&EPA
United States
Environmental Protection
Agency
Office of Water
(WH 585)
EPA-823-R-92-004
August 1992
Technical Guidance Manual
for Performing Waste Load
Allocations
Book III: Estuaries
Parts
Use Of Mixing Zone Models
In Estuarine Waste Load
Allocations
-------
Click here for
DISCLAIMER
Document starts on next page
TITLE: Technical Guidance Manual for Performing Wasteload Allocations,
Book III: Estuaries-
Part 3: Use of Mixing Zone Models in Estuarine Waste Load Allocations
EPA DOCUMENT NUMBER: EPA-823-R92-004 DATE: August 1992
POINT OF CONTACT: TBD
ABSTRACT
As part of ongoing efforts to keep EPA's technical guidance readily accessible to
water quality practitioners, selected publications on Water Quality Modeling and
TMDL Guidance available at http://www.epa.gov/waterscience/pc/watqual.html
have been enhanced for easier access.
This document is part of a series of manuals that provides technical information
related to the preparation of technically sound wasteload allocations (WLAs) that
ensure that acceptable water quality conditions are achieved to support
designated beneficial uses. The document provides information on the legal
requirements for mixing zones and describes the background and application of
predictive models for mixing zone analysis.
Book III Part 3 describes how the detailed prediction of conditions in the initial
mixing phase of a wastewater discharge relates to legal definitions of mixing
zones. It also gives an overview of the major physical processes that govern
hydrodynamic mixing of aqueous discharges, and introduces (1) jet integral
models that are applicable to a limited subset of near-field processes and (2) the
CORMIX expert system for mixing zones, that addresses both near-field and far-
field processes under a variety of conditions. Four case studies are included to
illustrate the application of the jet integral models and of CORMIX.
KEYWORDS: Wasteload Allocations, Estuaries, Modeling, Water Quality
Criteria, Mixing Zones
-------
MANUAL
FOR
III-
PART 3: Use of Mixing in
Allocations
Project Officer
Hi ran may Biswas, Ph.D.
Edited By
Robert B. Ambrose, Jr., P.E.1
James L. Martin, Ph.D., P.E.2
Prepared by
Gerhard H. Jirka, Ph.D., P.E.3
1. Center for Exposure Assessment Modeling,
Environmental Research Laboratory, U.S. EPA, Athens, GA
2. ASCI Corporation, U.S. EPA, Athens, Georgia
3. DeFrees Hydraulics Laboratory, School of Civil and Environmental Engineering,
Cornell University, Ithaca, NY
Prepared for
U.S. ENVIRONMENTAL PROTECTION AGENCY
401 M. Street, S.W.
Washington, D.C. 20460
-------
of
Acknowledgements xiii
7. Introduction 7-1
7.1 Initial Mixing in Estuaries and Coastal Waters 7-1
7.2 Mixing Zone Requirements: Legal Background 7-1
7.3 Summary 7-3
7.4 References 7-3
8. Physical Processes and Modeling Methodologies 8-1
8.1 Ambient and Discharge Conditions 8-1
8.2 Hydrodynamic Mixing Processes 8-1
8.3 Mathematical Predictive Models 8-5
8.4 Buoyant Jet Integral Models 8-7
8.5 CORMIX: Expert System Methodology for Mixing Zone Analysis 8-11
8.6 Mixing Zone Predictions Under Unsteady Reversing Tidal Currents .... 8-23
8.7 References 8-25
9. Case Studies of Mixing Zone Prediction 9-1
9.1 Introduction 9-1
9.2 Case AA - Single Port Discharge: Industrial Outfall in Tidal Fjord 9-2
9.3 Case BB - Multiport Diffuser: Municipal Sewage Discharge
into Coastal Bay 9-5
9.4 Case CC - Single Port Discharge: Brine Discharge From
an Oil Field 9-8
9.5 Case DD Multiport Diffusers: Cooling Water Discharge
into Shallow Sound 9-10
9.6 References 9-12
-------
Acute Toxicity1 - Any toxic effect that is produced
within a short period of time, usually 24-96 hours.
Although the effect most frequently considered is
mortality, the end result of acute toxicity is not neces-
sarily death. Any harmful biological effect may be the
result.
Aerobic1 - Refers to life or processes occurring only
in the presence of free oxygen; refers to a condition
characterized by an excess of free oxygen in the
aquatic environment.
Algae (Alga)1 - Simple plants, many microscopic,
containing chlorophyll. Algae form the base of the
food chain in aquatic environments. Some species
may create a nuisance when environmental condi-
tions are suitable for prolific growth.
AHochthonous1- Pertaining to those substances, ma-
terials or organisms in a waterway which originate
outside and are brought into the waterway.
Anaerobic - Refers to life or processes occurring in
the absence of free oxygen; refers to conditions char-
acterized by the absence of free oxygen.
Autochthonous1 - Pertaining to those substances,
materials, or organisms originating within a particular
waterway and remaining in that waterway.
Autotrophic1 - Self nourishing; denoting those organ-
isms that do not require an external source of organic
material but can utilize light energy and manufacture
their own food from inorganic materials; e.g., green
plants, pigmented flagellates.
Bacteria1- Microscopic, single-celled or noncellular
plants, usually saprophytic or parasitic.
Benthal Deposit2 - Accumulation on the bed of a
watercourse of deposits containing organic matter
arising from natural erosion or discharges of waste-
waters.
Benthic Region1 - The bottom of a waterway; the
substratum that supports the benthos.
Benthal Demand2 - The demand on dissolved oxygen
of water overlying benthal deposits that results from
the upward diffusion of decomposition products of the
deposits.
Benthos1 - Organisms growing on or associated prin-
cipally with the bottom of waterways. These include:
(1) sessile animals such as sponges, barnacles, mus-
sels, oysters, worms, and attached algae; (2) creep-
ing forms such as snails, worms, and insects; (3)
burrowing forms, which include clams, worms, and
some insects; and (4) fish whose habits are more
closely associated with the benthic region than other
zones; e.g., flounders.
Biochemical Oxygen Demand2 - A measure of the
quantity of oxygen utilized in the biochemical oxida-
tion of organic matter in a specified time and at a
specific temperature. It is not related to the oxygen
requirements in chemical combustion, being deter-
mined entirely by the availability of the material as a
biological food and by the amount of oxygen utilized
by the microorganisms during oxidation. Abbreviated
BOD.
Biological Magnification1 - The ability of certain or-
ganisms to remove from the environment and store in
their tissues substances present at nontoxic levels in
the surrounding water. The concentration of these
substances becomes greater each higher step in the
food chain.
Bloom1 - A readily visible concentrated growth or
aggregation of minute organisms, usually algae, in
bodies of water.
Brackish Waters1 - Those areas where there is a
mixture of fresh and salt water; or, the salt content is
greater than fresh water but less than sea water; or,
the salt content is greater than in sea water.
Channel Roughness2 - That roughness of a channel,
including the extra roughness due to local expansion
or contraction and obstacles, as well as the roughness
of the stream bed proper; that is, friction offered to the
flow by the surface of the bed of the channel in contact
with the water. It is expressed as roughness coeffi-
cient in the velocity formulas.
Chlorophyll1 - Green photosynthetic pigment present
in many plant and some bacterial cells. There are
seven known types of chlorophyll; their presence and
abundance vary from one group of photosynthetic
organisms to another.
Chronic Toxicity1 - Toxicity, marked by a long dura-
tion, that produces an adverse effect on organisms.
The end result of chronic toxicity can be death al-
though the usual effects are sublethal; e.g., inhibits
reproduction, reduces growth, etc. These effects are
reflected by changes in the productivity and popula-
tion structure of the community.
-------
Coastal Waters1 - Those waters surrounding the con-
tinent which exert a measurable influence on uses of
the land and on its ecology. The Great Lakes and the
waters to the edge of the continental shelf.
Component Tide2 - Each of the simple tides into
which the tide of nature is resolved. There are five
principal components; principal lunar, principal solar,
N2, K, and O. There are between 20 and 30 compo-
nents which are used in accurate predictions of tides.
Coriolis Effect2- The deflection force of the earth's
rotation. Moving bodies are deflected to the right in
the northern hemisphere and to the left in the southern
hemisphere.
Datum2 - An agreed standard point or plane of state
elevation, noted by permanent bench marks on some
solid immovable structure, from which elevations are
measured or to which they are referred.
Density Current2 - A flow of water through a larger
body of water, retaining its unmixed identity because
of a difference in density.
Deoxygenation2 - The depletion of the dissolved oxy-
gen in a liquid either under natural conditions associ-
ated with the biochemical oxidation of organic matter
present or by addition of chemical reducing agents.
Diagenetic Reaction - Chemical and physical
changes that alter the characteristics of bottom sedi-
ments. Examples of chemical reactions include oxi-
dation of organic materials while compaction is an
example of a physical change.
Dispersion2 - (1) Scattering and mixing. (2) The mix-
ing of polluted fluids with a large volume of water in a
stream or other body of water.
Dissolved Oxygen - The oxygen dissolved in water,
wastewater, or other liquid, usually expressed in mil-
ligrams per liter, or percent of saturation. Abbreviated
DO.
Diurnal2 - (1) Occurring during a 24-hr period; diurnal
variation. (2) Occurring during the day time (as op-
posed to night time). (3) In tidal hydraulics, having a
period or cycle of approximately one tidal day.
Drought2 - In general, an extended period of dry
weather, or a period of deficient rainfall that may
extend over an indefinite number of days, without any
quantitative standard by which to determine the de-
gree of deficiency needed to constitute a drought.
Qualitatively, it may be defined by its effects as a dry
period sufficient in length and severity to cause at
least partial crop failure or impair the ability to meet a
normal water demand.
Ebb Tide1- That period of tide between a high water
and the succeeding low water; falling tide.
Enrichment1 - An increase in the quantity of nutrients
available to aquatic organisms for their growth.
Epilimnion1 - The water mass extending from the
surface to the thermocline in a stratified body of water;
the epilimnion is less dense that the lower waters and
is wind-circulated and essentially homothermous.
Estuary1 - That portion of a coastal stream influenced
by the tide of the body of water into which it flows; a
bay, at the mouth of a river, where the tide meets the
river current; an area where fresh and marine water
mix.
Euphotic Zone1 - The lighted region of a body of water
that extends vertically from the water surface to the
depth at which photosynthesis fails to occur because
of insufficient light penetration.
Eutrophication1 - The natural process of the maturing
(aging) of a lake; the process of enrichment with
nutrients, especially nitrogen and phosphorus, lead-
ing to increased production of organic matter.
Firth1 - A narrow arm of the sea; also the opening of
a river into the sea.
Fjord (Fiord)1 - A narrow arm of the sea between
highlands.
Food Chain1 - Dependence of a series of organisms,
one upon the other, for food. The chain begins with
plants and ends with the largest carnivores.
Flood Tide2 - A term indiscriminately used for rising
tide or landward current. Technically, flood refers to
current. The use of the terms "ebb" and "flood" to
include the vertical movement (tide) leads to uncer-
tainty. The terms should be applied only to the hori-
zontal movement (current).
Froude's Number2 - A numerical quantity used as an
index to characterize the type of flow in a hydraulic
structure that has the force of gravity (as the only force
producing motion) acting in conjunction with the re-
sisting force of inertia. It is equal to the square of
characteristic velocity (the mean, surface, or maxi-
mum velocity) of the system, divided by the product
of a characteristic linear dimension, such as diameter
or expressed in consistent units so that the combina-
tions will be dimensionaless. The number is used in
VI
-------
open-channel flow studies or in cases in which the free
surface plays an essential role in influencing motion.
Heavy Metals2 - Metals that can be precipitated by
hydrogen sulfide in acid solution, for example, lead,
silver, gold, mercury, bismuth, copper.
Heterotrophic1 - Pertaining to organisms that are
dependent on organic material for food.
Hydraulic Radius2 - The right cross-sectional area of
a stream of water divided by the length of that part of
its periphery in contact with its containing conduit; the
ratio of area to wetted perimeter. Also called hydraulic
mean depth.
Hydrodynamics2 - The study of the motion of, and the
forces acting on, fluids.
Hydrographic Survey2 - An instrumental survey
made to measure and record physical characteristics
of streams and other bodies of water within an area,
including such things as location, areal extent and
depth, positions and locations of high-water marks,
and locations and depths of wells.
Inlet1 - A short, narrow waterway connecting a bay,
lagoon, or similar body of water with a large parent
body of water; an arm of the sea, or other body of
water, that is long compared to its width, and that may
extend a considerable distance inland.
Inorganic Matter2 - Mineral-type compounds that are
generally non-volatile, not combustible, and not bio-
degradable. Most inorganic-type compounds, or reac-
tions, are ionic in nature, and therefore, rapid
reactions are characteristic.
Lagoon1 - A shallow sound, pond, or channel near or
communicating with a larger body of water.
Limiting Factor - A factor whose absence, or exces-
sive concentration, exerts some restraining influence
upon a population through incompatibility with spe-
cies requirements or tolerance.
Manning Formula2 - A formula for open-channel flow,
published by Manning in 1890, which gives the value
of c in the Chezy formula.
Manning Roughness Coefficient2 - The roughness
coefficient in the Manning formula for determination
of the discharge coefficient in the Chezy formula.
Marsh1 - Periodically wet or continually flooded area
with the surface not deeply submerged. Covered
dominantly with emersed aquatic plants; e.g., sedges,
cattails, rushes.
Mean Level - The mean plane about which the
tide oscillates; the average height of the sea for all
stages of the tide.
Michaelis-Menton Equation2 - A mathematical ex-
pression to describe an enzyme-catalyzed biological
reaction in which the products of a reaction are de-
scribed as a function of the reactants.
Mineralization2 - The process by which elements
combined in organic form in living or dead organisms
are eventually reconverted into inorganic forms to be
made available for a fresh cycle of plant growth. The
mineralization of organic compounds occurs through
combustion and through metabolism by living ani-
mals. Microorganisms are ubiquitous, possess ex-
tremely high growth rates and have the ability to
degrade all naturally occurring organic compounds.
Modeling2 - The simulation of some physical or ab-
stract phenomenon or system with another system
believed to obey the same physical laws or abstract
rules of logic, in order to predict the behavior of the
former (main system) by experimenting with latter
(analogous system).
Monitoring2 - Routine observation, sampling and test-
ing of designated locations or parameters to deter-
mine efficiency of treatment or compliance with
standards or requirements.
Mouth2" The exit or point of discharge of a stream into
another stream or a lake, or the sea.
Nautical Mile2 - A unit of distance used in ocean
navigation. The United States nautical mile is defined
as equal to one-sixteenth of a degree of a great circle
on a sphere with a surface equal to the surface of the
earth. Its value, computed for the Clarke spheroid of
1866, is 1,853.248 m (6,080.20ft). The International
nautical mile is 1,852 m (6,070.10ft).
Nanoplankton2" Very minute plankton not retained in
a plankton net equipped with no. 25 silk bolting cloth
(mesh, 0.03 to 0.04 mm.).
Neap Tides1 - Exceptionally low tides which occur
twice each month when the earth, sun and moon are
at right angles to each other; these usually occur
during the moon's first and third quarters.
Neuston2 - Organisms associated with, or dependent
upon, the surface film (air-water) interface of bodies
of water.
Nitrogenous Oxygen Demand (NOD) - A quantita-
tive measure of the amount of oxygen required for the
biological oxidation of nitrogenous material, such as
vi i
-------
ammonia nitrogen and organic nitrogen, in wastewa-
ter; usually measured after the carbonaceous oxygen
demand has been satisfied.
Nutrients1 - Elements, or compounds, essential as
raw materials for organism growth and development;
e.g., carbon, oxygen, nitrogen, phosphorus, etc.
Organic1 - Refers to volatile, combustible, and some-
times biodegradable chemical compounds containing
carbon atoms (carbonaceous) bonded together and
with other elements. The principal groups of organic
substances found in wastewater are proteins, carbo-
hydrates, and fats and oils.
Oxygen Deficit1 - The difference between observed
oxygen concentration and the amount that would
theoretically be present at 100% saturation for exist-
ing conditions of temperature and pressure.
Pathogen1 - An organism or virus that causes a dis-
ease.
Periphyton (Aufwuchs)1 - Attached microscopic or-
ganisms growing on the bottom, or other submersed
substrates, in a waterway.
Photosynthesis1 - The metabolic process by which
simple sugars are manufactured from carbon dioxide
and water by plant cells using light as an energy
source.
Phytoplankton1 - Plankton consisting of plant life.
Unattached microscopic plants subject to movement
by wave or current action.
Plankton1 - Suspended microorganisms that have
relatively low powers of locomotion, or that drift in the
water subject to the action of waves and currents.
Quality2 - A term to describe the composite chemical,
physical, and biological characteristics of a water with
respect to it's suitability for a particular use.
Reaeration2 - The absorption of oxygen into water
under conditions of oxygen deficiency.
Respiration1 - The complex series of chemical and
physical reactions in all living organisms by which the
energy and nutrients in foods is made available for
use. Oxygen is used and carbon dioxide released
during this process.
Roughness Coefficient2 - A factor, in the Chezy,
Darcy-Weisbach, Hazen-Williams, Kutter, Manning,
and other formulas for computing the average velocity
of flow of water in a conduit or channel, which repre-
sents the effect of roughness of the confining material
on the energy losses in the flowing water.
Seiche1 - Periodic oscillations in the water level of a
lake or other landlocked body of water due to unequal
atmospheric pressure, wind, or other cause, which
sets the surface in motion. These oscillations take
place when a temporary local depression or elevation
of the water level occurs.
Semidiurnal2 - Having a period or cycle of approxi-
mately one half of a tidal day. The predominating type
of tide throughout the world is semidiurnal, with two
high waters and two low waters each tidal day.
Slack Water2 - In tidal waters, the state of a tidal
current when its velocity is at a minimum, especially
the moment when a reversing current changes direc-
tion and its velocity is zero. Also, the entire period of
low velocity near the time of the turning of the current
when it is too weak to be of any practical importance
in navigation. The relation of the time of slack water
to the tidal phases varies in different localities. In
some cases slack water occurs near the times of high
and low water, while in other localities the slack water
may occur midway between high and low water.
Spring Tide1 - Exceptionally high tide which occurs
twice per lunar month when there is a new or full
moon, and the earth, sun, and moon are in a straight
line.
Stratification (Density Stratification)1 -Arrange-
ment of water masses into separate, distinct, horizon-
tal layers as a result of differences in density; may be
caused by differences in temperature, dissolved or
suspended solids.
Tidal Flat1 - The sea bottom, usually wide, flat, muddy
and nonproductive, which is exposed at low tide. A
marshy or muddy area that is covered and uncovered
by the rise and fall of the tide.
Tidal Prism2 - (1) The volume of water contained in a
tidal basin between the elevations of high and low
water. (2) The total amount of water that flows into a
tidal basin or estuary and out again with movement of
the tide, excluding any fresh-water flows.
Tidal Range2 - The difference in elevation between
high and low tide at any point or locality.
Tidal Zone (Eulittoral Zone, Intertidal Zone)1 - The
area of shore between the limits of water level fluctua-
tion; the area between the levels of high and low tides.
Tide1 - The alternate rising and falling of water levels,
twice in each lunar day, due to gravitational attraction
VIM
-------
of the moon and sun in conjunction with the earth's
rotational force.
Tide Gage2 - (1) A staff gage that indicates the height
of the tide. (2) An instrument that automatically regis-
ters the rise and fall of the tide. In some instruments,
the registration is accomplished by printing the heights
at regular intervals; in others by a continuous graph in
which the height of the tide is represented by ordinates
of the curve and the corresponding time by the abscis-
sae.
Toxicant1 - A substance that through its chemical or
physical action kills, injures, or impairs an organism;
any environmental factor which, when altered, pro-
duces a harmful biological effect.
Water Pollution1 - Alteration of the aquatic environ-
ment in such a way as to interfere with a designated
beneficial use.
Water Quality Criteria1 - A scientific requirement on
which a decision or judgement may be based concern-
ing the suitability of water quality to support a desig-
nated use.
Water Quality Standard1 - A plan that is established
by governmental authority as a program for water
pollution prevention and abatement.
Zooplankton2 - Plankton consisting of animal life.
Unattached microscopic animals having minimal capa-
bility for locomotion.
1 Rogers, B.G., Ingram, W.T., Pearl, E.H., Welter, L.W.
(Editors). 1981, Glossary, Water and Wastewater
Control Engineering, Third Edition, American Public
Health Association, American Society of Civil Engi-
neers, American Water Works Association, Water
Pollution Control Federation.
2Matthews, J.E., 1972, Glossary of Aquatic Ecological
Terms, Manpower Development Branch, Air and
Water Programs Division, EPA, Oklahoma.
IX
-------
The document is the third of a series of manuals
providing information and guidance for the preparation
of waste load allocations. The first documents provided
general guidance for performing waste load allocations
(Book I), as well as guidance specifically directed
toward streams and rivers (Book II). This document
provides technical information and guidance for the
preparation of waste load allocations in estuaries. The
document is divided into four parts:
Part 1 of this document provides technical information
and policy guidance for the preparation of estuarine
waste load allocations. It summaries the important
water quality problems, estuarine characterisitics and
processes affecting those problems, and the simula-
tion models available for addressing these problems.
Part 2 provides a guide to monitoring and model cali-
bration and testing, and a case study tutorial on simu-
lation of waste load allocation problems in simplified
estuarine systems. Part 4 summarizes several histori-
cal case studies, with critical review by noted experts.
This part, "Part 3: Use of Mixing Zone Models in
Estuarine Wasteload Allocations" describes the initial
mixing of wastewater in estuarine and coastal environ-
ments and mixing zone requirements. The important
physical processes that govern the hydrodynamic mix-
ing of aqueous discharges are detailed, followed by
application of available models to four case study
situations.
A draft version of this document received scientific
peer review from the following modeling experts:
Donald R.F. Harleman,
Massachusetts Institute of Technology
Gerald T. Orlob,
University of California-Davis
Robert V. Thomann,
Manhattan College
Steven J. Wright,
University of Michigan
Their comments have been incorporated into the final
version.
Organization: "Technical Guidance Manual for Performing Waste Load Allocations. Book
Estuaries"
Part
1
2
3
4
Title
Estuaries and Waste Load Allocation Models
Application of Estuarine Waste Load Allocation Models
Use of Mixing Zone Models in Estuarine Waste Load Allocation Modeling
Critical Review of Estuarine Waste Load Allocation Modeling
XI
-------
The contents of this section have been removed to
comply with current EPA practice.
XIII
-------
PDF
C lid; Here £ Upgrade,
Expanded Features i
Unlimited Pages;
7. Introduction
7.1 Initial Mixing in Estuaries and Coastal
Waters
The discharge of waste water into an estuary or coastal
water body can be considered from two vantage points
regarding its impact on ambient water quality.
On a larger scale, or system wide context, care must
be taken that water quality conditions that protect
designated beneficial uses are achieved. This is the
realm of the general waste load allocation (WLA) pro-
cedures and models as discussed in the first two parts
of this manual. As noted, an additional benefit of a
technically sound WLA is that excessive degrees of
treatment which are neither necessary nor productive
of corresponding improvements in water quality for the
whole water body, or at least major sections thereof,
can be avoided.
On a local scale, or in the immediate discharge vicinity,
additional precautions must be taken to insure that
high initial pollutant concentrations are minimized and
constrained to small zones, areas or volumes. The
definition of these zones, commonly referred to as
"mixing zones", is embodied in United States water
quality regulations, on the Federal and/or State level.
The mixing zone is a legally defined spatial quantity -
with certain size and shape characteristics -that allows
for initial mixing of the discharge. More recent regula-
tions on discharges of toxic substances define an
additional subregion - labeled herein the "toxic dilution
zone" - within the usual mixing zone. The intent of
those regulations is to require rapid mixing of toxic
releases to limit the exposure of aqueous flora and
fauna to elevated concentrations. The detailed predic-
tion of pollutant concentrations and water quality con-
stituents in the initial mixing phase of a wastewater
discharge is the realm of mixing zone models. This is
the subject of this part of the manual. Mixing zone
models are intended to document for any given com-
bination of discharge and environmental conditions the
size and shape of legally defined "mixing zones", and
for toxic substances, of embedded "toxic dilution
zones", and the levels of pollutant concentration within
these zones and at their edge.
There may be a great diversity in the types of initial
mixing processes for wastewater discharge. First, the
size and flow characteristics of estuaries or coastal
water can vary widely: the water body may be deep or
shallow, stagnant or flowing, and may exhibit ambient
density stratification of various degrees. Secondly, the
discharge type and configuration can be highly vari-
able: the flow may contain various pollutants ranging
from conventional to toxic substances, vary greatly in
magnitude ranging from low flowrate for a small sewage
treatment plant to the substantial cooling water flow for
a large steam-electric power plant, issue with high or low
velocity, be denser or lighter than the ambient, be lo-
cated 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 envi-
ronmental conditions, there are a large number of pos-
sible flow patterns which will develop as the discharge
waste stream mixes in the ambient water. These flow
patterns will determine the configuration, size, and in-
tensity of the mixing process, and any impact of the
discharge on the water body surface, bottom, shoreline,
or other areas. This, in turn, requires that engineering
analyses, in the form of mixing zone models, be robust,
adaptable and reliable under a wide spectrum of flow
conditions.
7.2 Mixing Zone Requirements: Legal
Background
7.2.1 Pollutant Types
The Clean Water Act of 1977 defines five general cate-
gories of pollutants: 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 7-1 lists examples of
the first three pollutant categories.
Pollutants designated as "conventional" would be "gen-
erally those pollutants that are naturally occurring, bio-
degradable, oxygen demanding materials and solids. In
addition, compounds which are not toxic and which are
similar in characteristics to naturally occurring, biode-
gradable substances are to be designated as conven-
tional pollutants for the purposes of the provision".
Pollutants designated as "nonconventional" would be
"those which are not toxic or conventional" (Congres-
sional Research Service, 1978).
7.2.2 Mixing Zone Definitions
The mixing zone is defined as an "allocated impact
zone" where numeric water quality criteria can be ex-
ceeded as long as acutely toxic conditions are pre-
vented. A mixing zone can be thought of as a limited
area or volume where the initial dilution of a discharge
occurs (USEPA, 1984a). Water quality standards apply
at the boundary of the mixing zone, not within the mixing
zone itself. USEPA and its predecessor agen-
7-1
-------
PDF
Glicl," Here S, Upgrade ,
Expanded Features'
Unlimited Pages;:
Table 7-1. Examples of Conventional, Nonconventional, and
Toxic Pollutants [USEPA 1984 b]
Conventional
biochemical oxygen
demand (BOD)
PH
total suspended sol-
ids (TSS)
fecal coliform bacte-
ria
oils and grease
Nonconventional
chemical oxygen
demand (COD)
fluoride
aluminum
sulfide
ammonia
Toxic
chloroform/lead
fluorene
nickel
selenium
benzidine
cies have published numerous documents giving guid-
ance for determining mixing zones. Guidance publish-
ed by USEPA in Water Quality Standards Handbook
(1984a) supersedes these sources.
In setting requirements for mixing zones, USEPA
(1984a) requires that "the area or volume of an individ-
ual 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 com-
munity of aquatic life in the segment for which the uses
are designated," and the shape be "a simple configu-
ration that is easy to locate in the body of water and
avoids impingement on biologically important areas,"
and "shore hugging plumes should be avoided."
The USEPA rules for mixing zones recognize the State
has discretion whether 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. A review of
individual State mixing zone policies shows that 48 out
of 50 States (the exceptions are Arizona and Pennsyl-
vania) make use of a mixing zone in some form
(USEPA, 1984a, 1985). State regulations dealing with
streams or rivers generally limit mixing zone widths or
cross-sectional areas, and allow lengths to be deter-
mined on a case-by-case basis.
In the case of lakes, estuaries and coastal waters,
some states specify the surface area that can be
affected by the discharge. (The surface area limitation
usually includes the underlying water column and ben-
thic area.) If no specific mixing zone dimensions are
given the actual shape and size can be determined on
a case-by-case basis.
Special mixing zone definitions have been developed
for the discharge of municipal wastewater into the
coastal ocean, as regulated under Section 301 (h) of
the Clean Water Act (USEPA, 1982). For those dis-
charges the mixing zone was labeled as the "zone of
initial dilution" in which rapid mixing of the waste stream
(usually the rising buoyant fresh water plume within the
ambient saline water) takes place. USEPA (1982) re-
quires that the "zone of initial dilution" be a regularly
shaped area (e.g. circular or rectangular) surrounding
the discharge structure (e.g. submerged pipe ordiffuser
line) that encompasses the regions of high (exceeding
standards) pollutant concentrations under design condi-
tions. In practice, limiting boundaries defined by dimen-
sions equal to the water depth measured horizontally
from any point of the discharge structure are accepted
by the USEPA provided they do not violate other mixing
zone restrictions (USEPA, 1982).
7.2.3 Special Mixing Zone Requirements for
Toxic Substances
USEPA maintains two water quality criteria forthe allow-
able concentration of toxic substances: a criterion maxi-
mum 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.
In order 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
usually more restrictive than the legal mixing zone for
conventional and nonconventional pollutants. USEPA
(1991) recommends four alternatives for preventing
acute lethality. One alternative is to require that the CMC
be achieved within the pipe itself. The other three alter-
natives allow the use of a TDZ.
The first of these involves a high-velocity discharge
combined with a mixing zone spatial limitation. For this
option, USEPA recommends a minimum exit velocity of
3 meters per second (10 feet per second) and a spatial
limitation of 50 times the discharge length scale in any
direction. The discharge length scale is defined as the
square root of the cross-sectional area of any discharge
outlet.
The next alternative recommended by USEPA (1991) is
not to use a high-velocity discharge, but ratherto ensure
that the most restrictive of the following conditions is
met:
• 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.
7-2
-------
PDF
ClicI," Here £ Upgrade.
Expanded Features i
Unlimited Pages;
• 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 is intended to
ensure a dilution factor of at least 10 within this
distance under all possible circumstances, includ-
ing 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 priorto the installation of the
discharge outlet) prevailing under mixing zone
design condition (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 bot-
tom concentrations. (USEPA, 1991)
The latter of these geometric restrictions essentially
eliminates the use of surface (canal-type) discharges
for the discharge of toxic pollutants.
The final recommended alternative is for the dis-
charger to show that a drifting organism would not be
exposed to 1-hour average concentrations exceeding
the CMC, or would not receive harmful exposure when
evaluated by other valid toxicological analysis
(USEPA, 1991).
7.3 Summary
The following two chapters in Part 3 of this manual deal
with the background and the application of predictive
models for mixing zone analysis that address the
various legal requirements as outlined above.
Chapter 8 first gives an overview of the important
physical processes that govern the hydrodynamic mix-
ing of aqueous discharges. Emphasis is put herein on
submerged discharges, because of the practical limi-
tations on surface discharges, in particular as regards
toxic pollutants. Those processes are divided into
near-field processes (influenced directly by the dis-
charge geometry and dynamics and, to some extent,
controllable through appropriate design choices) and
into far-field processes (influenced primarily by the ex-
isting environmental conditions). It is shown that legal
mixing zone requirements can encompass, in general,
processes in both near-field and far-field. Then the
mathematical background and formulations for different
mixing zone models are reviewed. For practical routine
applications, these models fall into two classes: (i) jet
integral models that are applicable only to a sub-set of
near-field processes including submerged buoyant jets
without any boundary (surface or bottom) interaction,
and (ii) a mixing zone expert system, CORMIX, that
addresses both near-field and far-field processes under
a variety of discharge and ambient conditions.
Chapter 9 illustrates the application of jet integral models
and of the expert system CORMIX. Typical data require-
ments for the implementation of these models are dis-
cussed. Four case studies are presented in order to
demonstrate the capabilities and/or limitations of individ-
ual models.
7.4 References
Congressional Research Service, 1978. Legislative His-
tory of the Clean Water Act 1977. Congressional Re-
search Service, Library of Congress, October 1978, No.
95-14 P. 330.
USEPA. 1982. Revised Section 301 (h) Technical Sup-
port Document. EPA 430/9-82-011, Washington, DC.
USEPA. 1984a. Water Quality Standards Handbook.
Office of Water Regulations and Standards, Washing-
ton, DC.
USEPA. 1984b. Technical Guidance Manual for the
Regulations Promulgated Pursuant to Section 301 (g)
of the Clean Water Act of 1977 (Draft). Washington, DC,
August.
USEPA. 1985. Technical Support Document for Water
Quality-based Toxics Control. Office of Water, Washing-
ton, DC, September.
USEPA. 1991. Technical Support Document of Water
Quality-based Toxics Control. Office of Water, Washing-
ton, DC, March.
7-3
-------
Clicl," Here £ Upgrade.
Expanded Features i
PDF Unlimited Pages;
;
-------
8. Physical Processes and Modeling Methodologies
8.1 Ambient and Discharge Conditions
The mixing behavior of any wastewater discharge is
governed by the interplay of ambient conditions in the
receiving water body and by the discharge charac-
teristics.
The ambient conditions in an estuary or coastal water
body are described by geometric parameters - such as
plan shape of the estuary, vertical cross-sections, and
bathymetry, especially in the discharge vicinity and by
its dynamic characteristics. The latter are given by the
velocity and density distribution in the estuary, again
primarily in the discharge vicinity.
Many estuaries are highly energetic water bodies and
their velocity field with its vertical and temporal variabil-
ity may be influenced by many factors. Usually the
most significant velocity component is controlled by
tidal influences, but freshwater inflows, wind-driven
currents and wave-induced currents may also play
important roles and, in some cases, may even domi-
nate the flow. Furthermore the mean velocity field is
often superposed by secondary currents due to topo-
graphic effects or due to baroclinic influences giving
rise to complicated three-dimensional flow fields.
The density distribution in estuaries is usually strongly
coupled with the velocity field. Density differences are
mostly caused by the freshwater inflow and lighter,
less saline, water tends to overflow the more saline
ocean water. Estuaries are sometimes classified on
the basis of their density structure into well-stratified,
partially-stratified and vertically mixed estuaries (Fis-
cher et al., 1979). Well stratified estuaries, usually
those with weak tidal effects, exhibit a two-layer struc-
ture with an upper predominantly fresh water layer
flowing over a lower saline layer (the so-called salt
wedge). The dominant vertical velocity distribution in
that instance is a seaward flow in the upper layer and
a reversed landward flow in the lower layer. The other
end of the spectrum is given by vertically well mixed
estuaries with strong tidal energetics leading to nearly
complete vertical mixing although density gradients
may still exist in the horizontal direction (i.e. along the
axis of the estuary or tidal bay).
Clearly, a major feature of estuarine ambient condi-
tions is their time variability. For tidally controlled cur-
rents this is given by a time scale equal to the tidal
period. Other time scales, usually also of the order of
several hours, describe wind driven currents and
seiche motions. However, the time scale for initial
mixing processes of effluent discharges is usually much
shorter (of the order of minutes to tens of minutes) so
that it usually suffices to analyse certain flow and density
conditions under a steady-state assumption. The con-
sideration of tidal reversals and potential pollutant ac-
cumulation is discussed further below (Section 8.6).
The discharge conditions relate to the geometric and
flux characteristics of the submerged outfall installation.
For a single port discharge the port diameter, its eleva-
tion above the bottom and its orientation provide the
geometry; for multiport diffuser installations the ar-
rangement of the individual ports along the diffuser line,
the orientation of the diffuser line and construction
details represent additional geometric features. The flux
characteristics are given by the discharge flow rate from
the port, by its momentum flux and by its buoyancy flux.
The buoyancy represents the relative density difference
between discharge and ambient that, upon multiplica-
tion with the gravitational acceleration, is a measure of
the tendency for the effluent flow to rise (for positive
buoyancy) or to fall (for negative buoyancy).
8.2 Hydrodynamic Mixing Processes
The hydrodynamics of an effluent continuously dis-
charging into a receiving body of water can be concep-
tualized 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
buoyant jet subsurface flow and any surface or bottom
interaction, or in the case of a stratified ambient, termi-
nal 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 impor-
tant. Conditions existing in the ambient environment will
control trajectory and dilution of the turbulent plume
through buoyant spreading motions and passive diffu-
sion due to ambient turbulence. This region will be
referred to here as the "far-field'.
It is stressed at this point that the distinction between
near-field and far-field is made purely on hydrodynamic
grounds. It is unrelated to any legal mixing zone defini-
tions that address prescribed water quality standards as
discussed in Section 7.2.2. In many practical cases the
legal mixing zone may, in fact, include near-field hydro-
dynamic mixing processes. But that does not
-------
r (ROUND JET)
n (SLOT JET)
AMBIENT DENSITY pg - CONST
CONCENTRA TION—
cc
BUOYANCY^..
9c
D (ROUND JET)
B (PLANE JET)
uo- f>0
-------
a ) Deep water, high buoyancy,
vertical discharge
c ) Deep water, high buoyancy,
non-vertical discharge
AX A X .x
b ) Shallow water, low buoyancy,
vertical discharge
///A/VXAA/X W X 7 /
d) Shallow water, low buoyancy
non-vertical discharge
Figure 8-2. Stable or unstable near-field flows produced by submerged buoyant discharges.
to trapping of the flow at a certain level (trapping level
or terminal level).
8.2.1.2 Boundary Interaction Processes and Near-Field
Stability
Ambient water bodies always have vertical bounda-
ries: these are the water surface and the bottom, but
in addition "internal boundaries" may exist in the form
of layers of rapid density change (pycnoclines). De-
pending on the dynamic and geometric characteristics
of the discharge flow, a variety of interaction phenom-
ena can occur at such boundaries. Furthermore, in the
case of a continuously (e.g. linearly) stratified ambient
where flow trapping may occur, other interaction phe-
nomena may take place.
In essence, these interaction processes provide a
transition between the buoyant jet mixing process in
the near-field, and between buoyant spreading and
passive diffusion in the far-field.
Interaction processes can be (i) gradual and mild or (ii)
abrupt leading to vigorous transition and mixing proc-
esses, (i) If a buoyant jet is bent-over by the cross-flow
it will gradually approach the surface, bottom or terminal
level and will undergo a smooth transition with little
additional mixing.
(ii) If a jet is impinging normally, or near-normally, on a
boundary, it will rapidly spread in all directions (see
Figure 8-2). Different possibilities exist at that point: (a)
If the flow has sufficient buoyancy it will ultimately form
a stable layer at the surface (Figure 8-2a,c). In the
presence of weak ambient flow this will lead to an
upstream intrusion against the ambient current, (b) Ifthe
buoyancy of the effluent flow is weak or its momentum
very high, unstable recirculation phenomena can occur
in the discharge vicinity (see Figure 8-2b,d). This local
recirculation leads to re-entrainment of already mixed
water back into the buoyant jet region. Thus, simple
buoyant jet analyses no longer suffice to predict these
phenomena.
The aspect of near-field stability, i.e. the distinction into
stable or unstable conditions, is a key feature of pollu-
tion analyses. "Stable discharge" conditions, usually
occurring for a combination of strong buoyancy, weak
momentum and deep water, are often referred as "deep
8-3
-------
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 8-3. Bottom attachment processes for submerged
discharges.
water" conditions. "Unstable discharge" conditions, on
the other had, may be considered synonymous to
"shallow water" conditions. Further detail on discharge
stability can be found in Jirka (1982 a,b) and Holley
and Jirka (1986).
Yet another type of interaction process concerns sub-
merged buoyant jets discharging in the vicinity of the
water bottom into a stagnant or crossflowing ambient.
Two types of dynamic interaction processes can occur
that lead to rapid attachment of the effluent plume to
the water bottom (see Figure 8-3). These may be wake
attachment forced by the crossflow or Coanda attach-
ment (due to low pressure effects) forced by the en-
trainment demand of the effluent jet itself. In either
case the assumption of free buoyant jets is invalidated
and other analyses have to be pursued for these
bottom-attached flows.
8.2.1.3 Multiport Diffuser Induced Flows in Shallow
Water (Intermediate-Field)
Some multiport diffuser installations represent large
sources of momentum, while their buoyancy effects
may be relatively weak. Therefore these diffusers will
have an unstable near-field with shallow water condi-
tions. This is characteristic, for example, for cooling
water diffusers from thermal power plants. For certain
diffuser geometries (i.e. the unidirectional and the
staged diffuser types; see Section 8.3) strong motions
can be induced in the shallow water environment in the
form of vertically mixed currents that laterally entrain
ambient water and may extend over long distances
before they re-stratify or dissipate their momentum. In
a sense, these "diffuser plumes" extend beyond the
strict near-field (of the order of the water depth) and are
sometimes referred to as the "intermediate-field" (Jirka,
1982b).
8.22 Far-Field Processes
In the context of this report, far-field mixing processes
are characterized by the longitudinal advection of the
mixed effluent by the ambient current velocity.
8.2.2.1 Buoyant Spreading Processes
Buoyant spreading processes are defined as the hori-
zontally 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. If the dis-
charge is nonbuoyant, or weakly buoyant, and the am-
bient 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 fluid.
As an example, the definition diagram and structure of
surface buoyant spreading processes in unstratified
crossflow is shown in Figure 8-4. The laterally spread-
Front
Plan View
-Initial
Condition
Cross-section A-A
tf
^v8/:{b
^
Frontal Zone
, n
j>*%Pa-Xp$&
1 ^
1 Pa
\
H
Buoyant Surface Spreading
Figure 8-4. Buoyant spreading processes in the far-field
(Example: surface spreading).
-------
ing 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. Further-
more, the flow may interact with a nearby bank or
shoreline (not shown in the figure). The layer thickness
may decrease during this phase.
Depending on source and ambient characteristics,
buoyant spreading processes can be effective trans-
port mechanisms that can quickly spread a mixed
effluent laterally over large distances in the transverse
direction. This can be particularly pronounced in cases
of strong ambient stratification in which the effluent at
the terminal level that may initially be of considerable
vertical thickness collapses into a thin but very wide
layer unless this is prevented by lateral boundaries.
8.2.2.2 Passive Ambient Diffusion Processes
The existing turbulence in the ambient environment
becomes the dominating mixing mechanism at suffi-
ciently 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 8-5). Furthermore, it may interact with the chan-
nel bottom and/or banks.
The strength of the ambient diffusion mechanism de-
pends on a number of factors relating mainly to the
geometry of the ambient shear flow and the ambient
stratification. In the context of classical diffusion theory
(i.e. gradient diffusion, see Fischer et al., 1979) diffu-
sion processes in bounded flows (e.g. rivers or narrow
estuaries) can be described by constant diffusivities in
the vertical and horizontal direction that depend on
turbulent intensity and on channel depth or width as
the length scales. On the other hand, wide "un-
bounded" channels or open coastal areas are charac-
Plan View
, Possible Bank Interaction
—.^Y*?
Side View
Possible Bottom Interaction
terized by plume size dependent diffusivities leading to
accelerating plume growth described, for example, by
the "4/3 law" of diffusion. In the presence of a stable
ambient stratification the vertical diffusive mixing is gen-
erally strongly damped.
8.3 Mathematical Predictive Models
8.3.1 Modeling Methodology
In principle, one can conceive of two approaches to the
prediction of effluent discharges in the water environ-
ment: complete models or zone models.
(i) Complete models: These are three-dimensional nu-
merical models that directly solve a finite difference or
finite element approximation for the full dynamic and
mass conservation equations with various assumptions
for the turbulent shear and mass transport terms. In
principle, with the advent of powerful computing facili-
ties, even on the desktop, such a complete modeling
approach that encompasses the entire fluid domain of
interest with all individual mixing processes appears
feasible. However, successful applications to date have
been limited. Apparent reasons for the present short-
comings include (1) lack of fully workable turbulence
closure techniques under the influence of buoyancy
while considering the full range of jet-induced geophysi-
cal turbulence; (2) the difficult trade-off of modeling a
large enough domain while providing sufficient resolu-
tion in a three-dimensional model (computer capacity
and costs); and (3) the unknown nature of the open fluid
boundary conditions which need to be specified as part
of the elliptic equation system. These boundaries may,
in general, contain a combination of stratified inflow and
outflow that is inherently difficult to specify. For these
reasons, complete numerical models are usually not
used in routine mixing zone analyses of effluent dis-
charges and this is expected to remain so for at least
the next decade.
(ii) Zone Models: Instead of attempting to integrate the
general governing equations over the whole region of
interest it is frequently useful to divide the region into
several zones with distinct behavior (such as individual
mixing processes in the near-field and in the far-field).
Within these zones it is then possible to simplify the
governing equations by dropping unimportant terms.
This gives a considerable advantage in the mathemati-
cal treatment and improved accuracy in the solution.
However, a challenge remains because the solutions
are restricted to specific zones. Thus, criteria need to
be established for a meaningful division of the whole
region into zones, and to provide transition conditions
between zones.
Figure 8-5. Passive ambient diffusion processes.
3-5
-------
Current practice in pollution analyses relies on zone
models. Such models that deal with individual flow
processes are described in the specialized research
literature as well as in several monographs (e.g. Fis-
cher et al., 1979, Holley and Jirka, 1986). However, a
problem arises because there is limited guidance to
the model user on the limits of applicability of each
model, and on how to combine the individual models
for an overall prediction of the entire flow process. The
use of an integrated expert system framework (see
below) promises to alleviate this problem.
An important group of zone models are the so-called
buoyant jet integral models that are limited to the
buoyant jet mixing process as described in Section
8.2.1.1 without attention to any problems of boundary
interaction and near-field instability. Several of such
integral model formulations are available as computer
programs. Whenever their applicability has been as-
certained, these models have been found through
numerous data-model comparisons to be reliable and
accurate. Jet integral models will be reviewed in Sec-
tion 8.4.
An integrated framework of zone models for aN impor-
tant near-field and far-field mixing processes that effect
effluent mixing has recently been developed. This
framework is in the form of an expert system that
classifies each discharge/ambient condition as to
which flow processes are important and provides a
prediction through a sequence of zone models with
appropriate transition conditions. The zone modeling
expert system methodology CORMIX (Doneker and
Jirka, 1990; Akar and Jirka, 1991) is discussed in
Sections 8.5 and 8.6.
8.3.2. Zone Model Schematizations of
Discharge and Ambient Conditions
All zone models require some schematization of the
complex and arbitrary ambient and discharge condi-
tions that may prevail at any discharge site. These
simplifications are needed to conform to the require-
ments of the individual models.
A schematic definition diagram for a single port dis-
charge is given in Figure 8-6. The bottom is assumed
to be flat (constant depth) while any banks (if consid-
ered in the analysis) are assumed to be vertical.
A corresponding diagram for multiport diffusers is pro-
vided in Figure 8-7. Of particular interest for this case
is the alignment angle y between the crossflow direc-
tion and the diffuser axis, the orientation angle p be-
tween the individual port axes and the diffuser line, and
the vertical angle 9 between port axis and the horizon-
tal plane. Three major diffuser types have evolved in
actual design practice and can be characterized by
these angles (see Figure 8-8).
In the unidirectional diffuser, all the ports point in the
same direction perpendicular to the diffuser axis
(p=90°). In the staged diffuser, all ports point along the
diffuser line (P = 0°). In the alternating diffuser, the
ports are arranged in an alternating fashion and point in
opposite directions (P=+90°). The undirectional and
the staged diffusers possess a net horizontal momen-
tum input with a tendency to induce currents within the
ambient water body. The alternating diffuser has a zero
net horizontal momentum, and a lesser tendency to
generate currents and circulations.
Of course, there are variations on the basic theme for
each of the three diffuser types. Some of these design
possibilities are shown in Figure 8-8. There may be
double or triple nozzle arrangements (with a small inter-
nal angle) for both unidirectional or staged diffusers, and
the port orientation angle p may differ somewhat from
the nominal value, 90° or 0°, respectively. Or, in case
of the alternating diffuser, there may be multiple port
assemblies for each riser with several ports arranged in
a circular fashion. Furthermore, alternating diffusers for
thermal discharges in shallow water may have a vari-
able port orientation along the diffuser axis to control
instabilities and horizontal circulations (for details, see
Jirka, 1982b). Another special case of
CROSS-SECTION
1Z
"a
f
—
PLAN VIEW
y
. Pa
X^o
•A '
'/ "-x
>
Nearest bank
D, U0, Aft,, C0
Figure 8-6. Schematics of single port discharge geometry in
ambient channel with rectangular cross-section
(width W may be finite or unlimited).
Cross-Section
Figure 8-7. Schematics of multiport diffuser geometry in
ambient channel with rectangular cross-section
(width W may be finite or unlimited).
-------
'i
g<90°
0 = 90° 00«e"9°°
Without control
a) Unidirectional diffuser, eas 0°
¥ in n in ;?,
= ±90°
90°
.1 ^1 t 1 j t j-l-pt, e-±*r
Control: Fanned design
V^y
o < 90°
Vertical
S0=90°
V
b) Staged diffuser, S0=08
> }/J 1 1 ii { <
c) Alienating diffuser, 90 = variable
Control ;
' Fannea design
LD
Figure 8-8. Schematic plan views of three major diffuser types: a) Unidirectional diffuser, b) Staged Diffuser, c) Alternating
diffuser. Any of those diffusers may have a variable alignment y relative to the ambient current.
an alternating diffuser is given by a vertical discharge
from all ports. olumeflux: Q = 2n\_urdr= 2n/i ucbz (1)
Any diffuser can be deployed with arbitrary alignment
y. However, the two major arrangements are the
perpendicular alignment ( y«90°) and the parallel
alignment (y= 0°).
8.4 Buoyant Jet Integral Models
8.4.1 Basic Elements: Stagnant Unstratified
Ambient
The narrow elongated shape of the turbulent zone
within a buoyant jet (see Figure 8-1) suggests bound-
ary-layer type simplifications to the equations of fluid
motion and mass transport. The equations may be
further simplified by integrating across the local jet
cross-section thereby yielding a one-dimensional
equation setforthe actual three-dimensional problem.
This is the essence of jet integral models which solve
the equation set with a simple integration scheme
marching forward along the trajectory.
The integral method is demonstrated in the following
for a round buoyant jet issuing into a stagnant unstrati-
fied ambient (Figure 8-1). The jet-trajectory is assumed
to lie within an x-z coordinate system. Local integration
across the buoyant jet gives the following flux (integral)
quantities:
oo
olume flux: Q = 2n\ urdr = 2nl\ ucb2
JQ
Momentum flux (kinematic):
M = 2n \ u2rdr=2nl2Ucb2
0
Scalar (pollutant) mass flux:
ucrcfr= 271/3 ucccb2
Buoyancy flux:
ug'rdr=2nl3UCg'cb2
(2)
(3)
(4)
in which u = mean velocity in the trajectory direction, r
= transverse coordinate from local jet centerline, c =
mean concentration, and g = mean buoyant accelera-
tion relative to the outside fluid where
Pa- P
9 = E L 9
pa
(5)
p = local density, pa = ambient density, and g = gravita-
tional acceleration. In the rightmost integrated quanti-
ties, the subscript c indicates centerline values, and the
width b is a measure of the width of the jet (see below).
The profile constants I\,Ii,/3, are simple numerical
values that depend on the chosen profile shape and on
the width definition (see Holley and Jirka, 1986). Fre-
quently, a bell-shaped Gaussian profile is
3-7
-------
chosen and the width b is conveniently defined by the
"1/e width" where the local quantities are 1/e = 37% of
the centerline value.
When the conservation laws are applied to these four
flux quantities using a control volume of differential
length ds where s = axial direction along trajectory the
following differential equations arise:
Volume flux conservation: — = 2n a uc b (6)
CIS
i.e. the volume flux (discharge) increases due to en-
trainment along the jet periphery.
Axial momentum flux conservation:
—:—= 271/4Qcb2sin 9
OS
(7)
i.e., only the sin 9 component of buoyancy produces
acceleration in the axial direction, in which 9 = local
vertical angle.
Horizontal momentum flux conservation:
-fj- (M cos 9) = 0 (8)
i.e., no acceleration in the horizontal direction.
Scalar flux conservation:
dQc
ds
= 0
(9)
dJ
Buoyancy flux conservation: — = 0 (10)
CIS
i.e. in the uniform ambient environment both fluxes
stay constant.
In addition, it is necessary to relate the local coordinate
system (s, 9) to the fixed global one (x, y)
= cos 9
— = sin 9
ds
(11)
(12)
This system of seven ordinary differential equations is
fully specified by seven initial conditions at s = 0. These
are the initial bulk fluxes M0 , Jo , Qo , and QCo (alter-
natively,given by U0 , go = g (pa - po)/pa , c0 , and D
and the geometry x0 , z0 , and 90.
Solution of this ordinary differential equation system by
any chosen numerical method yields the seven local
buoyant jet measures. These are M, J, Q, and Qc (or
alternatively, the related variables uc, gc , cc , and b)
and the trajectory measures x,z, and 9 .The local bulk
(flux-averaged) dilution is then given by the ratio
Q/Qo and the local centerline (minimum) dilution by the
ratio
Two fundamental difficulties exist in the jet integral
method:
(i) The closure problem: Entrainment and mixing of
ambient fluid is a turbulent flow phenomenon. The
volume flux conservation, Equation 6, presupposes that
the mean entrainment velocity ve , (see Figure 8-1) is
linearly related to the centerline velocity, ve = auc,
where a= entrainment coefficient. Inspection of data
on buoyant jets that undergo a transition from initial
jet-like (momentum-dominated) to final plume-like
(buoyancy-dominated) behavior shows that a is quite
variable. In some integral models a geometric equation
is used instead of Equation 6, namely
Jet spreading: — = k
CIS
(6a)
In which k = spreading coefficient with somewhat less
variability between the jet-like and plume-like stages.
The actual choice of the appropriate equation, Eqs. 6 or
6a, and the specification of the coefficient that may be
a function of local flow conditions is generally referred
to as the "closure problem". The closure is made differ-
ently in the various integral models. A more detailed
discussion is given by Holley and Jirka (1986).
(ii) The zone of flow establishment: The above equation
set is, strictly speaking, not valid in a short initial zone
of flow establishment in which a gradual adjustment
between the efflux profile (approximately uniform) to the
final bell-shaped profile takes place. Since this zone is
short ( = 5Dto 10D, where D = diameter of the discharge
port), no major error is introduced if it is simply ne-
glected. This is the case in some integral models.
Alternately, some models include an adjustment via a
virtual origin or others perform a detailed, though ap-
proximate, analysis of this zone.
The derivation of integral jet equations for the slot
buoyant jet (see the alternative source conditions indi-
cated in Figure 8-1) is quite analogous to the round jet.
It is omitted here for brevity (see Holley and Jirka, 1986).
The slot buoyant jet is an important element of the
analysis of subsurface multiport diffuser plumes that are
formed after merging of the individual round jets.
8.4.2 Extensions to Flowing Stratified Ambients
The advantage of jet integral models is their ready
extension to more complex environmental conditions,
such as ambient stratification and crossflow.
-------
BUOYANT
JET EFFLUX
Figure 8-9. Round buoyant jet in ambient crossflow with drag and entrainment forces (Example: vertical discharge).
If the receiving water is stratified with a stable density
gradient (cfpa/cfz<0, i.e. the ambient density
= pa (z) decreases upward), then the buoyancy flux is
not conserved along an upward jet trajectory but is
constantly decreasing. Eventually the buoyant jet will
reach, and may even overshoot, its terminal level zt at
which the local internal jet density is equal to the
ambient density pa (z t). The jet will become trapped
at this level and spread horizontally in the form of a
gravitational current. The jet mechanics prior to the
terminal level are readily described with the integral
technique if two extensions are made. First, the buoy-
ancy profiles are now defined with respect to the local
reference buoyancy
Pa(z)
(13)
instead of Equation 2, leading to modification of Equa-
tions 3 and 7, respectively. Second, from mass bal-
ance requirements, the buoyancy flux is decreasing at
the same rate at which it is diluted with ambient water
of lesser density. This leads to
ds
(14)
for the round jet, instead of Equation 10. Inherent in
these expressions is the assumption that the average
density of the entrained water is equal to the density at
the level of trajectory (centerline). This excludes cases
of very rapid local changes, such as steep pycnoclines
in estuaries.
When a round buoyant jet is discharged into an ambient
crossflow of velocity ua, then it will be deflected in the
direction of the crossflow. This deflection is brought
about by two force mechanisms, a pressure drag force
FD and a force Fe due to the entrainment of crossflow
momentum. Referring to Figure 8-9, this situation is
readily described in the integral analysis framework
provided that several adjustments are made. First, ne-
glecting the horseshoe or "kidney" shape (Fischer et al.,
1979) which actually exists and assuming that the jet
may be approximated by a circular cross-section, the
velocity profile in the jet cross-section is given by the
sum of the ambient velocity component in the direction
of the trajectory, ua cos 9, and the bell-shaped jet pro-
file. This, then, affects the definition of all jet bulk flux
variables, M, J, Q and Qc. The definition of the drag
force normal to the jet axis, and per unit length of the jet
axis, is (in kinematic units)
FD = CD ua sin2
9 (2Jb)
(15)
in which CD is a drag coefficient (of order of unity), and
the width of the "jet body" is simply taken as 2b. The
-------
entrainment force (entrainment of ambient momen-
tum) is
dQ
(16)
The governing momentum equations, Equations 7 and
8 are amplified to
dM ' 2
—j— = 2n /4 gc b sin 9 + Fe cos 9
CIS
-£- (M cos 9) = Fe + FD sin 9
(17)
(18)
Also, it is observed in bent-over jets that the entrain-
ment mechanism is considerably more vigorous and
the entrainment velocity not simply proportional to uc
as in the previous case. Several analyses have sug-
gested that jet entrainment in crossflows has a second
contribution once the jet is strongly bent-over but still
slowly rising. This second contribution is similar to that
of a horizontal line element of fluid that is rising due to
an initial vertical impulse of momentum or due to initial
buoyancy in a stagnant ambient fluid. The rising line
element experiences turbulent growth and entrain-
ment that is proportional to the velocity of rise. Since
the strongly bent-over jet is similar to this line element,
this second entrainment mechanism can be added to
the original entrainment mechanism associated with
the excess of forward jet velocity relative to the sur-
rounding fluid. The result is
—r- = 2na
2na.2 ua Jbsin 9 cos 9 (19)
where a is of the same form as for a buoyant jet in
stagnant ambient (Equation 6) and oc2 is the crossflow
induced entrainment coefficient.
8.4.3 Overview of Jet Integral Models Available
for Mixing Zone Analysis
A large number of jet integral models for submerged
single port or multiport discharges are reported in the
literature. However, only a few of these are available
for practical mixing zone analysis in the form of com-
puter programs accessible to the analyst. Several of
these are discussed below.
The validity and reliability of a jet integral model should
be promulgated on at least two considerations: First,
is its theoretical formulation sound and does it perform
accurately under limiting conditions (e.g. the pure jet
or pure plume)? Second, how do the model predic-
tions compare with available data, preferably field
data? No complete evaluation on these grounds of
integral jet models is attempted here, but some impor-
tant model features will be addressed in Section 3. It is
stressed again that none of the following integral jet
models include any form of boundary interaction proc-
esses; in a sense they all assume an unlimited receiving
water body.
The U.S. EPA has published a set of five buoyant jet
integral models (Muellenhoff etal., 1985), all with differ-
ent capabilities. These models include computer pro-
grams written in FORTRAN for micro or minicomputers.
(1) The computer model UPLUME describes a buoyant
jet issuing from a single port into a stagnant environment
with arbitrary stratification. UPLUME is based on Abra-
ham's (1963) original development using a jet spreading
equation for closure. Empirical adjustment expressions
are included for the zone of flow establishment.
(2) The model UOUTPLM (based on Winiarski and
Frick, 1976) uses a somewhat different Lagrangian
description of buoyant jet mechanics instead of the
Eulerian system of equations given in Section 8.4.1.
Thus, a plume element is tracked in its time-dependent
evolution. However, the mechanisms actually included
are similar to the ones discussed above with the excep-
tion of the omission of the ambient drag force. The
model is applicable to a uniform crossflow with co-flow-
ing or cross-flowing single port orientation (excluding
counterflows) and with arbitrary density stratification.
The model is not applicable for stagnant conditions.
(3) The model UMERGE is an extension of UOUTPLM
applicable to multiport diffusers with perpendicular
alignment. Merging is assumed to occur when geomet-
ric overlap of the individual equally spaced round jets
occurs. After merging, the flow is described by the
time-dependent motion of two-dimensional plume ele-
ments.
(4) UDKHDEN is a model that computes three-dimen-
sional trajectories from either single port or multiport
discharges in crossflows with arbitrary velocity (shear
flow) and density distributions. The model is based on
the development by Hirst (1971) and later generaliza-
tions by Kannberg and Davis (1976). The initial zone of
flow establishment is computed in detail with Hirst's
model. The three-dimensional equation system is a
generalization of the type discussed in the preceding
section. An entrainment function with dependence on a
local densimetric Froude number is used for closure. A
special geometric merging routine describes the grad-
ual transition from individual round plumes to the two-
dimensional plume. However, the same entrainment
coefficient is used for round and for plane buoyant jets,
making it impossible to verify the model
-------
for well-known asymptotic conditions. The diffuser
alignment relative to the crossflow must be predomi-
nantly perpendicular.
(5) The model ULINE is strictly speaking not a jet
integral model but uses an analytical solution for the
two-dimensional slot plume dilution as a function of
elevation. This solution is modified on the basis of
Roberts' (1977) experimental results for the effect of
alignment on a diffuser line plume in crossflow. Also a
stepwise algorithm is included to compute local mixing
in an arbitrary crossflow and stratification. The model
omits the merging process, thus assuming an initially
merged (e.g. closely spaced) diffuser discharge.
Another buoyant jet model is that of Jirka and Fong
(1981) to predict general three-dimensional trajecto-
ries for a single port discharge in a crossflow with
arbitrary stratification. The model uses empirical de-
scriptions for the zone of flow establishment as pro-
posed by Schatzmann (1978). The model includes an
entrainment closure that meets several limiting condi-
tions and that has been extensively verified by Wong
(1984) in application to ambient stratification. An addi-
tional element of the Jirka-Fong model is the descrip-
tion of the internal vortex mechanism in crossflow that
can lead to plume bifurcation when a flow boundary or
terminal level is encountered.
8.5 CORMIX: Expert System Methodology
for Mixing Zone Analysis
8.5.1 Introduction
The Cornell Mixing Zone Expert System (CORMIX) is
a series of software elements for the analysis and
design of submerged buoyant or nonbuoyant dis-
charges containing conventional ortoxic pollutants into
stratified or unstratified watercourses, with emphasis
on the geometry and dilution characteristics of the
initial mixing zone. Subsystem CORMIX1 (Doneker
and Jirka, 1990) deals with single port discharges and
subsystem CORMIX2 (Akar and Jirka, 1991) ad-
dresses multiportdiffusers [Another subsystem, COR-
MIX3 (Jones and Jirka, 1991), has been developed for
surface discharges, but is not discussed here given the
limitations of surface discharges in meeting toxic dilu-
tion criteria; see Chapter 7]. The system is imple-
mented on microcomputers with the MS-DOS
operating system.
The user supplies CORMIX with information about the
discharge and ambient environment. CORMIX 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, CORMIX also
presents information about legal mixing zone dimen-
sions and dilution and about toxic mixing zone require-
ments.
CORMIX contains two key elements. The first is a
rigorous flow classification scheme that classifies any
given discharge/environment situation into one of sev-
eral 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 considered.
The second key element is a collection of predictive
elements (modules) that are executed according to a
protocol that pertains to each distinct flow class as
determined by the classification scheme. These predic-
tive elements are all based on simple analytical pertur-
bation solutions for each flow process. Furthermore,
transition rules are used to describe the spatial extent
of each flow process.
The final result is a robust composite flow and mixing
zone prediction that is applicable to a diverse variety of
discharge/ambient conditions. CORMIX1 and 2 have
been extensively validated with both laboratory and field
data.
The geometric schematizations assumed in CORMIX
have been summarized in Figures 8-6 to 8-8, respec-
tively. In addition, CORMIX assumes a uniform un-
sheared ambient velocity profile represented by the
mean velocity ua. Furthermore, CORMIX requires that
the ambient density profile be approximated by one of
four representative stable profiles as shown in Figure
8-10. A dynamically correct approximation of the actual
distribution should keep a balance between over- and
under-estimation of the actual density data. The sim-
plest case is a linear density profile shown in Figure
8-1 Oa (Stratification Type A). Figure 8-1 Ob describes
two uniform density layers with a density jump (pycno-
cline) between layers (Stratification Type B). Figure
8-1 Oc illustrates a two layer profile in which the upper
layer is uniform, the lower layer has a linear stratifica-
tion, and a density jump occurs between layers (Strati-
fication Type C). Finally, Figure 8-1 Od 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 are representative for
the well mixed upper layer that is found in many types
of ambient water bodies and occurs due to wind induced
turbulent mixing.
8-11
-------
H
4
—* 1
\
\
,*\
\
\
\
hint
Linear
Two-Layer
_S2_
Figure 8-10. Schematic ambient density profiles for use in expert system CORMIX.
8.5.2 Length Scales
Length scales, obtained from dimensional analysis,
describe the relative importance of discharge volume
flux, momentum flux, buoyancy flux, ambient cross-
flow, and density stratification in controlling flow behav-
ior. The length scales will describe the distance over
which these dynamic quantities control the flow, in
particular within the subsurface buoyant jet regions of
the mixing process.
8.5.2.1 Single Port Discharges
Given the important flux parameters, Q0 , M0 , and
Jo (see Figure 8-5), the ambient velocity ua, and the
buoyancy gradient e = -(g/pa)(cfpa/c/z) of a line-
arly stratified ambient, the following dynamic length
scales can be derived for a single port discharge:
LQ = Q0/Mo2= discharge (geometric) scale
LM = Mo*/Jo2 = jet/plume transition scale
Lm = Mo2/ua = jet/crossflow scale
Lb = Jo/ill = plume/crossflow scale
Lm = (M0 /e )/4 = jet/stratification scale
Lb = JoVe /8 = plume/stratification scale
The meaning of these scales is further illustrated in
Figure 8-11. For example, the jet/crossflow length
scale is a measure for the distance over which a pure
jet will intrude into a crossflow before it gets strongly
deflected (or affected). It should be noted that the
length measures are only "order of magnitude"; pre-
cise coefficients have to be determined from experi-
ments or from more detailed flow analysis.
8.5.2.2 MultiportDiffusers
The general diffuser flow field is, of course, three-dimen-
sional. However, for near-field mixing analyses the two-
dimensional flow parameters are dynamically relevant.
For this purpose, the details of individual discharge jets
with port diameter D and spacing S are neglected and
replaced by an equivalent slot width B =(nD2)/(4S) on
the basis of equivalency of momentum flux per unit
diffuser length. This concept has been discussed by
Jirka (1982b) among others, and has been shown to be
a dynamically accurate representation. The main pa-
rameters for the two-dimensional slot discharge are the
diffuser total flowrate Qc and the discharge buoyancy
g0. This leads to the following flux parameters (per unit
diffuser length), all expressed in kinematic units:
qo = QO/LD = volume flux (flowrate)
m0 = qo U0= Uo B = momentum flux
jo = qg'o = U0g'o B = buoyancy flux,
in whichf/0 = discharge velocity, and
LD = diffuser length.
Through interaction with the ambient parameters, the
following length scales describe a multiport diffuser
discharge:
lq = q 'o/mo = discharge geometric scale
Im = m0/u^ = plane jet/crossflow scale
3-12
-------
Transition
s
Discharge
ua=0
Plume-iiki
Jet-like
a) Buoyant Jet in Stagnant Uniform Environment
\Transition
\
€ « 0
\ /* S/f .x" Strongly Deflected Jet
f/s
"Weakly Deflected Jet
b) Pure Jet in Uniform Crossflow
0(LJ
€«0
rr Strongly Deflected Plume
/Weakly Otflscted Plume
u =
€>0
u =
Transition
Otnsify current
"Jet-like
d) Pure Jet in Stagnant Stratified Ambient
Density current
™~ ™»
X
e) Pure Plume in Stagnant Stratified Ambient
c) Pure Plume in Uniform Crossflow
Figure 8-11. Length scales measuring the effects of momentum flux, buoyancy flux, crossflow and stratification of submerged jet behavior.
8-13
-------
IM = m0//o2/3 = plane jet/plane plume scale
Im = (m0/£)/3 = plane jet/stratification scale
lb=jo3/£/2= plane plume/stratification scale
la = ua/E/2 = crossflow/stratification scale
It is interesting to note that no plume/crossflow length
scale can be defined on dimensional grounds for the
two-dimensional plume. This is in contrast to the three-
dimensional round plume and arises from the fact that
the vertical velocity of a two-dimensional plume is
constant, ~j o3, leading in the presence of a constant
crossflowto a straight-line trajectory. Thus, no distinc-
tion can be made of a plane plume in a weakly de-
flected stage followed by a strongly deflected stage.
However, it is possible to define a non-dimensional
parameter j 0/U% whose magnitude will be a measure
of the slope of the plume trajectory.
8.5.3 Near-Field Flow Classification
The classification scheme used in CORMIX puts major
emphasis on the near-field flow configuration. This is
because a large number of flow configurations can
occur due to the multiplicity of possible interaction
processes; in contrast the far-field flow is generally
much simpler with limited shoreline or bottom contact
possibilities.
8.5.3.1 Single Port Discharges (CORMIX1)
In the near-field the dynamic length scales
LM , Lm , Lb , Lm and L/j (Lg has less significance) de-
scribe the interaction with the geometric properties of
the water body, its depth H or the depth hint to the
density jump (in general, both of those are indicated
by a layer depth Hs). Also the orientation angles 9o
and o0 of the discharge are important (Figure 8-6).
Given the possible ambient stratification types a clas-
sification procedure (in Doneker and Jirka, 1990) is
used to classify the near-field behavior of a given
discharge into one of 35 generic flow classes that are
summarized in Figures 8-12 to 8-15. The four major
flow categories indicated by CORMIX1 are:
i) flows affected by linear stratification leading to inter-
nal trapping (S classes, Figure 8-12)
ii) buoyant flows in a uniform ambient layer (V and H
classes, Figure 8-13)
iii) negatively buoyant flows in a uniform ambient layer
(NV and NH classes, Figure 8-14)
iv) bottom attached flows (A classes, Figure 8-15).
Each of the flow classes is indicated on the figures by
a sketch that shows its main features in a side view or
plan view. All flow criteria shown on the figures are given
as "order of magnitude" relations; somewhat different
forms and numerical constants may be contained in
CORMIX1.
A wide spectrum of near-field flow configurations is
possible: these range from flows trapped in linear strati-
fication, buoyant jets that are strongly affected by the
crossflow and gradually approach the layer boundary
(surface or pycnocline), weakly deflected buoyant jets
that impinge on the boundary leading to upstream
spreading and/or unstable recirculation, negatively
buoyant jets that form density currents along the bot-
tom, and dynamic attachment along the bottom with or
without eventual buoyant lift-off. It is stressed also that
(i) each of these flow classes can occur in combination
with an upper stratified layer (see stratification types B,
C, or D on Figure 8-10) and (ii) the designation "uniform
ambient layer" in Figures 2-13 and 2-14 can, in fact, also
apply to a stratified layer if it has been found that the
stratification is too weak to trap the flow. Thus, in
essence, the actual number of flow configurations that
can be classified by CORMIX1 is much larger than the
35 generic flow classes shown on these figures.
8.5.3.2 M ultiport Diffusers (CORMIX2)
The classification scheme used by CORMIX2 relies on
the same methodology as for single port discharges.
The length scales of the two-dimensional slot jet,
IM Jm Jb , Im , and la , are compared with the layer
depth Hs and with the diffuser variables, its length LD
and its orientation angles, 9, y, p, o (see Figure 8-7).
The classification procedure (see Akar and Jirka, 1991,
for details) yields 31 generic flow classes that fall into
three major categories: (i) flows affected by linear strati-
fication leading to internal trapping (MS classes, Figure
8-16), ii) buoyant flows in uniform ambient layers (MU
classes, Figure 8-17), and iii) negatively buoyant flows
in uniform ambient layers (MNU classes, Figure 8-18).
While there are some obvious analogies in their appear-
ance to the flows produced by single port discharges,
the major difference for multiport diffusers lies in the
vertically fully mixed (over the layer depth) plumes that
can be produced by the large momentum sources of
unidirectional or staged diffusers.
8.5.4 Predictive Elements
The detailed hydrodynamic prediction of the effluent
flow and of associated mixing zones in CORMIX is
carried out by appropriate flow modules that are ex-
8-14
-------
TEST FOR PLUME TRAPPING
IN A LINEARLY STRATIFIED
LAYER (HEIGHT Ht)
Cress-f few
T@rmin@l
STRATIFSCATIW4
UNIKIPOWTANT
Vgftt€0?
ICGATIVCLY BUOYANT JET
Cor J@ll
BEHAVIOR DOMINATES
FLOW CLASSES
FOR
AMBIENT STRATIFICATION
Figure 8-11. Length scales measuring the effects of momentum flux, buoyancy flux, crossflow and stratification of submerged jet behavior.
8-15
-------
90* < A, < 45"
FLOW CLASSIFICATION
BUOYANT SUBMERGED
DISCHARGES IN
UNIFORM DENSITY LAYER
Steiiow
Lo^er
with
Strong
>l
Figure 8-13. CORMIX1 sub-classification: flow classes for positively buoyant single port discharges in uniform ambient layer.
8-16
-------
NEGATIVELY BUOYANT JET
COR DOWNWARD ORIENTED JET)
IN UNIFORM DENSITY LAYER (HEIGHT H,)
Buoyoncy^
Dominatti
Co-
ross- ®r CroM-f
far-flow
Figure 8-14. CORMIX1 sub-classification: flow classes for negatively buoyant single port discharges in uniform ambient layer.
8-17
-------
CLASSIFICATION BOTTOM ATTACHMENT
VI.V2.SI Hl,H2
NVt,NV2 NHS.NH2
J _ I
end-
WAKE
ATTACHMENT
Ytf
Lit!-Off
{..IAS
-9
Fteekoafeftew
No
No Lift-Off
Recirculation
lS3. HI, H3, H4
h
ton te<0.a-a
With Ufi»Qff
Yes
COANOA
Ffan
Ski*
!M2
tan ®e < 0.2-:
H® Lift-Of I
Cwith WsiS |et
Dominates
Figure 8-15. CORMIX1 sub-classification: assessment of dynamic bottom attachment processes and flow classes for bottom-attached flows.
8-18
-------
TEST FOR PLUME TRAPPING
IN A LINEARLY STRATIFIED
LAYER (HEIGHT Hs)
(Jet-Like
i _
-
Plume-Like/ _|^
Cross-flow
Dominated
Alignment
Angle
X
>.>Slralificolion
\Dominofed
Vertical
Angle
8
Cross- flow/,.
Dominated/ 45" \ Vertica!/>459 \ Perpendiculor/>45" \ Vertical/>45°
<45eiPorollel I <45iHorii0ntal 1 <45"lparaIIel 1 <45'lHorizontdl
Terminal height Zj
AMBIENT STRATIFICATION
UNIMPORTANT
Approximate Ambient Density
with Vertical Mean Value
NEGATIVELY BUOYANT
JET BEHAVIOR DOMINATES
Figure 8-16. CORMIX2 sub-classification: assessment of density stratification and flow classes for internally trapped multiport discharges.
8-19
-------
POSITIVELY BUOYANT
MULTIPORT DIFFUSER DISCHARGE
IN UNIFORM LAYER IHEIGHT HSJ
I
Deep Layer
Sloble Discharge
H.
Shallow Layer
Unstable Dischorge
Weak
Cur re n
MUIV
i 'iiunn-Ult Ij
Current
Alignment
Angle
y
Perpendicular/ > 45*
<45elPorQllel
MUZ
Perpendicular
Current,
Strong Weak
Current Currert'
Alignment
Angle
y
Perpendicular
MU4
MU5
MU6
= Side View
P = Plon View
Figure 8-17. CORMIX2 sub-classification: flow classes for positively buoyant multiport discharges in uniform ambient layer.
8-20
-------
NEGATIVELY BUOYANT
MULTIPQRT OIFFUSER DISCHARGE
IN UNIFORM LAYER (HEIGHT H
Strong
Cross-flow
P»PIon View
Dlffuser-lnducid Flews Near Bottom
(not fully mixed!
>l
Shallow Layer
Flow Classes MNU7-MNUI4
(Vertically Fully Mixed)
(Correspond lo Flow Classes
MU2-MU9, Respectively,
with the Exception of
Bottom Restrafificoliort
in the Far Field I
Figure 8-18. CORMIX2 sub-classification: flow classes for negatively buoyant muitiport discharges in uniform ambient layer.
8-21
-------
Table 8-1. Flow Prediction Modules of CORMIX1 (Single Port
Discharges)
Table 8-2. Flow Prediction Modules of CORMIX2 (Multiport
Diffusers)
Modules for Buoyant Jet Near-Field Flows
:one of flow establishment
weakly deflected jet in crossflow
weakly deflected wall jet in crossflow
near-vertical jet in linear stratification
lear-horizontal jet in linear stratification
strongly deflected jet in crossflow
strongly deflected wall jet in crossflow
weakly deflected plume in crossflow
strongly deflected plume in crossflow
Modules for Boundary Interaction Processes
lear-horizontal surface/bottom/pycnocline approach
near-vertical surface/bottom/pycnocline impingement
with buoyant upstream spreading
lear-vertical surface/bottom/pycnocline impingement with
vertical mixing
lear-vertical surface/bottom/pycnocline impingement,
upstream spreading, vertical mixing, and buoyant
restratifi cation
:erminal layer stratified impingement/upstream spreading
:erminal layer injection/upstream spreading
Modules for Buoyant Spreading Processes
suoyant layer spreading in uniform ambient
suoyant spreading in linearly stratified ambient
Modules for Attachment/Detachment Processes
wake recirculation
ift-off/fall-down
Modules for Ambient Diffusion Processes
sassive diffusion in uniform ambient
sassive diffusion in linearly stratified ambient
ecuted according to a protocol that pertains to each
distinct flow configuration as determined by the classi-
fication scheme. These flow protocols have been con-
structed on the basis of the same length scale
arguments that have been used for the flow classifica-
tion. The spatial extent of each flow module is gov-
erned by transition rules. These determine transitions
between different near-field and far-field mixing re-
gions, and distances to boundary interaction.
The flow modules for single port discharge predictions
(CORMIX1) are listed in Table 8-1. All modules pre-
sent basic analytical solutions for one particular flow
process with the perturbing influence of one or more
other variables superimposed. For example, the mod-
ule for the weakly deflected jet in crossflow (MOD11)
is based on a pure jet solution that experiences a
gradual advection by the crossflow. The group of near-
field modules (MOD01 to MOD22) represents, in total,
the same predictive ability as buoyant jet integral mod-
els (valid in the subsurface region without boundary
interaction).
The flow modules for multiport diffuser prediction
(CORMIX2) are given in Table 8-2. Several groups of
modules, notably those for the far-field, are similar, or
even identical, to those of CORMIX1.
simulation Modules for Buoyant Multiport Diffusers:
Subsurface Near-Field Flows
Jischarge module
Jischarge (staged diffuser)
weakly deflected plane jet in crossflow
weakly deflected (3-D) wall jet in crossflow
lear-vertical plane jet in linear stratification
lear-horizontal plane jet in linear stratification
strongly deflected plane jet in crossflow
weakly deflected (2-D) wall jet in crossflow
weakly and strongly deflected plane plume in crossflow
suoyant plane plume in stratified stagnant ambient
legatively buoyant line plume
simulation Modules for Unstable Multiport Diffusers:
Mixed Near-Field Flows
jnidirectional acceleration zone
:ee acceleration zone
strongly deflected tee diffuser plume
staged acceleration zone
strongly deflected staged diffuser plume
alternating perpendicular diffuser in unstable
near-field zone
legatively buoyant staged acceleration zone
Simulation Modules for Boundary Interaction Processes
for Stable Multiport Diffusers
lear-vertical surface/bottom impingement with buoyant
upstream spreading
lear-vertical surface/bottom impingement, upstream
spreading, vertical mixing, and buoyant
restratification
lear-horizontal surface/bottom/pycnocline approach
:erminal layer stratified impingement/upstream spreading
:erminal layer injection/upstream spreading
Simulation Modules for Unstable Multiport Diffusers:
ntermediate Field Flows
Jiffuser plume in co-flow
Jiffuser plume in crossflow
Simulation Modules for Buoyant Spreading Processes
suoyant layer spreading in uniform ambient
suoyant spreading in linearly stratified ambient
tensity current developing along diffuser line
nternal density current developing along diffuser line
Jiffuser induced bottom density current (2-D)
Jiffuser induced bottom density current (3-D)
Simulation Modules for Ambient Diffusion Processes
sassive diffusion in uniform ambient
sassive diffusion in linearly stratified ambient
Extensive comparisons have been conducted for COR-
MIX1 and 2 with available laboratory data and a few
limited field data cases, as well as with buoyant jet
integral models. These comparisons (Doneker and
Jirka, 1990; Akar and Jirka, 1991) demonstrate that for
subsurface flow the CORMIX predictions were at least
of the same quality as that of jet integral models. The
agreement with data (+20% for trajectories and dilu-
tions) is of the same order as the usual scatter among
different data sources.
-------
Moreover, CORMIX has been shown to be a robust
and accurate predictive methodology for more com-
plex flows with various degrees of boundary interac-
tion, such as near-field instabilities, buoyant spreading
processes, and dynamic bottom interaction. CORMIX
appears to correctly diagnose these processes
through its classification scheme and then provides
quantitatively reliable predictions of the sequence of
mixing processes that characterize a given discharge.
However, as all models that are based on some geo-
metric schematizations and dynamic simplifications,
CORMIX will not be applicable to all possible discharge
configurations. To avoid model misuse in such in-
stances, specific safeguards, warning labels, and use
restrictions have been included in CORMIX. In any
case, recent experience has shown that CORMIX is
applicable and predicts properly for the vast majority
of actual submerged discharge situations (better than
95% for CORMIX1 and better than 80% for CORMIX2
because of the considerably greater geometric com-
plexities of diffuser installations). Furthermore, the
user's manuals contain special advice sections for the
user dealing with any of the more limiting cases.
8.6 Mixing Zone Predictions Under
Unsteady Reversing TidaS Currents
As has been remarked earlier in Section 8.1, the time
scale for initial mixing processes is usually short
enough relative to the tidal period, so that it is accept-
able to apply initial mixing models under steady-state
conditions, e.g. corresponding to certain stages within
the tidal cycle. However, this approach is no longer
valid if predictions are desired over a larger area
encompassing distances that, in fact, provide a transi-
tion to the far-field.
In the present state-of-the-art no complete models for
pollutant predictions in the water environment are
available (see Section 8.2). This restriction stems from
the difficulties of representing the variety of transport
processes that govern the distribution in unconfined
estuarine or coastal water bodies in a single analytical
or numerical technique. Therefore, an integration of
near-field mixing models and of predictive techniques
for the far-field effects must be employed. Far-field
processes, that include the transport by the varying
tidal flow, turbulent diffusion, and various biochemical
transformation phenomena, have been addressed in
Parts I and II of this estuarine waste load allocation
manual. The following comments provide some guid-
ance on estimating, the interaction between near-field
mixing and far-field accumulation effects. The method-
ology is adapted from that suggested by Jirka et al.
(1976).
8.6.1 Far-Field Accumulation Effects
The two major methods for estimating the unsteady
far-field accumulation of discharged material, at vari-
able distances from the outfall and in an unsteady tidal
flow, are either numerical models or field dispersion
tests. In the following it is assumed that a dispersion
test is being employed, but the comments apply
equally well to the results of an unsteady numerical
model.
The schematics of a field dispersion test in a reversing
tidal current system are shown in Figure 8-19. The
tracer release line may represent the location of a
submerged multiport diffuser with alternating nozzles.
The tidal system is assumed as approximately periodic
as indicated by the velocity curve. The figure also
shows the hypothetical dye concentration trace C(x,y)
measured at some point (x,y) as a function of time.
(Note that in practice, fewer discrete measurements
over time would be available). If the field dispersion
test consists of a tracer release period, tidal cycles
long, then the continuous monitoring would usually
indicate a period of concentration build-up, a quasi-
steady period and a fall-off period. If an accurate
simulation of the pollutant discharge over a large-scale
and fora long-term is required, then consideration (and
measurement) for at least two of these periods is
necessary.
Considering the maximum dye concentration during
any tidal cycle at (x,y)/he following sequence is
generally observable: During the first cycle Cmax is
found, in the second cycle the concentration is
plus some fraction of dye tracer returning from the
previous cycle, thus C max + /c/ C max = C max (1 +rd )•
If these are continuously repeated, then the quasi-
steady maximum concentration Cmax is given by the
geometric series
Cmax=Cmax(1
or, in the limit,
c=Cr
1
' max — o max'
(20)
(21)
The quantity /yis labelled the dye return rate of mass
discharged in the previous cycle (ra implicitly includes
any dye mass decay during the tidal period). The
complement quantity (1-fd ) is frequently referred to
as flushing rate. The return rate will depend on the
characteristics of the tidal flow, notably tidal excursion,
mean velocity, diffusion, etc. ra is also dependent on
the position (x,y) with respect to the release area.
Quasi-steady conditions are typically encountered af-
ter about 5 to 10 tidal cycles. Build-up curves, similar
to Equation 20 correspond also to other quantities of
-------
interest, such as the minimum or average concentra-
tions during a tidal cycle, thus
Ci(x,y,t)=Ci(x,y,t)-l
i~'
(22)
where C/ ( x, y ) is a single cycle concentration quantity
of interest (Cmax ,Cmin ,Cavg , etc.).
For the actual pollutant discharge the quasi-steady
condition is usually of primary importance. From Equa-
tion 22 it is seen that this depends on two factors: the
mixing characteristics C/ within a single tidal cycle, and
the return rate from previous cycles. To translate the
quasi-steady dye concentration conditions into pollut-
ant concentration, therefore, two adjustments are
needed:
(a) Within a tidal cycle, the pollutant concentration c is
related to the dye concentration C
d
Qdo
(23)
where f/(x, y) = time interval between occurence of
event ; (maximum, minimum concentration) at
(x , y) and time of release of that tracer patch, i.e.,
travel time. QCo is the pollutant mass release rate and
Qdo is the dye mass release rate. kc and k
-------
Instantaneous
Concentration
Distribution
(Ebb Tide)
Flood
Tidal Velocity
Tracer
Release Points
Shoreline
Ebb \
Tracer Concentration at
-Tracer Release Period n
max
0
I 2 3
Build - up
Tidal
Periods
max
Quasi - Steady
n
n+I n + 2
Fall off
Period
Periods
Period Period
Figure 8-19. Schematics of a field tracer dispersion test in a periodically reversing tidal system.
8-25
-------
• For Toxic Dilution Zone (TDZ) predictions, the
effect of far-field return is always negligible (rc« 0)
due to the strong spatial restriction of the TDZ.
• For most Legal Mixing Zone predictions, the rc
factor can be expected to vary in the range of <0.1
to ~ 0.5 (highly conservative estimate). It is very
small (< 0.1) for deep water discharges in the open
coastal zone that are often associated with internal
trapping or buoyant surface layer formation. In
those cases, the initial (buoyant jet) mixing is, in
fact, quite independent of far-field effects. It may
be reasonably high (up to 0.5) for shallow water,
vertically mixed, discharges in strongly restricted
estuaries with weak flushing. For additional flush-
ing estimates in such tidal channels, see the meth-
ods discussed in Fischer et al. (1979).
8.7 References
Abraham, G. 1963. Jet Diffusion in Stagnant Ambient
Fluid. Publ. No. 29, Delft Hydraulics Laboratory, The
Netherlands.
Akar, P. J., and G. H. Jirka. 1991. CORMIX2: An
Expert System for Hydrodynamic Mixing Zone Analy-
sis of Conventional and Toxic Submerged Multiport
Diffuser Discharges. Technical Report, U.S. EPA, En-
vironmental Research Laboratory, Athens, GA, (in
preparation).
Doneker, R. L, and G. H. Jirka. 1990. CORMIX1: An
Expert System for Hydrodynamic Mixing Zone Analy-
sis of Conventional and Toxic Submerged Single Port
Discharges. Technical Report EPA 600/3-90/012, U.S.
EPA, Environmental Research Laboratory, Athens,
GA.
Fischer, H. B. et al. 1979. Mixing in Inland and Coastal
Waters. Academic Press, NY. 483 pp.
Hirst, E.A. 1971. Analysis of Buoyant Jets Discharged
to Flowing Stratified Ambients. Rep. ORNL-TM-4685,
U.S. Atomic Energy Commission, Oak Ridge National
Lab., Oak Ridge, TN.
Holley, E. R. and G. H. Jirka. 1986. Mixing in Rivers,
Technical Report E-86-11, U.S. Army Corps of Engi-
neers, Washington, DC.
Jirka, G. H. 1982a. Turbulent Buoyant Jets in Shallow
Fluid Layers, in Turbulent Jets and Plumes, W. Rodi
(Ed.), Pergamon Press.
Jirka, G. H. 1982b. Multiport Diffusers for Heat Dis-
posal -A Summary. Journal of the Hydraulics Div.,
ASCE, Vol. 108, December.
Jirka, G. H., G.Abraham, and D.R.F. Harleman. 1976.
An Assessment of Techniques for Hydrothermal Pre-
diction. Technical Report NUREG-0044, U.S. Nuclear
Regulatory Commission, Washington, DC.
Jirka, G. H. and L.M. Fong. 1981. Vortex Dynamics
and Bifurcation of Buoyant Jets in Crossflow. Journal
of the Engineering Mechanics Division, American So-
ciety of Civil Engineers, Vol. 107, No. EMS, June.
Jones, G.R. and G.H. Jirka. 1991. CORMIX3: An
Expert System forthe Analysis and Prediction of Buoy-
ant Surface Discharges, Technical Report, DeFrees
Hydraulics Laboratory, School of Civil and Environ-
mental Engineering, Cornell University. Also to be
published by U.S. Environmental Protection Agency,
Technical Report, Environmental Reasearch Lab, Ath-
ens, GA.
Kannberg, L. D., and L.R. Davis. 1976. An Experimen-
tal/Analytical Investigation of Deep Submerged Multi-
ple Buoyant Jets. EPA-600/3-76-101. U.S.
Environmental Protection Agency, Corvallis, OR. 266
pp.
Muellenhoff, W. P., et al. 1985. Initial Mixing Charac-
teristics of Municipal Ocean Discharges (Vol. 1&2).
U.S.EPA. Environmental Research Laboratory, Narra-
gansett, R.I.
Roberts, P.J.W. 1977. Dispersion of Buoyant Waste
Discharge from Outfall Diffusers of Finite Length. Rep.
No. KH-R-35. W. M. Keck Lab. of Hydraulics and
Water Resources, California Institute of Technology,
Pasadena, CA, 183 pp.
Schatzmann, M. 1978. The Integral Equations for
Round Buoyant Jets in Stratified Flows. J. Appl. Math
and Physics 29: 608-20.
USEPA. 1982. Revised Section 301 (h) Technical
Support Document. EPA 430/9-82-011, Washington,
DC.
Winiarski, L. D., and W.E. Frick. 1976. Cooling tower
plume model. EPA-600/3-76-100. U.S. Environ-
mental Protection Agency, Corvallis, OR.
Wong, D. R. 1984. Buoyant Jet Entrainment in Strati-
fied Fluids. Ph.D. Thesis, Civil Engineering Dept., The
University of Michigan, Ann Arbor, Ml.
-------
9. of
9.1 Introduction
9.1.1 Objectives
This case study section has several objectives: (i) To
demonstrate the typical procedures and data require-
ments involved in mixing zone analysis; (ii) To demon-
strate that legal mixing zone definitions may require
the analysis of both near-field and far-field processes;
and (iii) To show the relative merits and flexibility of
different methodologies, including jet integral models
and the expert system CORMIX.
All four case studies deal with hypothetical conditions
that may, however, exhibit some features of existing
discharges. In the first case study major emphasis is
put on various regulatory criteria. None of the case
studies is intended to document model validation. This
cannot be done since no actual field or laboratory data
exist for these hypothetical situations. For validation of
models reference should be made to the original litera-
ture on the various models as listed in Chapter 8.
However, a few comments on model validity are made
in the first case study in order to explain some large
differences in various model predictions.
9.1.2 Data Needs
As discussed in Section 8.1, the initial mixing of an
effluent depends on the interaction of ambient and
discharge conditions. In estuaries or coastal waters
these conditions may be highly variable. In evaluating
water quality effects and mixing zone compliance,
appropriate design conditions must be chosen. Gen-
erally, the critical design conditions relate to those
environmental and discharge factors that lead to the
lowest dilution and at times when the environment is
most sensitive. However, it is not always straightfor-
ward for the analyst to estimate exactly what combina-
tion of factors will lead to this critical condition. For this
reason, an evaluation under a variety of conditions
always seems necessary to obtain information on mix-
ing zone behavior and its sensitivity to design criteria.
Data uncertainty is also a factor of concern. The fol-
lowing considerations, taken from Muellenhoff et al.
(1985), apply here:
"Predicting dilution reliably depends on the availability
of statistically valid data with which to estimate ambient
conditions. The statistical uncertainty in estimates of
absolute worst case conditions is generally great. Also
there are inherent biases to some oceanographic
measurements. For example, current measuring in-
struments have finite thresholds. It therefore becomes
difficult to distinguish low values (which may be as high
as 5.0 cm/sec) from zeroes in these data sets. In esti-
mating environmental conditions, a more reliable esti-
mation can be made at the lowest 10 percentile on a
cumulative frequency distribution. Data on ambient den-
sity structure are not routinely collected. Consequently,
there is not usually an existing data set for the site under
consideration. To increase the reliability of 'worst-case'
estimates, data should be evaluated not only for the
discharge site but for nearby coastal areas of similar
environmental setting."
"Defining 'worst-case' conditions as a combination of
those conditions affecting initial dilution, each taken at
the worst 10 percentile on cumulative frequency distri-
butions, is recommended by USEPA. This approach
allows a reliable estimation of these conditions to be
made and prevents the unlikely occurence of more
extreme conditions from biasing the predictions. The
probability of these conditions occurring simultaneously
is much less than 10 percent, ensuring that the predicted
dilution will be exceeded most of the time. Application of
multiple 'worst case' factors (i.e. flows, stratification and
currents) to determine a minimum dilution must be done
carefully, however, and in recognition of the criteria for
which compliance is being determined. For example,
although application of an absolute 'worst case' dilution
may be appropriate for determining compliance with an
acute toxicity limit, it is more appropriate to identify the
lowest 6-month median dilution to determine compli-
ance with a 6-month median receiving water limitation."
Since the discharge conditions can also vary (e.g. its
flowrate or pollutant concentration) it is necessary to
combine the occurences of the varying pollutant loading
with the varying ambient parameters in order to find the
critical design conditions.
Finally, any set of ambient and discharge conditions will
require some degree of schematization in order to meet
the predictive model assumptions. This has been dis-
cussed in Section 8.3.2 along with Figures 8-6, 8-7 and
8-8. The literature or user's manuals for the various
models usually contain some guidance on how to pre-
pare the data. As with any model application, it is nec-
essary to evaluate the prediction sensitivity to input data
through repeated model use. The expert system COR-
MIX, in fact, has on-screen advice on data preparation
available to the user.
All available mixing zone models assume a conservative
pollutant discharge neglecting any physical, chemical or
biological decay or transformation processes. For most
substances this is reasonable due to the
-------
z(m);
16 -
12
0
1,005
o
--\
°\
\ /-CORMIX1 approximation
\ / Profile C
\
\
\
\
o
\
\
\
_i—i—i—i—\s—i—i—i—».
1,010
Figure 9-1. Design case AA: vertical ambient density profile
in typical summer conditions.
rapidity of the mixing process, especially in the near-
field, relative to the reaction time scale of most pollut-
ants. If first order reaction processes can be assumed
then the model results on concentration can usually be
converted with an exponential factor to include the
decay process (see Doneker and Jirka, 1990). The
consideration of pollutant reactions in the context of
far-field accumulation involving a larger time scale has
also been addressed in Section 8.6.1.
9.2 AA -Single Port Discharge:
industrial Outfall in Tidal Fjord.
9.2.1 Ambient and Discharge Conditions
A manufacturing plant is located near the upstream
end of a narrow tidal fjord that receives a substantial
amount of fresh water inflow. The typical cross-section
of the fjord is 600 m wide with an average depth of
16 m. The preferred discharge location is about 90 m
from shore where the local water depth is 17.5 m.
During typical winter conditions the characteristic am-
bient (average tidal) velocity is 0.15 m/s and the verti-
cal ambient density distribution is quite uniform with a
value of 1,005.5 kg/m3. During summer design condi-
tions, however, the ambient velocity is lower at 0.10
m/s and a significant vertical stratification exists as
shown in Figure 9-1. The density varies from a bottom
value of 1,010.0 kg/m3 down to a surface value of
1,005.8 kg/m3. The plant operation is also variable. In
winter the discharge flow rate is 0.15 m3/s and has a
discharge temperature of 10°C. In summer the flow
rate is lower at 0.10m3/s with a temperature of 15°C.
The discharge flow is essentially freshwater but con-
tains 1000 ppb of some organic toxic material.
Applicable state regulations limit the mixing zone to 25%
of the width of the estuary. Furthermore, the special
mixing zone requirements for toxic substances (see
Section 7.2.3) apply with a CMC value of 100 ppb for
the discharged toxicant.
9.2.2 Case AA1: Initial Design, Winter Conditions
An inital design proposal calls for a single port discharge
with 0.2m port diameter and 0.5 m port height above the
bottom. The discharge velocity is 4.8 m/s. The port is
oriented in a co-flowing arrangement pointing horizon-
tally along the direction of the ambient current.
Figure 9-2 shows a side view of the near-field of the
discharge plume predicted by CORMIX1 (flow class A5).
The model shows strong dynamic attachment of the
plume to the bottom. After this a gradual buoyant rise to
the surface takes place with a minimum surface.dilution
= 164. The extent of the toxic dilution zone (TDZ)
is about 10m, essentially comprising the entire bottom
attached zone. Thus, benthic organisms will be exposed
to toxicant concentrations above CMC values. This in-
itial design is considered undesirable and rejected from
further consideration.
In view of this bottom attachment, none of the jet integral
models, included in Section 8.4, i.e. the USEPA models,
UOUTPLM and UDKHDEN or the Jirka-Fong model,
would be applicable. Therefore, their predictions are not
shown on Figure 9-2.
9.2.3 Case AA2: Modified Design, Winter
Conditions
In order to eliminate plume bottom interference, a modi-
fied design is proposed with an increased port height of
1.0m and a vertical discharge angle of 10°. This modi-
fied design, indeed, does not exhibit any bottom attach-
ment as shown in Figure 9-3.
The trajectory predictions of three buoyant jet integral
models (UOUTPLM, UDKHDEN and JF [Jirka-Fong])
and of CORMIX1 (flow class H2) are given in Figure 9-3.
Also shown is the width prediction for CORMIX1. All four
submerged plume trajectories are qualitatively similar;
the deviations among trajectories is contained within the
plume outline (as indicated by CORMIX1) and well
within the usual scatter of experimental data. The TDZ
is again limited (order of 10 m) as predicted by any of
the four models. The jet integral models are, of course,
limited in their applicability to the submerged jet region
before surface interaction. Only CORMIX1 is applicable
to the actual interaction process and the subsequent
buoyant spreading along the water surface. This proc-
ess is indicated by the width boundary in Figure 9-3.
-------
O.I5m/s
100 x(m)
Bottom
Attachment
Case AAI : Initial Design, Unstratified Winter Conditions
Figure 9-2. Case AA1: single port discharge (initial design) exhibiting bottom attachment as predicted by CORMIX1.
Considerable differences exist in the predicted surface model predictions are divided by a factor of 1.7, in order
dilution at the point of surface interaction. UOUTPLM to account for the typical ratio of flux-averaged and
and UDKHDEN predict a flux-averaged dilution of 212 minimum dilutions a considerable difference remains
and 495, respectively. On the other hand, JF and relative to the lower dilution value of CORMIX1. To shed
CORMIX1 predict minimum (centerline) dilutions of further light on this disagreement the predictions of the
z(m)j
10
L
4
2!2 I46 Smin=220
= 495
t r t
storted)
1.0 m
20
40
60
80
100 x(m)
Figure 9-3. Case AA2: single port discharge (modified design) in unstratified winter conditions; comparison of jet integral
models and CORMIX1.
220 and 146, respectively. Even if the UDKHDEN four models can be compared to what is probably the
-------
I CI-
10'
10'
10
UKHDEN
UDUTPLMj
Jirka and
Fong
Regression Smln
Lee and Neville-Jones
(1987)
CORMIX1 Sn
O Gosport
D Bridpor*
A Hastings (I979)
• Hastings (I960)
IOU
I01
10'
H/U
Figure 9-4. Comparison of observed minimum surface
dilution for three submerged single port outfalls
(Lee and Neville-Jones, 1987) with predictions of
jet integral models and CORMIX1.
most reliable and comprehensive available field data
set on submerged discharges. Lee and Neville-Jones
(1987) report several hundred individual observations
of minimum surface dilution for three single port sub-
merged outfalls for municipal discharges in the United
Kingdom. All of these outfalls are somewhat more
dominated by buoyancy than design case AA2. (This
is indicated, for example, by the fact that CORMIX1
predicts a flow class H1 for these outfalls). The predic-
tions of all four models are compared with the normal-
ized field observations for minimum surface dilution
(Figure 9-4). The solid line presents the best-fit regres-
sion line for all data points. The average dilution given
by both USEPA models is a factor of 4 (300%) larger
than the observed minimum dilution. When the dilution
predictions are converted to minimum dilutions (factor
1.7) the overprediction is still by about 130%. The JF
model overprediction is about 50%. CORMIX1, on the
other hand, lies within about 15% with the observa-
tions. (Note that the model coefficients of CORMIX1
have been chosen through extensive comparison with
basic laboratory data, so that this good agreement
presents indeed a model validation and not some
forced best-fit). On the basis of this comparison it may
be concluded that the jet integral models (notably
UOUTPLM and UDKHDEN) are quite non-conserva-
tive and tend to overestimate actual plume dilutions, at
least for unstratified ambients. The prediction dis-
agreement for Case AA2 (Figure 9-3) may be consid-
ered in light of this conclusion.
The legal mixing zone LMZ (25% width) is not attained
in the hydrodynamic near-field but rather in the far-field
as shown by the CORMIX1 predictions of Figure 9-5. In
fact, the LMZ is reached at a downstream distance of
about 600 m when the surface plume is in the buoyant
spreading regime. At this point, the average dilution has
increased to about 250 and the plume half-width is about
75 m with a plume thickness of 1.7 m. Actual plume
interaction with the bank takes place at a further down-
stream distance of about 760 m. This result illustrates
the practical fact that legal mixing zone definitions can
often imply sufficiently large distances which then in-
clude far-field mixing processes. Simple jet integral
models do not address this aspect, while CORMIX1 has
been implemented to deal with such generalities.
9.2.4 Case AA3: Modified Design, Summer
Conditions
The drastic effect of ambient stratification on plume
near-field behavior is shown in Figure 9-6. With any of
the four predictive models the plume is predicted to
reach its terminal level of about 3 to 5 m above the
bottom at a distance of about 10m downstream. The
differences among the predicted trajectories are small.
The TDZ is reached about 8 m downstream as indicated
by CORMIX1 (flow class S3). The predicted dilution
values at the terminal level show, again, more variability.
If minimum terminal dilutions are compared, then
UOUTPLM, = 16/1.7 = 9, CORMIX1, =16, and
UDKHDEN, = 26/1.7 = 15, provide lower-end (con-
servative) predictions, while JF, = 26, is somewhat
higher.
The CORMIX1 predictions in Figure 9-6 also show the
formation of the internal stratified layer (initial thickness
2.4 m) and its gradual collapse and widening with addi-
tional mixing. The full development in the far-field is
illustrated again in Figure 9-5. The behavior under strati-
fied summer conditions is in marked contrast with the
unstratified winter conditions (Case AA2). The differ-
ence in dilution is notable (related to the much shorter
buoyant jet trajectory in the near-field) as is the much
thinner internal layer. The LMZ is reached at about 680
m where the plume half-width is about 75 m and the
plume thickness about 0.3 m.
9.3 Case BB -Multiport Diffuser: Municipal
Sewage Discharge into Coastal Bay
9.3.1 Ambient and Discharge Conditions
A multiport diffuser is used for the discharge of treated
sewage water from a municipality located on a bay. The
-------
y(m),
Bonk Interaction
a) Plan View (undistorted)
^=^dtr—•
LMZ^MZ"
Win1er Summer
LMZ S=380
200
400
600
xfm)
b) Side View (distorted)
Figure 9-5. Cases AA2 and AA3: predicted (CORMIX1) far-field behavior for single port discharge (modified design) in winter
and summer conditions.
proposed diffuser location is 10 km offshore with an from 1,023.2 kg/m3 at the surface to 1,026.4 kg/m3 at the
ambient water depth of 30 m. In a preliminary evalu- bottom. Figure 9-7 shows the actual density varia-
ation two ambient design cases are to be investigated; tion, together with the schematizations adopted for dif-
z(m),
15
10
5
f
-
.,
\(
^^^T-DZ
-UOUTPLM St=l6 Side View (distorted)
rCORMIXI St=l6
rUDKHDEN St = 26
rJF St=26 S = I8
1 Half Widlh=20m
"J ,, CORM!X1 ~ — •
I 1 I _™_L I I 1 n»
10 20 30 40 x(
Figure 9-6. Case AA3 : single port discharge (modified design) in stratified summer conditions; comparison of jet integral
models and CORMIX1.
1) A weakly stratified ambient with a density variation ferent models. 2) A uniform ambient with a density of
-------
\
\ /-UDKHDEN, ULINE
t
\
CORMIX1
1,022
(kg/m3)
Figure 9-7. Design case BB: vertical ambient density profile
for design conditions.
1,026.0 kg/m3. In both cases the ambient design ve-
locity is 0.156 m/s for the prevailing coastal current.
The discharge flow rate is 20 m3/s (460 MGD) with a
freshwater density of 998.0 kg/m3.
The preliminary design calls for a total diffuser length
of 2000 m with a perpendicular alignment relative to
the prevailing current direction. The diffuser employs
80 vertical risers with 8 ports attached per riser and
discharging in a circular fashion. The port diameter is
0.14 m, the port height is 1.5 m above bottom and the
z(m)4
30
20
The legal mixing zone (LMZ) is prescribed by a distance
of 30 m extending in any direction from the diffuser line.
No toxic substances are included in this discharge.
9.3.2 Case BB1: Stratified Ambient
When applying any model to a complex diffuser geome-
try with riser/port assemblies, some model simplification
is needed. In case of the USEPA multiport models
(UDKHDEN,UMERGE and ULINE) the user must, in
fact, substitute a series of single ports equally spaced
along the diffuser line (thus, in this present case 80 x 8
= 640 ports). On the other hand, the input element of
CORMIX2 collects all the pertinent information about the
riser/port assemblies, the system then concludes that
the net horizontal momentum flux for this diffuser is zero
and treats the diffuser as an alternating diffuser with a
vertical equivalent slot discharge. Thus, in either case,
the local details of the eight individual buoyant jets
discharging from each assembly are neglected.
Figure 9-8 summarizes the predictions of the jet models
UDKHDEN and ULINE and of the expert system COR-
MIX2 (flow class MS5). All three models indicate a
terminal layer at about 10 m above the bottom varying
between 8 m and 12 m. Also all three models show
limited variability_for the predicted average dilution at the
terminal level, ~ , which is 137 for ULINE, 212 for
UKHDEN, and 166 x 1.4 = 232 for CORMIX2, using an
average/minimum dilution factor of 1.4 for two-dimen-
sional buoyant jets. All these dilution values
may be scrutinized as to whether the mixed effluent flow
per unit diffuser length," / , exceeds the available
ambient approach flow, , for the layer between
bottom and terminal level. Denoting the ratio
= (~ / )/( ) one finds =0.7 for ULINE, =1.7
Side View (undistorted)
= 8.lm
•St=ll6
ULSNE: zt=l2.lm, St=l37
(no spatial data)
80
IOO x(m)
Figure 9-8. Case BB1: multiport diffuser discharge under stratified conditions; comparison of jet integral models and CORMIX2.
port angle is 0° (i.e. horizontal).
-------
(Submerged plume)
Cose BBh Stratified
Ave. dilution S = 292
Layer thickness h = 5.9m
'
Case BB2: Uniform
(Surface plume)
Figure 9-9. Cases BB1 and BB2: predicted (CORMIX2) far-field behavior for multiport diftuser plume in stratified and uniform
conditions.
two-dimensional flow (i.e. if a diffuser section or the
entire diffuser length were bounded by lateral walls)
any value > 1 is not possible in steady-state. How-
ever, for the actual three-dimensional diffuser the dif-
fuser entrainment demand can also be met by lateral
flow toward the diffuser line. Futhermore, additional
freedom to entrain water exists for the internally
trapped plume ( < where is the water depth).
Also, note that for low ambient velocity conditions
->0) the above test becomes unreliable for evalu-
ating model performance. Thus, for the present case
of an internally trapped plume from a three-dimen-
sional diffuser all three model predictions appear rea-
sonable.
Note that trajectory information is provided by
UDKHDEN and CORMIX2 while ULINE does not pro-
vide any spatial data on plume behavior. The LMZ is
predicted by CORMIX2 to have a minimum dilution of
116.
At the transition to the far-field CORMIX2 indicates an
initial internal layer thickness of about 16 m. As shown
in the far-field plan view of Figure 9-9 this internal layer
is gradually spreading, decreasing in thickness, and
experiencing a slight additional mixing in the buoyant
spreading phase. Thus, at 10 km downstream from the
diffuser line the average dilution is 313, with a half-
width of the effluent field of 4.2 km and a thickness of
4.7m.
9.3.3 Case BB2: Uniform Ambient
The corresponding model predictions for the unstratified
case are given in Figure 9-10.CORMIX2 indicates a flow
class MU8 which includes a vertically fully mixed near-
field with an average dilution, ~ = 512. Although its model
printout does not specifically state so, ULINE also pre-
dicts a vertically mixed flow with a lower dilution ~ = 368.
In contrast, UDKHDEN does not recognize the destabi-
lizing effect of the vertically limited environment in cross-
flow and predicts a plume with a high surface dilution
= 835 and with width dimensions that are of the order of
the water depth (Figure 9-10). Defining the ratios
= ( / )/( ) one finds =0.8 for ULINE, =1.0
for CORMIX2 and = 1.8 for UDKHDEN. The latter
result, together with the fact that the model — while
predicting plume dimensions of the order of the water
depth — does not address the constraint of the limited
ambient depth, indicates that UDKHDEN is not applica-
ble in this case. More generally, it appears that
UDKHDEN is an unreliable model for most multiport
diffuser applications in unstratified ambients. The same
reservation would hold for the model UMERGE (not
plotted here). ULINE indicates slightly more conserva-
tive dilution values than CORMIX2. It may be overly
conservative, however, since the ULINE model coeffi-
cients are based on a single set of experiments by
Roberts (1977) which did not include the additional
mixing effect of the high velocity discharge jets as is
common in actual diffuser installations (this has been
pointed out in a discussion by Jirka, 1979).
The far-field behavior of the diffuser plume is plotted in
Figure 9-9. While the plume is fully mixed in the near-
-------
UDKHDEN
5 = 835
CORMSX2
S = 5i2 (fully mixed)
UQ 20
10
-------
z(m)A
_ 0 = 0,10m
u0=3.8 m/s
LM2 (x = 2Qm):
S = 40
thickness h=0.35m
hoSf-width b= 18.0m
z(m)J
LMZ:
0
f f5
0.25 m/s
x(m)
10
0
Upstrtom Smin= 22 56
intrusion
(ii) View Looking
Downstream
(undistorted)
z(m)
5
5 f Urn) 10 f
22 140
(ii)
Cross-section of
impingement
yM 0
a) Case CCI: Low Velocity Design
Weak Current
y (m) 0
-5
b) Case CC2: Low Velocity Design
Strong Current
Figure 9-11. Cases CC1 and CC2: negatively buoyant discharge from single port; low exit velocity design under a) weak and b)
stronger ambient current.
minimized. Figure 9-11 b shows CORMIX1 (flow class
NV2) and JF predictions. The discrepancy between
predicted minimum dilutions is further increased
( = 22 versus 140). Such complex three-dimen-
sional trajectories represent some of the most severe
tests for model application, and in the absence of
detailed experimental data for such phenomena it is
difficult to favor one model over another.
The upstream intrusion along the bottom is minimal in
the present case (order of 2 m) and the bottom density
current is thicker and less wide. At the LMZ distance
the plume half-width is only 8.0 m with a thickness of
0.60 m and an average dilution of 45.
9.4.4. Case CC3: High Discharge Velocity
Design, Strong Current
In order to maximize near-field dilution a high exit
velocity design (15.2 m/s) is evaluated by halving the
port diameter to 0.05 m. The results are shown in
Figure 9-12. When compared to Figure 9-11b, this
shows the significant effect of increased jet diffusion in
the near-field. The buoyant jet shows much more rapid
mixing, and, consequently, is more liable to advection
by the ambient current. CORMIX1 (flow class NV1) no
longer predicts an upstream intrusion after the more
gradual bottom approach. There are differences in the
predicted jet trajectories, as far as maximum height of
rise and bottom approach are concerned. At the LMZ
these buoyant jets are predicted to be in the water
column without any bottom contact yet. The minimum
dilution values are = 247 for JF and 119 for
CORMIX1, respectively. The comparison between
Figure 9-11 b and 9-12 illustrates how LMZ constraints
sometimes are met in the hydrodynamic near-field and
at other times in the far-field, depending on the inter-
play of ambient and discharge conditions.
9.5 Case DD Multiport Diffusers: Cooling
Water Discharge into Shallow Sound
9.5.1 Ambient and Discharge Conditions
A once-through cooling water system for a thermal-
electric power plant discharges the heated cooling
-------
z(m)
i) Side View (distorted)
0.25 m/s
!00 x(m)
Smin=580
(ii) View Looking Downstreom
(undisiorted)
Case CC3: High Velocity Design
Strong Current
y (m)
-10
Figure 9-12. Case CCS: negatively buoyant discharge from single port; high exit velocity design with strong ambient current.
water through a submerged multiport diffuser. At a
distance of 500 m offshore, a shallow relatively flat
area exists with an ambient water depth of 10.3 m.
The water is unstratified with an average temperature
of 20°C and ocean salinity. The velocity field is tidal
ranging from slack tide (0.0 m/s) to weak velocities
(about 0.1 m/s) to a maximum velocity (0.5 m/s). The
cooling water flow rate is 67 m3/s with a discharge
temperature rise of 20.5°C above ambient and the
same salinity.
A staged diffuser design of 260 m length is proposed
with a perpendicular alignment relative to the tidal
currents. The diffuser consists of 32 ports with a port
height of 0.5 m, port diameter of 0.6 m and a vertical
angle of 20° above horizontal.
No LMZ is specified. Rather, the predictive results are
to be interpreted so as to make an LMZ proposal to the
state regulatory authority.
9.5.2 DD1: Weak Tidal Current
None of the USEPA diffuser models are applicable for
such shallow water diffusers with strong momentum
flux and unstable near-field mixing. If they were used,
UOUTPLM and UDKHDEN would predict vertical
plume width far in excess of the available water depth.
ULINE, on the other hand, is limited to pure plume
discharges without any directed discharge momentum
flux.
Thus, reliable predictions are limited to CORMIX2 as
shown in the plan view of Figure 9-13. For this case of
a weak current, CORMIX2 (flow class MU5) indicates
an initially, vertically fully mixed diffuser plume. The
plume gets gradually deflected by the weak crossflow
and begins to re-stratify (lift off the bottom) after a
distance. Gradual, lateral spreading and vertical thin-
ning of the diffuser plume takes place. The induced
temperature rise is 2.7°C in the near-field and drops to
1.0°C at a distance of about 1500 m. (Any potential
heat loss to the atmosphere is neglected in these
conservative mixing predictions).
-------
y (mi-
Plume restrotificotion
2.7 8C fully mixed
500 1000 x(m)
Case DDI: Weak Tidal Current (O.I m/s)
Figure 9-13. Case DD1: staged multiport dittuser for cooling
water discharge; CORMIX2 predictions for weak
tidal current.
Figure 9-13 illustrates vividly the strong effect of the
directed momentum flux from shallow multiport dif-
fusers and the ability to induce currents over consider-
able distances.
9.5.3 Case DD2: Slack Tide
Stagnant ambient conditions always represent a limit-
ing case for any mixing analysis. Since there is no
ambient advective mechanism they are always asso-
ciated with an unsteady flow field and mixing process,
including potential large scale recirculation effects.
The CORMIX2 (flow class MU5) predictions are given
in Figure 9-14 for unsteady conditions. The plume is
now undeflected, but has similar mixing characteristics
as the slightly deflected plume of Case DD1. However,
at some distance (about 680 m) the predictions are
terminated since the induced plume velocities have
become negligibly small so that a transient recirculat-
ing flow would be set up. Corresponding messages are
printed out by the expert system along with the advice
to conduct predictions for stagnant ambients only as a
special limiting condition.
y(m)j.
IOOO
Plan View
Distance to unsteady
recirculation
Stagnant
|2.2°C
1— Plume re-stratification
2.7°C fully mixed
•i - 1 - 1 - 1 - 1 - 1
500 IOOO
Case DD2 : Slack Tide
dm)
Figure 9-14. Case DD2: staged multiport diffuser for cooling
water discharge; CORMIX2 predictions for slack
tidal conditions.
y (m)
IOOO
Plan View
500
0.5 m/s
CORMIX2
f\ "---^ 500
Plume
restratification
IOOO
x (rn)
Case DD3: Strong Tidal Current (0.5 m/s!
Figure 9-15. Case DD3: staged multiport diffuser for cooling
water discharge; CORMIX2 predictions for
strong tidal current.
9.5.4 Case DD3: Strong Tidal Current
The effect of a strong tidal current (0.5 m/s) is to
generate a strongly deflected diffuser plume (Figure
9-15) as predicted by CORMIX2 (flow class MU6). A
rapid deflection and greatly increased mixing take
place within the diffuser vicinity. The re-stratifying
plume is then advected by the ambient current and
grows in width and diminishes in vertical thickness, in
form of a surface buoyant spreading process.
-------
In summary, the great variability among diffuser plume
patterns (Figures 9-13, 9-14, and 9-15) suggests that
a complete assessment of initial mixing processes
should, indeed, include the whole spectrum of ambient
conditions. It is often difficult to define a single "typical"
design condition for mixing analysis. On the other
hand, a rapid evaluation of several ambient conditions
and of alternative designs is readily possible within the
framework of presently available models.
9.6
Doneker, R.L., and G.H. Jirka. 1990. CORMIX1: An
Expert System for Hydrodynamic Mixing Zone Analy-
sis of Conventional and Toxic Submerged Single Port
Discharges. Technical Report, U.S. EPA, Environ-
mental Research Laboratory, Athens, GA.
Jirka, G.H. 1979. Discussion of "Line Plume and
Ocean Outfall Dispersion" by P.J.W. Roberts, J. of the
Hydraulics Div., ASCE, Vol. 105, HY 12.
Lee, J.H.W. and P. Neville-Jones. 1987. Initial Dilution
of Horizontal Jet in Crossflow. J. Hydraulic Engrg.,
ASCE, Vol. 113, No. 5.
Muellenhoff, W.P., et al. 1985. Initial Mixing Charac-
teristics of Municipal Ocean Discharges (Vol. 1&2).
U.S.E.P.A., Environmental Research Laboratory, Nar-
ragansett, R.I.
Roberts, P.J.W. 1977. Dispersion of Buoyant Waste
Discharge from Outfall Diffusers of Finite Length. Rep.
No. KH-R-35. W.M. Keck Lab. of Hydraulics and Water
Resources, California Institute of Technology,
Pasadena, CA, 183 pp.
-------
DISCLAIMER
We have made efforts to ensure that this electronic document is an accurate
reproduction of the original paper document. However, this document does not
substitute for EPA regulations; nor is it a regulation itself. Thus, it does not and
cannot impose legally binding requirements on EPA, the states, tribes or the
regulated community, and may not apply to a particular situation based on the
circumstances. If there are any differences between this web document and the
statute or regulations related to this document, or the original (paper) document,
the statute, regulations, and original document govern. We may change this
guidance in the future.
Supplemental material such as this disclaimer, a document abstract and glossary
entries may have been added to the electronic document.
------- |