less
radially at the terminal  level  forming  an internal layer.
In  particular,  the  flow spreads  some  distance  upstream
against the ambient flow, and laterally across the ambient
flow. This spreading  is  dominated  by the  buoyant collapse
of   the  internal   layer  within   the  linear   ambient
stratification.

***  The zones  listed above  constitute  the HYDRODYNAMIC
MIXING ZONE in which strong  initial mixing takes place.***

4) Buoyant spreading in internal layer:  The discharge flow
within  the  internal layer  spreads  laterally while  it  is
being advected by the ambient current. The plume thickness
may  decrease  during  this  phase.  The  mixing  rate  is
relatively small.  The plume  may  interact with a nearby bank
or shoreline.

5)  Passive  ambient  mixing:   After some   distance  the
background turbulence in  the ambient  shear flow becomes the
dominating mixing mechanism.  The passive  plume  is growing
in depth and  in width. The plume may interact with the upper
layer boundary, channel bottom and/or banks.
*** Predictions will be terminated  in zone 4  or 5 depending
on the  definitions  of the LEGAL MIXING  ZONE or  the REGION
OF INTEREST.  ***

SPECIAL CASE:  If the ambient is stagnant, then advection and
diffusion by  the  ambient flow  (zones 4 and 5)  cannot  be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at  this stage.  Such  stagnant water  predictions may  be a
useful  initial mixing   indicator  for  a  given  site  and
discharge design.  For practical  final predictions, however,
the advection and diffusion  of the  ambient flow - no matter
how small in magnitude - should be considered.
C.4 NV-Plow Classes

FLOW CLASS NV1

A submerged negatively  buoyant  effluent issues vertically
or near- vertically from the discharge port. The effect of
ambient  velocity  is  relatively  strong.  The  discharge
configuration  is hydrodynamically  "stable",  that  is the
discharge strength (measured by its momentum flux) is weak
                            222

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in  relation  to  the  layer  depth  and  in  relation  to  the
stabilizing  effect  of  the negative  discharge  buoyancy
(measured by its buoyancy  flux).  The  following flow zones
exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the upward effluent momentum (jet-like) and is
weakly deflected by the ambient current.

2)  Momentum-dominated  far-field  jet:  The  jet  becomes
strongly deflected by  the ambient current. It  rises  to a
maximum  height,  less  than the  layer  depth,  which  is
controlled by the opposing action  of the negative buoyancy.
3)  Buoyancy-dominated  far-field plume: After  the maximum
height of rise,  the negative discharge buoyancy becomes the
dominating  factor  giving  plume-like  flow.  The  strongly
deflected plume is slowly descending toward the bottom.

4) Bottom approach: The bent-over submerged plume approaches
the    bottom   boundary.   Within  a  short  distance  the
concentration    distribution  becomes  relatively  uniform
across the plume width and thickness.

***  The   zones  listed above  constitute  the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

5) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient  current.  The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.

6)  Passive  ambient  mixing:   After  some  distance  the
background turbulence in the ambient shear flow becomes the
dominating mixing mechanism.  The passive  plume is growing
in depth and in  width. The plume may interact with the layer
surface and/or banks.

*** Predictions will be  terminated in zone 5 or 6 depending
on the definitions  of the  LEGAL MIXING ZONE  or the REGION
OF INTEREST. ***
FLOW CLASS NV2

A submerged negatively  buoyant  effluent issues vertically
or near- vertically from the discharge port. The effect of
ambient velocity  is weak.   The  discharge configuration is
hydrodynamically  "stable",  that  is  the discharge strength
(measured by its momentum flux)  is weak in relation to the
layer depth and in relation to the stabilizing effect of the
                            223

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negative discharge buoyancy (measured by its buoyancy flux) .
The following flow zones exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the upward effluent momentum (jet-like) and is
weakly  deflected by the  ambient current.  It  rises  to  a
maximum  height,  less   than   the  layer  depth,  which  is
controlled by the opposing action of the negative buoyancy.

2) Buoyancy-dominated  near-field plume: After  the maximum
height of rise,  the  negative discharge buoyancy becomes the
dominating factor (plume-like  flow). The strongly deflected
plume is rapidly falling toward the bottom.

3)  Bottom  boundary impingement/upstream  spreading:  The
weakly bent jet/plume impinges on the bottom boundary at a
near-vertical angle.  After impingement the flow spreads more
or less radially along the bottom.  In particular, the flow
spreads some distance upstream against the ambient flow, and
laterally  across  the   ambient  flow.  This  spreading  is
dominated by the strong buoyancy of the discharge.

***  The zones  listed   above  constitute the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4) Buoyant spreading at bottom boundary: The plume spreads
laterally along the  bottom while it is being  advected by the
ambient current.  The plume thickness may  decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.

5)  Passive   ambient  mixing:   After  some   distance  the
background turbulence in the ambient  shear flow becomes the
dominating mixing mechanism.  The passive  plume is growing
in depth and in  width. The plume may interact with the layer
surface and/or banks.

*** Predictions will be terminated  in zone 4 or 5 depending
on the  definitions  of  the LEGAL MIXING ZONE or the REGION
OF INTEREST. ***

SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion  by the ambient flow  (zones  4 and 5)  cannot be
considered. The mixing  is  limited to the hydrodynamic mixing
zone  (zones  1 to 3)  and the predictions will be terminated
at this stage.   Such stagnant water predictions  may  be a
useful  initial  mixing  indicator  for  a  giv^n  site  and
discharge design. For practical final predictions, however,
the advection and diffusion of the  ambient flow  -  no matter
how small  in magnitude  -  should be considered.
                            224

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FLOW CLASS NV3

A submerged negatively  buoyant  effluent issues vertically
or near- vertically from the discharge port. The effect of
ambient  velocity  is  relatively  strong.   The  discharge
configuration  is hydrodynamically  "stable",  that  is  the
discharge strength (measured by its momentum flux) is weak
in  relation  to  the  layer  depth  and  in relation  to  the
stabilizing  effect  of  the negative  discharge  buoyancy
(measured by its buoyancy  flux).  The following flow zones
exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the upward effluent momentum (jet-like) and is
weakly deflected by the ambient current.

2)  Momentum-dominated  far-field  jet:  The  jet  becomes
strongly deflected by the ambient current.

3)  Layer  boundary   approach:   The  bent-over  submerged
jet/plume approaches  the layer  boundary (water surface or
pycnocline).  Within   a  short  distance  the concentration
distribution becomes  relatively uniform across  the plume
width and thickness.

4) Fall  down:  Because of the negative  buoyancy  the plume
detaches  from  the layer boundary  and  starts to descend
toward the bottom.

5) Buoyancy-dominated far-field plume:  After  the maximum
height of rise, the negative discharge buoyancy becomes the
dominating  factor  giving  plume-like  flow. The  strongly
deflected plume is slowly descending toward the bottom.

6) Bottom approach: The bent-over submerged plume approaches
the   bottom   boundary.  Within  a  short   distance   the
concentration distribution becomes relatively uniform across
the plume width and thickness.

***  The  zones  listed  above  constitute the  HYDRODYNAMIC
MIXING ZONE in which  strong initial  mixing takes place.***

7) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being  advected by the
ambient  current. The  plume thickness may  decrease during
this phase.  The mixing rate is relatively small.  The plume
may interact with a nearby bank or shoreline.

8)  Passive  ambient   mixing:   After  some  distance  the
background turbulence in the ambient shear flow becomes the
dominating mixing  mechanism. The  passive plume is growing
                            225

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in depth and in width. The plume may interact with the layer
surface and/or banks.

*** Predictions will be  terminated  in zone 7 or 8 depending
on the definitions  of the LEGAL MIXING  ZONE  or the REGION
OF INTEREST. ***
FLOW CLASS NV4

A submerged negatively buoyant  effluent issues vertically
or near-vertically from the discharge port. The layer depth
is limited.  The discharge configuration  is hydrodynamically
"unstable",  that is the discharge strength  (measured by its
momentum  flux)  dominates   the  flow in  relation to  the
limited layer depth. The role of the negative buoyancy is
secondary.  The following flow zones exist:

1) Momentum-dominated near-field jet: The flow is dominated
by the effluent momentum  (jet-like) and  is weakly deflected
by the ambient  current.

2)  Layer  boundary  impingement/full  vertical mixing:  The
weakly  bent jet  impinges on  the  layer  boundary  (water
surface or  pycnocline) at a near-vertical  angle. Given the
shallow layer depth and the weak buoyancy of the discharge,
the flow becomes unstable  after impingement. This results
in  a recirculating  region    immediately  downstream  that
extends over the full layer depth.

3) Passive ambient mixing: The vertically fully mixed plume
is    further  advected by the  ambient  flow and  spreads
laterally through ambient diffusion.  The plume may interact
with a nearby bank or shoreline.

*** The ambient flow plays an important role in this flow
configuration. Hence,  all the zones listed  above constitute
the HYDRODYNAMIC  MIXING  ZONE with strong  initial mixing.
Predictions will be terminated  in  zone  3  depending on the
definitions  of the  LEGAL MIXING  ZONE or the REGION  OF
INTEREST. ***
PLOW CLASS NV5

A submerged  negatively  buoyant effluent issues vertically
or near-vertically from the discharge port, the layer depth
is limited. The discharge configuration  is hydrodynamically
"unstable", that is the discharge  strength  (measured by its
momentum flux) dominates the flow in relation to the limited
layer depth and in relation to the weak stabilizing effect
of the discharge buoyancy  (measured by its buoyancy flux).
However, the  negative  buoyancy is generally strong enough
                            226

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to affect the flow at larger distances downstream from the
unstable  initial  region.  The following  flow  zones exist:
1) Unstable recirculation/buoyant restratif ication/upstream
spreading:  The  buoyant  jet  rises  near-vertically  and
impinges   on   the  layer   boundary  (water   surface  or
pycnocline).  After impingement the mixed flow recirculates
over  the  limited  layer   depth   and  becomes  partially
re-entrained  into  the  discharge  jet.  The  degree    of
recirculation - and hence the  overall  mixing in this region
- is controlled by restratification of the flow at the edge
of this recirculating  region.  The  restratified flow spreads
along the layer bottom. In particular,  the flow spreads some
distance upstream against the ambient current, and laterally
across the ambient flow.

*** The region described above constitutes the HYDRODYNAMIC
MIXING  ZONE  in which  strong initial mixing takes place.***

2)  Buoyant spreading  at layer  bottom:  The plume  spreads
laterally along the bottom while it is  being advected by the
ambient  current.  The  plume thickness may decrease during
this phase. The mixing rate is relatively small.  The plume
may interact with a nearby bank or shoreline.

3)  Passive   ambient  mixing:   After   some   distance  the
background turbulence  in the ambient shear flow becomes the
dominating mixing mechanism.  The  passive plume is  growing
in depth and in width. The plume may interact with the layer
upper boundary and/or banks.

*** Predictions will be terminated in  zone 2 or 3 depending
on the definitions of the  LEGAL MIXING  ZONE  or the REGION
OF INTEREST.***

SPECIAL CASE:  If the ambient is  stagnant, so that advection
and diffusion by the ambient flow  (zones  2 and 3)  cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zone

1) and the predictions  will be terminated at  this stage.
Such stagnant water predictions  may  be a useful  initial
mixing indicator for a given site  and  discharge design. For
practical  final predictions,  however,  the advection and
diffusion  of  the ambient  flow  -   no  matter  how small  in
magnitude - should be considered.
                            227

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c.5 NH-Flow Classes

FLOW CLASS NH1

A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The effect of
ambient velocity is relatively strong. Alternatively, this
flow  may  arise -  even  though  the discharge   may  be
positively buoyant  - when the discharge is oriented downward
and   is   arrested   near   the   bottom  by   some  ambient
stratification.       The    discharge   configuration   is
hydrodynamically "stable", that is  the discharge strength
(measured by its momentum flux)  is weak in  relation to the
layer depth and in relation to the stabilizing effect of the
negative discharge buoyancy (measured by  its buoyancy flux).
The following flow zones exist:

1) Momentum-dominated near-field jet:  The flow is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected  by  the ambient  current.  It rises to a  maximum
height (less than the layer depth)  which  is controlled by
the negative  buoyancy.

2)  Buoyancy-dominated far-field plume:  After  the  maximum
height of  rise, the negative discharge buoyancy  becomes the
dominating factor (plume -like flow). The strongly deflected
plume is slowly descending toward  the bottom.

3) Bottom approach: The bent-over submerged plume approaches
the   bottom  boundary.   Within   a   short   distance  the
concentration    distribution  becomes relatively  uniform
across the plume width and  thickness.

***  The   zones  listed above  constitute the HYDRODYNAMIC
MIXING ZONE in which  strong initial mixing takes place.***

4) Buoyant spreading  at bottom boundary: The plume spreads
laterally along the bottom while it is being  advected by the
ambient  current. The plume thickness may  decrease during
this  phase. The mixing rate is  relatively small. The plume
may interact  with a  nearby bank or shoreline.

5)  Passive  ambient   mixing:   After  some   distance  the
background  turbulence in  the ambient shear flow becomes the
dominating mixing  mechanism. The passive plume is growing
in  depth and in width.  The  plume may  interact with the
layer surface and/or  banks.

*** Predictions will be terminated in zone 5  or  6 depending
on  the definitions  of the LEGAL MIXING  ZONE or the REGION
OF  INTEREST. ***
                            228

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FLOW CLASS NH2

A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The effect of
ambient   velocity is  weak.  Alternatively,  this  flow may
arise - even though the discharge may be positively buoyant
- when the  discharge  is oriented  downward and is arrested
near  the  bottom  by  some  ambient  stratification.  The
discharge configuration is hydrodynamically "stable", that
is the discharge  strength (measured  by  its  momentum flux)
is weak in  relation to the  layer  depth  and  in relation to
the stabilizing effect of the  negative  discharge buoyancy
(measured by  its  buoyancy flux).  The following flow zones
exist:

1) Momentum-dominated near-field jet: The  flow  is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected by  the ambient current.  It  rises to  a  maximum
height (less  than  the  layer depth)  which  is controlled by
the negative buoyancy.

2) Buoyancy-dominated  near-field plume: After the maximum
height of rise, the negative discharge buoyancy becomes the
dominating factor (plume-like flow). The strongly deflected
plume is rapidly falling toward the bottom.

3)  Bottom  boundary  impingement/upstream spreading:  The
weakly bent jet/plume  impinges on the bottom boundary at a
near-vertical angle. After impingement the  flow spreads more
or less radially along the bottom. In particular, the flow
spreads some distance upstream against the  ambient flow, and
laterally  across  the  ambient  flow.  This  spreading  is
dominated by the strong buoyancy of the discharge.

***  The  zones  listed  above  constitute  the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being  advected by the
ambient current.  The  plume thickness may decrease during
this  phase. The mixing rate is  relatively small. The plume
may interact  with a nearby bank or shoreline.

5)  Passive   ambient   mixing:   After  some   distance  the
background  turbulence  in the ambient shear flow becomes the
dominating mixing  mechanism.  The passive plume is growing
in depth  and in width.  The   plume may interact with the
layer surface and/or banks.

*** predictions will be terminated  in zone 4 or 5 depending
on the definitions of  the LEGAL MIXING  ZONE or the REGION
OF INTEREST. ***
                            229

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SPECIAL CASE:  If the ambient is stagnant, then advection and
diffusion by  the  ambient flow  (zones  4  and 5)  cannot be
considered.  The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this  stage.  Such   stagnant water predictions  may be a
useful  initial mixing  indicator  for  a   given   site  and
discharge design.  For practical final predictions, however,
the advection and  diffusion of the ambient flow -  no matter
how small in magnitude  - should be considered.
FLOW CLASS NH3

A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The discharge
is cross-  flowing or  counterflowing  with respect  to the
ambient   flow,   and   the  ambient   velocity   is   weak.
Alternatively,  this  flow may  arise  -   even  though  the
discharge may be positively buoyant - when the discharge is
oriented downward and  is  arrested near the  bottom by some
ambient  stratification.    The  discharge  configuration  is
hydrodynamically "stable", that  is the  discharge strength
(measured by its momentum flux)  is weak in relation to the
layer depth and in relation to the stabilizing effect of the
negative discharge buoyancy (measured by its buoyancy flux).
The following flow zones exist:

1) Momentum-dominated near-field jet: The  flow is initially
dominated by the effluent momentum (jet-like) and is weakly
deflected by the ambient current.

2) Buoyancy-dominated near-field plume:  After some distance,
the  negative  discharge  buoyancy becomes the  dominating
factor (plume- like flow). The strongly deflected plume is
descending toward the bottom.

3) Bottom approach: The bent-over submerged plume approaches
the   bottom  boundary.   Within   a   short   distance   the
concentration distribution becomes relatively uniform across
the plume width and thickness.

4) Wall jet: The bottom attached flow forms a wall jet that
propagates across or against the ambient flow.

5) Flow  turning: At  some distance  the  wall  jet  becomes
turned   into  the  ambient  flow  direction.   Also,   the
concentration distribution becomes relatively uniform across
the plume width and thickness.

***  The   zones  listed  above  constitute  the HYDRODYNAMIC
MIXING ZONE  in which strong initial mixing takes place.***
                            230

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6) Buoyant spreading at bottom boundary: The plume spreads
laterally along the bottom while it is being advected by the
ambient current.  The plume thickness may  decrease during
this phase. The mixing rate is relatively small. The plume
may interact with  a  nearby  bank  or shoreline.   7) Passive
ambient  mixing:   After  some  distance   the   background
turbulence in the ambient shear flow becomes the dominating
mixing mechanism. The passive  plume is growing in depth and
in width.  The plume may  interact with the  layer surface
and/or banks.

*** Predictions will  be terminated in zone  6 or 7 depending
on the definitions of  the  LEGAL  MIXING  ZONE or the REGION
OF INTEREST.***

COUNTERFLOW  DISCHARGE:  If  the  discharge   is opposing the
ambient  flow  then  the  flow  pattern  tends  to  become
complicated   and  irregular   with   potential   unsteady
pulsations. This is an  UNDESIRABLE  discharge configuration.

CORMIX1  WILL  NOT PROVIDE  A  DETAILED  PREDICTION FOR  A
COUNTERFLOW DISCHARGE GEOMETRY.

SPECIAL CASE: If the ambient is stagnant, then advection and
diffusion  by the  ambient  flow  (zones  4  to 7)  cannot  be
considered. The mixing  is limited to the hydrodynamic mixing
zone (zones 1 to 3) and the predictions will be terminated
at this  stage.  Such stagnant water predictions  may  be a
useful  initial  mixing indicator  for  a   given  site  and
discharge design. For practical final predictions, however,
the advection and diffusion of the ambient  flow - no matter
how small in magnitude - should be considered.
FLOW CLASS NH4

A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The effect of
ambient velocity is relatively strong.  Alternatively, this
flow may arise - even though the  discharge may be positively
buoyant  -  when the discharge is oriented  downward and is
arrested near the bottom by some  ambient stratification. The
following flow zones exist:

1) Momentum-dominated near-field jet: The flow is initially
dominated by the effluent momentum  (jet-like) and is weakly
deflected by the ambient current.

2)  Momentum-dominated  far-field  jet:   The  jet  becomes
strongly deflected  by the ambient current. It  rises to a
maximum  height,   less  than the  layer  depth,  which  is
controlled by the opposing action of the negative buoyancy.
                            231

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3) Buoyancy-dominated  far-field plume: After  the maximum
height of rise,  the negative discharge buoyancy becomes the
dominating factor in plume-like flow.  The strongly deflected
plume is slowly descending toward the bottom.

4) Bottom approach: The bent-over submerged plume approaches
the  bottom   boundary.  Within   a   short   distance   the
concentration distribution becomes relatively uniform across
the plume width and thickness.

***  The zones  listed  above  constitute  the HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

5) Buoyant spreading at bottom boundary:  The plume spreads
laterally along the bottom while it is being  advected by the
ambient  current.  The plume thickness may decrease during
this phase. The mixing rate is relatively small. The plume
may interact with a nearby bank or shoreline.

6)  Passive   ambient   mixing:   After  some   distance  the
background turbulence in  the ambient  shear flow becomes the
dominating mixing mechanism.  The  passive  plume is growing
in depth and  in width. The plume may interact with the layer
surface and/or banks.

*** Predictions will be terminated in zone 5  or 6 depending
on the  definitions  of  the LEGAL MIXING ZONE or the REGION
OF INTEREST.***
FLOW CLASS NH5

A submerged negatively buoyant effluent issues horizontally
or near-horizontally from the discharge port. The discharge
is cross-  flowing or  counterflowing  with respect  to the
ambient   current.     The  discharge  configuration  is
hydrodynamically "unstable", that is the discharge strength
(measured  by  its  momentum flux)  dominates  the  flow  in
relation to the limited layer depth. The effect of  buoyancy
is negligible and the initial discharge is  usually  attached
to the bottom.   This is a highly  complicated and UNDESIRABLE
discharge configuration. The discharging jet tends to full
vertical mixing and will block the ambient flow. This will
cause  a  recirculating  eddy  region  downstream  of  the
discharge. There is no reliable prediction methodology for
this flow.

CORMIX1 WILL NOT PROVIDE  A  DETAILED PREDICTION  FOR THIS
CASE.
                            232

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C.6 Attached Flow Classes

FLOW CLASS (..)A1

Irrespective of the buoyancy or direction of the discharge,
the near-field of  this  flow configuration  is dominated by
wake attachment.  The ambient  crossflow effect  is  strong
and/or the height of the discharge port  above the bottom is
too small. This leads to rapid attachment of the discharge
flow to the bottom with a recirculation wake in the lee of
the discharge  structure.  Following the recirculation the
discharge  flow will lift off  from  the bottom due  to its
strong buoyancy.


FLOW CLASS (..)A2

Irrespective of the buoyancy or direction of the discharge,
the near-field of  this  flow configuration  is dominated by
wake attachment.  The ambient  crossflow effect  is  strong
and/or the height of the discharge port  above the bottom is
too small. This leads to rapid attachment of the discharge
flow to the bottom with a recirculation wake in the lee of
the discharge  structure.  Following the recirculation the
discharge flow will remain attached to the bottom  due to its
weaker negative buoyancy.  In the absence of wake attachment
the dominant flow class would be given by the prefix  (..).
You may  request  detailed  information on that  flow class
further below. Additional  advice on how to prevent bottom
attachment (e.g.  by increasing the height of the discharge
port)  will be provided in the summary program element SUM.
The following flow zones exist:

1) Recirculation zone:  The  discharge  flow  becomes quickly
deflected by the ambient flow  and  attaches to the bottom.
A  recirculation  eddy exists in  the  lee of  the  discharge
structure.

2)  Buoyant  spreading  at   bottom:  In  case  of  negative
discharge buoyancy only, the plume spreads laterally along
the bottom while  it  is  being  advected  by the  ambient
current.  The plume  thickness may decrease during this phase.
The mixing rate is  relatively small. The plume may interact
with a nearby bank or shoreline.

3)  Passive  ambient  mixing:   After   some  distance  the
background turbulence in the ambient shear  flow becomes the
dominating mixing  mechanism. The passive plume is growing
in thickness and in width.  The plume may interact with the
layer upper boundary and/or banks.

***The ambient flow plays  an important role in this  flow
configuration. Hence, all the zones listed above constitute


                            233

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the HYDRODYNAMIC  MIXING  ZONE with strong  initial  mixing.
Predictions will be terminated  in zones 2 or 3 depending on
the definitions of the LEGAL MIXING  ZONE or  the REGION OF
INTEREST.***
FLOW CLASS (..)A3

Controlled primarily by the geometry of the discharge, the
near-field of this flow configuration is dominated by Coanda
attachment. The port orientation  is more or less horizontal
and/or the height of the discharge port above the bottom is
too small. This  leads to  rapid dynamic attachment (Coanda
attachment) of  the  discharge flow  to the bottom  and the
formation of a wall jet. At some distance the discharge flow
will lift off from the bottom due to its  strong buoyancy.
In the absence  of Coanda attachment the dominant flow class
would be given  by the prefix  (..). You may request detailed
information on  that  flow class  further below.  Additional
advice  on  how  to   prevent  bottom  attachment  (e.g.  by
increasing the vertical angle of the discharge port)  will
be  provided in  the  summary program  element  SUM.    The
following flow zones exist:

I)  Momentum-dominated near-field  wall jet:  The  rapidly
attaching discharge flow  (wall  jet)  is initially dominated
by the effluent momentum and weakly deflected by the ambient
current.

2) Momentum-dominated far-field wall jet:  The wall jet has
become strongly deflected  by the ambient current.  Depending
on the ratio of the  jet to plume  transition length scale to
the jet  to crossflow length scale  this  flow  zone  may be
absent.

3)  Lift-off:  Because of  the positive buoyancy  the plume
detaches from the bottom and starts to rise upward.

4)  Buoyancy-dominated far-field  plume: The plume has been
strongly  deflected  by the current  and  is slowly rising
toward the surface.

5)  Layer   boundary   approach:   The  bent-over  submerged
jet/plume  approaches the  layer boundary  (water surface or
pycnocline).  Within  a  short  distance the  concentration
distribution becomes relatively  uniform  across  the plume
width and thickness.

***  The  zones  listed above constitute  the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

6)  Buoyant  spreading at  layer  boundary:  The plume spreads
laterally along the  layer boundary (surface or pycnocline)


                            234

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while it is being advected by the ambient current. The plume
thickness may decrease during  this  phase.  The mixing rate
is relatively small. The plume may  interact with a nearby
bank or shoreline.

7)  Passive  ambient  mixing:   After   some  distance  the
background turbulence in  the  ambient shear  flow becomes the
dominating mixing mechanism. The  passive  plume is growing
in depth  and in width.  The plume  may interact  with the
channel bottom and/or banks.

*** Predictions will be terminated in  zone  6 or 7 depending
on the definitions  of the  LEGAL MIXING ZONE or the REGION
OF INTEREST.***
FLOW CLASS (..)A4

Controlled primarily by the geometry of the discharge, the
near-field of this flow configuration is dominated by Coanda
attachment. The  port orientation  is more or less horizontal
and/or the height of the  discharge port above the bottom is
too small. This  leads to rapid dynamic attachment (Coanda
attachment) of  the  discharge  flow  to  the bottom  and the
formation of a wall jet. At some distance the discharge flow
will lift off from the bottom  due to its  strong buoyancy.
In the absence of Coanda  attachment the dominant flow class
would be given by the prefix  (..) . You may request detailed
information on  that  flow class  further below.  Additional
advice  on  how   to   prevent  bottom  attachment  (e.g.  by
increasing the vertical  angle  of the discharge  port)  will
be  provided in  the  summary  program  element  SUM.    The
following flow zones exist:

1)  Momentum-dominated  near-field  wall jet:  The  rapidly
attaching discharge flow (wall  jet)  is initially dominated
by the effluent momentum and weakly deflected by the ambient
current.

2)  Lift-off: Because of the positive buoyancy the  plume
detaches from the bottom and starts  to rise upward.

3) Buoyancy-dominated near-field plume: The plume is quickly
rising and weakly deflected by  the  ambient current.

4) Layer boundary impingement/upstream spreading: The weakly
bent jet/plume impinges on the layer boundary (water surface
or pycnocline)  at a near-vertical angle.  After impingement
the  flow  spreads more  or  less  radially  along the  layer
boundary.   In particular, the  flow  spreads some  distance
upstream against the ambient  flow, and laterally across the
ambient flow. This  spreading  is dominated by  the strong
buoyancy of the discharge.


                           235

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***  The zones  listed above  constitute the  HYDRODYNAMIC
MIXING ZONE in which strong  initial mixing takes place.***

5) Buoyant spreading  at  layer boundary:  The plume spreads
laterally along the layer boundary (surface or pycnocline)
while it is being advected by the ambient current. The plume
thickness may decrease during this phase.  The mixing rate
is relatively small.  The plume may interact with a nearby
bank or shoreline.

6)  Passive  ambient  mixing:   After  some  distance  the
background turbulence in  the ambient  shear flow becomes the
dominating mixing mechanism.  The  passive plume is growing
in depth  and in width.  The  plume may  interact  with the
channel bottom and/or banks.

*** Predictions will be terminated in zone 5 or 6 depending
on  the definitions of the LEGAL MIXING ZONE or the REGION
OF  INTEREST.***

SPECIAL CASE: If the ambient is stagnant,  then advection and
diffusion  by the  ambient flow (zones 5 and  6)  cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones  1 to 4) and the predictions will be terminated
at this stage.  Such  stagnant water  predictions may  be a
useful  initial mixing   indicator  for  a  given  site  and
discharge design. For practical final predictions, however,
the advection and diffusion  of the ambient  flow - no matter
how small in magnitude - should be considered.
FLOW CLASS  (..)A5

Controlled primarily by the geometry of the discharge, the
near-  field of  this flow  configuration  is  dominated by
Coanda  attachment.  The port  orientation  is  more  or less
horizontal and/or the height of the discharge port above the
bottom is too small.  This  leads  to  rapid dynamic attachment
(Coanda attachment) of the discharge flow  to the bottom and
the formation of a wall jet. The discharge flow will remain
attached to the bottom due to its weak or negative buoyancy.
In the absence of Coanda attachment the dominant  flow class
would be given by the prefix (..).  You may request detailed
information on  that  flow class further  below.  Additional
advice  on  how  to  prevent  bottom attachment  (e.g.  by
increasing  the  vertical angle of  the discharge port) will
be  provided  in the  summary program  element  SUM.    The
following flow  zones exist:

1)  Momentum-dominated  near-field  wall  jet: The  rapidly
attaching discharge  flow  (wall jet) is initially dominated
                            236

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by the effluent momentum and weakly deflected by the ambient
current.

2) Momentum-dominated far-field wall jet: The wall jet has
become strongly deflected by the ambient current.

3)  Flow  turning:  At  some distance  the wall jet becomes
turned   into  the  ambient  flow  direction.   Also,   the
concentration distribution becomes relatively uniform across
the plume width and thickness.

***  The  zones  listed above  constitute the  HYDRODYNAMIC
MIXING ZONE in which strong initial mixing takes place.***

4) Buoyant spreading at bottom: The plume spreads laterally
along the bottom while it is being advected by the ambient
current.  The plume thickness may decrease during this phase.
The mixing rate  is relatively small. The plume may interact
with a nearby bank or shoreline.

6)  Passive   ambient  mixing:   After   some  distance  the
background turbulence in  the ambient shear  flow becomes the
dominating mixing mechanism. The  passive plume  is growing
in  depth and  in  width.  The plume  may interact  with the
channel bottom and/or banks.

***Predictions will be terminated in zone 4 or 5 depending
on the definitions  of the LEGAL MIXING ZONE or  the REGION
OF INTEREST. ***

SPECIAL CASE:  If the ambient is stagnant,  then advection and
diffusion by  the  ambient  flow  (zones  4 and 5)  cannot be
considered. The mixing is limited to the hydrodynamic mixing
zone (zones 1 to 3)  and the predictions will be terminated
at  this  stage.  Such  stagnant  water  predictions  may  be a
useful  initial  mixing  indicator  for  a  given   site  and
discharge design.  For practical final predictions, however,
the advection and  diffusion of  the ambient  flow - no matter
how small in magnitude - should be considered.
                            237

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                            Appendix D

                   HYDRO output File  Example

     This Fortran output  file corresponds  to the AB Chemical

Company Design Case No.2 in Section  7.1.2.



SIMULATION /  CASE DESCRIPTION

 SITE NAME:   AB-L
 DISCHARGER NAME:  NEW
 POLLUTANT NAME:  ANGLES-HO
 DESIGN CASE:  TEST

 DOS FILE NAME:    AB-1
 DATE AND TIME OF FORTRAN SIMULATION:  06-08-1989_15:09:37

ENVIRONMENT PARAMETERS (METRIC UNITS)

 BOUNDED SECTION
 BS   -   262.75    AS -   3153.00
 BANK -  left       YB -     37.50
 HA   -    12.00    HD -     12.00
 UA           .30    F  -       .0198

 UNIFORM DENSITY ENVIRONMENT

 RHOA -  998.39

DISCHARGE PARAMETERS (METRIC UNITS)

 DO     -.15000E+00  AO     -.17671E-01  HO   -       .40
 THETAO - 30.00      SIGMAO -270.00
 UO     -.30000E+01  QO     -.53014E-01
 RHOO   - 987.80    DRHOO  - 10.5840    GPO   -  .1040E+00
 CO     -.50000E+03

FLUX PARAMETERS  (METRIC UNITS)

QO -.53014E-01      MO  -.15904E+00     JO   - .5511E-02   SIGNJO - 1.0


FLOW CLASSIFICATION

 FLOW CLASS:  HI
 FLOW DIRECTION: upward
                                238

-------
 ATTACHMENT TYPE: NONE

 HS -     12.00


NON-DIMENSIONAL PARAMETERS

 FRO -  24.02        R  - 10.00

LENGTH SCALES (METRIC UNITS)

 LQ  -     .1329       LM  -   3.3924       Lm  -   1.3293      Lb   -
.2041

MIXING ZONE / TOXIC DILUTION / AREA OF INTEREST PARAMETERS

 CO     -.50000E+03
 NTOX - 1            CMC -   .25E+02
 XINT   -   .30E+04
 LEGMZ  - 1          LEGSPC - 2          LEGVAL -    26.27
 XLEG   -   .OOE+00  WLEG   -   .26E+02  ALEG   -   .OOE+00
 XMAX   -   .30E+04
 NSTEP  =  6

 SUBSURFACE FLOW: MDNF -> MDFF -> BDFF
 BEGIN MOD01: DISCHARGE MODULE

 PREDICTION

      X       Y      Z       S      C         B

     .00      .00    .40    1.00  .500E+03    .08

 END OF MOD01: DISCHARGE MODULE
 BEGIN MOD11 MDNF: MOMENTUM DOMINATED NEAR-FIELD

 COORDINATES

 GAMMA -  90.00    DELTA - 150.00

 45 < GAMMA < 135 DEGREES
 JET INTO CROSSFLOW

 STARTING VALUES


                                 239

-------
ETAI  -
ETAIP -
.4000   XI   -
.7385   XIP -
.0000  YI
.0775  YIP
 .0000 ZI
-.6396 ZIP
.4000
.3714
VIRTUAL ORIGIN LOCATION

ETAV  -   -.3385  XV  -   -.0775 YV  -    .6396 ZV

FINAL VALUES
                                              .0286
ETAF - 2 .
ETAFP - 2.
PREDICTION
X
.00
.08
.19
.33
.50
.70
.93
END OF MOD11
3201
6586

Y
.00
-.28
-.55
-.83
1.11
1.39
1.66
MDNF
XF -
XFP - 1

Z
.40
.56
.73
.90
1.08
1.27
1.46
: MOMENTUM
.9275
.0050

S
1.00
1.43
1.87
2.30
2.73
3.17
3.60
YF - -
YFP - -

C
. 500E+03
.349E+03
.268E+03
.217E+03
.183E+03
.158E+03
.139E+03
1.6629 ZF -
2.3025 ZFP -

B
.08
.12
.15
.19
.22
.26
.29
1.4569
1.4283



DOMINATED NEAR- FIELD

BEGIN MOD16
MDFF:
MOMENTUM
DOMINATED FAR
FIELD

STARTING VALUES
ETAI - 2 .
ETAIP - 1.
2108
4562
XI -
XIP -
.9275
.4266
YI - -
YIP - -
1.6629 ZI -
1.2611 ZIP -
1.4569
.7280
VIRTUAL ORIGIN LOCATION

ETAV  -    .7546  XV  -

FINAL VALUES

ETAF  -   4.4015  XF  -
ETAFP -   3.6469  XFP -

PREDICTION

     X       Y      Z
                .5008 YV  -   -.4018 ZV  -
               7.2018 YF
               6.7009 YFP
             -3.5601 ZF
             -3.1583 ZFP
                              .7289
               2.0958
               1.3669
                                240

-------
.93
1.97
3.02
4.06
5.11
-1.66
-2.31
-2.68
-2.96
-3.19
1.46
1.75
1.88
1.97
2.03
3.60
8.22
11.76
14.82
17.59
.139E+03
.608E+02
.425E+02
.337E+02
.284E+02
.44
.66
.79
.89
.97
THE POLLUTANT CONCENTRATION IN THE PLUME FALLS BELOW THE
CMC VALUE OF   .25E+02 IN THE CURRENT PREDICTION INTERVAL.

THIS IS THE EXTENT OF THE TOXIC DILUTION ZONE.

   6.16    -3.39   2.07   20.16  .248E+02   1.03
   7.20    -3.56   2.10   22.57  .221E+02   1.09

END OF MOD16 MDFF: MOMENTUM DOMINATED FAR FIELD
BEGIN MOD22 BDFF: BUOYANCY DOMINATED FAR-FIELD
STARTING VALUES

XI  -   7.2018
XIP -  13.7306
YI  -  -3.5601 ZI
YIP -  -4.4148 ZIP
                                         2.0958
                                         3.3763
                           .8548 ZV
                      -1.2805
VIRTUAL ORIGIN LOCATION

XV  -   -6.5288   YV  =

FINAL VALUES

XF  - 100.:
XFP - 107.J

PREDICTION

     X

   7.20
  22.77
  38.33
  53.89
  69.46
  85.02
 100.58

END OF MOD22 BDFF: BUOYANCY DOMINATED FAR-FIELD
84
13

-3
-4
-5
-6
-6
-7
-7
2
0
Y
.56
.83
.70
.38
.95
.45
.90
YF
YFP
Z
2.
4.
6.
7.
9.
10.
12.
-
M

10
31
15
78
28
68
00
-7.
-8.

22
61
109
162
220
283
349
9005
7553
S
.57
.99
.40
.73
.89
.18
.11
ZF - 12
ZFP = 13
C
.222E+02
.807E+01
.457E+01
.307E+01
.226E+01
.177E+01
.143E+01
.0000
.2805

1
1
2
2
3
3
3
B
.01
.68
.23
.72
.17
.59
.98
                                241

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 BEGIN MOD31:  LAYER/BOUNDARY/TERMINAL LAYER APPROACH

 CONTROL VOLUME

 PREDICTION
      X       Y      Z       S      C         B

   100.58   -7.90  12.00   349.3  .143E+01   3.98

    X       Y      Z       S      C         BV      BH      ZU      ZL

 108.55   -7.90  12.00   593.9  .842E+00   7.24   7.24   12.00    4.76

END OF MOD31:  LAYER/BOUNDARY/TERMINAL LAYER APPROACH
*** END HYDRODYNAMIC MIXING ZONE (HMZ) ***
BEGIN MOD41: BUOYANT AMBIENT SPREADING

 PREDICTION STAGE 1 NOT BANK ATTACHED
    X       Y      Z       S      C         BV      BH      ZU      ZL
 108.55   -7.90  12.00   593.9  .842E+00   7.24    7.24   12.00    4.76

** LEGAL MIXING ZONE BOUNDARY **
 IN THIS PREDICTION INTERVAL THE PLUME WIDTH MEETS OR EXCEEDS
 THE LEGAL VALUE -    26.27 M.  THIS IS THE EXTENT OF  THE  LEGAL MIXING
 ZONE.

  X       Y       Z       S       C       BV      BH      ZU      ZL

 229.67   -7.90  12.00   717.3  .697E+00   4.11   15.42   12.00    7.89
 350.78   -7.90  12.00   781.9   .639E+00   3.17   21.77   12.00    8.83
 471.89   -7.90  12.00   827.4  .604E+00   2.68   27.30   12.00    9.32
 593.01   -7.90  12.00   863.0  .579E+00   2.36   32.31   12.00    9.64
 714.12   -7.90  12.00   892.5   .560E+00   2.13   36.96   12.00    9.87
 835.23   -7.90  12.00   917.9   .545E+00   1.96   41.33   12.00   10.04
 END MOD41: BUOYANT AMBIENT SPREADING
                                 242

-------
BOTTOM COORDINATE FOR FAR-FIELD IS DETERMINED BY AVERAGE DEPTH,
ZFB -  0.0

 BEGIN MOD61: PASSIVE AMBIENT MIXING IN UNIFORM AMBIENT

 VERTICAL DIFFUSIVITY OF AMBIENT FLOW:    EDIFFV -     .0358(M**2/S)

 HORIZONTAL DIFFUSIVITY OF AMBIENT FLOW: EDIFFH -     .0894(M**2/S)

 PREDICTION STAGE 1 NOT BANK ATTACHED
X
835
898
960
1023
1086
1149
.23
.00
.77
.53
.30
.06
Y
-7.90
-7.90
-7.90
-7.90
-7.90
-7.90
Z
12.00
12.00
12.00
12.00
12.00
12.00
S
917
2489
3449
4238
4937
5581

.9
.0
.9
.3
.4
.0
C
.545E+00
.201E+00
.145E+00
.118E+00
.101E+00
.896E-01
BV
1.96
5.23
7.13
8.63
9.90
11.02
BH
41.33
42.04
42.73
43.41
44.09
44.75

12
12
12
12
12
12
ZU
.00
.00
.00
.00
.00
.00
ZL
10.04
6.77
4.87
3.37
2.10
.98
PLUME INTERACTS WITH BOTTOM
THE PASSIVE DIFFUSION PLUME BECOMES  VERTICALLY FULLY MIXED WITHIN THIS
PREDICTION INTERVAL.
1211.83   -7.90  12.00  6166.1  .811E-01  12.00   45.40   12.00
.00
 SIMULATION LIMIT BASED ON MAXIMUM SPECIFIED DISTANCE -     3000.00(M).

 THIS IS THE REGION OF INTEREST LIMITATION.

 PREDICTION STAGE 2 BANK ATTACHED
X
1211.83
1509.86
1807.89
2105.91
2403.94
2701.97
3000.00

37
37
37
37
37
37
37
Y
.50
.50
.50
.50
.50
.50
.50
Z
12.00
12.00
12.00
12.00
12.00
12.00
12.00
S
6166.1
6269.6
6371.5
6471.7
6570.4
6667.7
6763.5
C
.811E-01
.797E-01
.785E-01
.773E-01
.761E-01
.750E-01
.739E-01
BV
12.00
12.00
12.00
12.00
12.00
12.00
12.00
BH
90.
92.
93
95.
96.
98
99.
80
33
.83
30
75
.19
60
ZU
12.
12.
12
12.
12.
12
12.
00
00
.00
00
00
.00
00
ZL
.00
.00
.00
.00
.00
.00
.00
END MOD61: PASSIVE AMBIENT MIXING IN UNIFORM LAYER
                                 243

-------
                            Appendix E

    SUM  Case Summary  and Design Recommendations  Example

     The following represents  the SUM  knowledge base output
file  from  the  winter  design  case  for  the  MN  municipal
treatment  plant  in section 7.2.2.

************************** CASE SUMMARY ******************************

SIMULATION / CASE DESCRIPTION
Site name:         MN-2
Discharger name:   WEAK
Pollutant name:    STRATIFICATION
Design case:       TEST
Dos file  name:        MN-2
Date and  time of FORTRAN simulation:   08-09-1989 08:47:46


DISCHARGE/ENVIRONMENT DATA:

ENVIRONMENT  PARAMETERS (METRIC UNITS)

Bounded section                 - no
Bounded section width           - 88888.8  (m)
Nearest bank                   - left  (m)
Location of  discharge from bank - 1000.  (m)
Average depth                  =     24.35  (m)
Depth at  discharge              -     24.35  (m)
Ambient velocity                -       .25  (m/s)
Darcy F                                .02

Stratification Type  -   A
Surface density      -   1025.60 (kg/m**3)
Pycnocline density   - 0.0 (kg/m**3)
Bottom density      -   1025.76 (kg/m**3)
Layer height        -     24.35 (m)

DISCHARGE PARAMETERS (METRIC UNITS)

Port diameter                -       .5 (m)
Port area                    -       .19635  (m**2)
Discharge port height         - 0.5 (m)
Vertical angle of discharge   -     30 (deg)
Horizontal  angle of  discharge -        (deg)
Discharge velocity            -      3. (m/s)
Discharge density             -   1015.00  (kg/m**3)
Density difference            - 10.679932  (kg/m**3)
Buoyant acceleration         -       .10  (m**2/s)


                                244

-------
Discharge concentration       -    100.000000

FLUX PARAMETERS (METRIC UNITS)
Discharge flow rate  - 0.589032 m**3/s
Momentum flux        -      1.76 m**4/s**2
Buoyancy flux        - 0.060147 m**4/s**3
NON-DIMENSIONAL PARAMETERS

Froude Number   - 13.276936
Velocity Ratio  - 12
DISCHARGE/ENVIRONMENT LENGTH SCALES (m):

LQ -       .44     Lm  -      5.31      Lb -      3.84
LM -      6.24     Lm' -  99999.90     Lb'  -  99999.90

(These  refer  to  the  final discharge/environment  length  scales  as
concluded in CLASS)
MIXING ZONE / TOXIC DILUTION ZONE / AREA OF INTEREST PARAMETERS

Toxic discharge                 - yes
CMC concentration               -     10.000000
Legal mixing zone               - yes
Legal mixing zone specification - width
Legal mixing zone value          - 200. (m, or m**2)
Region of interest              - yes
Region of interest distance     - 2000. m
*** SUMMARY OF HYDRODYNAMIC SIMULATION AND MIXING ZONE  PREDICTION ***

Flow Class -   HI
Attachment type -   NONE

This flow configuration  applies  to a layer corresponding to  the  full
water depth at the discharge site.   The  ambient density  stratification
at  the    discharge  site  is  relatively weak  and unimportant so  the
discharge flow   penetrates  to  the surface  and/or  breaks  down  the
existing stratification through vigorous mixing.
HYDRODYNAMIC MIXING ZONE (HMZ) CONDITIONS :

Note: The HMZ is the zone of strong initial  mixing.  It has no legal
implication.  However,  this  information may be useful for the discharge
designer because  the  mixing in  the  HMZ is  usually sensitive to  the
discharge design conditions.
                                 245

-------
Pollutant concentration at edge of HMZ -       .67
Dilution at edge of HMZ -    149.19

HMZ Location (centerline coordinates) (m):
x -     81.79  y -       .00  z -     24.35
HMZ Plume Dimensions (ra):
plume half-width -     13.25  plume thickness -     13.25
REGION OF INTEREST (ROI) CONDITIONS :

Minimum pollutant concentration at edge of ROI -       .339
Corresponding dilution at edge of ROI  -       294.8
ROI Location (centerline coordinates)   (m):
x -   2000.00 y -       .00  z -     24.35
ROI Plume Dimensions (m):
plume half-width -   202.     plume thickness -      1.72
******************* MIXING ZONE PREDICTION SUMMARY ********************
LEGAL MIXING ZONE (LMZ) CONDITIONS :
Predicted minimum pollutant concentration at edge of LMZ -      .402060
Corresponding dilution at edge of LMZ -    248.719300
LMZ Location (centerline coordinates)  (m):
x -    753.166900 y -       .000000 z -     24.350000
LMZ Plume Dimensions (m):
plume half-width -    102.400900  plume thickness -      2.861374
At this position, the flow is still unattached to any bank.
****************** XOXIC DILUTION ZONE SUMMARY ********************
TOXIC DILUTION ZONE (TDZ) ANALYSIS:
Criterion maximum concentration (CMC) -     10.000000
Toxic dilution zone downstream distance -     16.28 (m) .

The exit velocity of the discharge from the port is equal
to  3. m/s and is greater than the minimum of 3.0 m/s.

* The discharge velocity test for TDZ has been satisfied. *
The downstream distance equal to 16.28 (m) at which to flow equals the
criterion maximum concentration (CMC) is less  than or equal to 50 times
the discharge length scale of LQ = .44 (m).

* The discharge  length  scale test for TDZ has been satisfied.  *   The
criterion maximum concentration (CMC) has been met at a distance
downstream equal to  16.28 (m) which is less than or equal to 5 times
the ambient water depth HD - 24.35 (m) .
                                 246

-------
* The ambient depth test for TDZ has been satisfied.*
The criterion maximum concentration (CMC) of CMC has been met
at  16.28 (m) downstream which is less than or  equal  to  one  tenth the
distance  of the  of  the  legal  mixing  zone  of       753.166900  (m)
downstream.

* The legal mixing zone test for TDZ has been satisfied.  *

**** An  criteria for  TDZ  are satisfied for this configuration.  ****
TOXIC DILUTION ZONE (TDZ) CONDITIONS :

Note: The TDZ corresponds to  the criteria issued in the USEPA Technical
Support Document  "Technical  Support Document for Water  Quality-based
Toxics Control". Office of Water,  Washington, D.C.,  September, 1985.

Maximum pollutant concentration at edge of TDZ -      9.83
Corresponding dilution at edge of TDZ -     10.165760

TDZ Location (centerline coordinates)  (m):
x -     16.28  y -       .00  z -      8.25

TDZ Plume Dimensions (m):
plume half-width -      2.68 plume thickness -       .00
***************************** NOTICE *********************************

If you desire detailed printed information on the present discharge case
you can obtain this  by issuing the following DOS command after you have
returned to DOS:

  print c:\cmx\sim\MN-2.cxo

This  gives  a  detailed  listing  of  the  results of  the  hydrodynamic
simulation  program element  HYDRO.  This  information may be  useful  if
you want to construct graphical  displays  of the flow  configuration  or
if you want  to compare results with available field or laboratory data.

  print c:\cmx\desc\Hldes
The detailed description of  the flow configuration for  the  unattached
flow class HI will be printed.
A reliable environmental analysis and mixing zone prediction is possible
only if  each  design case is  evaluated  through several iterations  of
CORMIX1.  Small changes in ambient or discharge design conditions  can
sometimes cause drastic shifts in the applicable flow configuration
                                 247

-------
(flow class) and the size or appearance  of mixing zones.  Iterative use
of CORMIX1 will  give information on the sensitivity of predicted results
on  design  and  ambient   conditions.Each  predictive  case  should  be
carefully assessed as to:   - size and  shape  of LMZ  -  conditions in the
TDZ (if present)- bottom impact of the discharge flow  -  water surface
exposure- bank  attachment,  and other  factors.  In general,  iteration
should be conducted in the following order:

A) Discharge design changes (geometry variations)

B) Sensitivity  to ambient conditions

C) Discharge flow changes (process variations)

When  investigating these  variations  the  CORMIX1  user  will  quickly
appreciate  the fact that mixing conditions at short distances

(near-field) are usually quite sensitive  and  controllable.  In contrast,
mixing   conditions at large distances  (far-field)  often show  little
sensitivity  unless the  ambient  conditions  change  substantially  or
drastic process variations are introduced.

A)  DISCHARGE DESIGN  CHANGES  (GEOMETRY  VARIATIONS):    Most  of  the
following  recommendations  are motivated  by  the desire  of  improving
conditions   in   the   applicable   mixing   zones   (i.e.   minimizing
concentrations and/or areal extent).

     1) Outfall  location: Consider moving the discharge farther offshore
     to a larger water depth in order to  delay  flow interaction with the
     bank and/or surface,  and to improve near-field mixing.

     2) Height  of  discharge port:  For  positively  buoyant  or  neutral
     discharges  it is usually desirable  to minimize  the port height in
     order  to provide a low  submerged jet/plume  trajectory.   However,
     if the port height  is  too  small undesirable flow bottom  attachment
     may result.  A typical range  for port  heights is  from  two to ten
     diameters.   For negatively buoyant  discharges,  on the other hand,
     it may be   desirable  to maximize  the  port height.  Navigational
     requirements may put further limits on large port heights.

     3) Vertical angle of discharge: Near-field dilution for  positively
     or neutrally buoyant discharges is often improved by providing a
     near-horizontal discharge. In order co  prevent bottom interference
     a slight  upward orientation (in the range of  +15 to +30 degrees)
     may be advisable.  In contrast, a vertical or  near-vertical angle
     may be favorable for  negatively buoyant discharges.

     4) Horizontal  angle of discharge:  This angle provides the discharge
     orientation relative  to  the  ambient  current.   A co-flow design
     (angle  of  about  0 degrees) or a cross-flow design (about 90 or 270
     degrees, respectively) are preferable. A counter-flow design (about
                                 248

-------
     180 degrees)  is   undesirable from  the  viewpoint of mixing  zone
     predictability and  bottom impacts.   Cross-flow  designs  may  be
     particularly effective in optimizing near-field mixing, and if they
     are chosen,  the port should point in the offshore direction.

     5) Port diameter/area (discharge  velocity):  Remember that for  a
     given discharge flow rate  the port area and discharge velocity are
     inversely related: a small discharge port implies a high discharge
     velocity,  and   a  consequently high  discharge  momentum flux.
     Typically,  a  high velocity  discharge  will  maximize  near-field
     mixing.   Note, however,  that high velocity  discharges a) may  lead
     to  unstable   near-field   flow  configurations  perhaps  involving
     undesirable  mixing patterns, and b) usually have  little,  if  any,
     effect  on  dilutions  over   the  far-field  where  a  LMZ  may
     apply .Discharge velocities in typical engineering designs may range
     from 3 m/s  to 8 m/s. Very high velocities may lead  to excessive
     pumping energy  requirements.   Very low  velocities (less than 0.5
     m/s) may  lead to  undesirable sediment  accumulation within the
     discharge pipe.

B) SENSITIVITY TO  AMBIENT CONDITIONS:Variations -  of  the order of  10
percent  -  of the following  ambient  design  conditions  should  be
considered:- ambient velocity (or ambient flowrate)  - ambient depth (or
river/tidal  stage)  -  ambient  density  structure   (notably   density
differences)Such variability is important for two reasons:

     1) the usual uncertainty in ambient environmental data,

     2)  the  schematization employed  by  CORMIX1 Please  refer  to the
     detailed  advice   on  the  specification  of  environmental data,
     including the density structure,  that  is  available in  program
     element  DATIN.  In  particular,  note  the  advisory  comments  on
     stagnant ambient  conditions.

C) DISCHARGE FLOW CHANGES (PROCESS VARIATIONS):  Actual process  changes
can result in variations of one or more of three  parameters  associated
with the discharge:  flowrate,  density,  or  pollutant  concentration.  In
some cases,  such  process  changes  may be difficult to  achieve  or too
costly. Note, that "off-design" conditions in  which a discharge operates
below its full capacity also fall into this category.

     1)  Pollutant  mass flux:  The  total  pollutant  mass  flux  is the
     product of discharge flow (m**3/s)  times the discharge pollutant
     concentration (in arbitrary units). Thus, decreasing the pollutant
     mass flux will,  in   general, decrease  the resulting pollutant
     concentration in the near-field   and far-field.  This  occurs,  of
     course,  during off-design conditions.

     2) Discharge flow:  For a given  pollutant mass flux, an increase  in
     discharge  flow  implies  an   increase   in  discharge  pollutant
     concentration,and vice  versa. For  the  variety  of  flow  classes
     contained in CORMIX1  there is no universal rule whether high or low
                                 249

-------
     volume discharges are preferable for optimizing near-field mixing.
     Mostly, the sensitivity is small,  and  even more so for far-field
     effects. Note  that  a  change  in discharge  flow  will influence in
     turn the discharge velocity and hence momentum flux.

     3) Discharge  density:  The actual  density of the  discharge flow
     controls  the  buoyancy  effects relative   to  the  ambient  water.
     Occasionally,   the discharge  density is controllable  through the
     amount of process heating  or  cooling occurring prior to discharge.
     Usually, near-field mixing is   enhanced by  maximizing the total
     density difference  (positive or negative)  between discharge flow
     and ambient water. In most cases,  however, this  effect is minor.
You have now completed the analysis of the design case MN-2.  At this
time you have three options:

     1) Quit this session of CORMIX1.
     2) Perform another  iteration of CORMIX1 for  this general design
     (You will only change  the  discharge  and mixing zone data bases).

     3) Perform another  iteration of COPxMIXl for  this general design
     (You will only change the mixing zone data base).

     4) Start another design case  (You  will  enter  a complete new data
     base).

     When the next screen appears, choose '8)Quit' option to return  to
     DOS.
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                                  250

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