Environmental Monitoring Series
PLUME DISPERSION IN  STABLY  STRATIFIED
           FLOWS OVER  COMPLEX TERRAIN
                                        ise 2
                          Office if
                          O.S. Environment)
                     Research Triangle Part, North Carolina 27711

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                 RESEARCH  REPORTING SERIES

 Research reports of the Office of Research and Development, U.S. Environmental
 Protection  Agency, have been grouped .into five series. These five broad
 categories were established to facilitate further development and application of
 environmental technology. Elimination of traditional grouping was consciously
 planned to foster technology transfer and a maximum interface in related fields.
 The five series are:

     1.    Environmental Health Effects Research
     2.    Environmental Protection Technology
     3.    Ecological Research
     4.    Environmental Monitoring
     5.    Socioeconomic Environmental Studies

 This report has been assigned  to the ENVIRONMENTAL MONITORING series.
 This series describes research conducted to develop new or improved methods
 and instrumentation for the identification and quantification of environmental
 pollutants at the lowest conceivably significant concentrations. It also includes
 studies to determine the ambient concentrations of pollutants in the environment
 and/or the variance of pollutants as a function of time or meteorological factors.
This document is available to the public through the National Technical Informa-
tion Service. Springfield, Virginia 22161.

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                                                  EPA-600/4-76-022
                                                  May 1976
PLUME DISPERSION IN STABLY STRATIFIED FLOWS
           OVER COMPLEX TERRAIN
                  Phase 2
                    by
          H. T. Liu and J. T. Lin
            Flow Research, Inc.
         Kent, Washington   98031
          Contract No.  68-02-1293
              Project Officer

             William H. Snyder
    Meteorology and Assessment Division
Environmental Sciences Research Laboratory
   Research Triangle Park, N.C.   27711
ENVIRONMENTAL SCIENCES RESEARCH LABORATORY
    OFFICE OF RESEARCH AND DEVELOPMENT
   U. S. ENVIRONMENTAL PROTECTION AGENCY
   RESEARCH TRIANGLE PARK, N.C.   27711

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                                       DISCLAIMER
     This report has been reviewed by the Environmental  Sciences Research Laboratory, U s<
Environmental  Protection Agency, and approved for publication.  Approval does not signif
that the contents necessarily reflect the views and policies of the U. S. Environmental
Protection Agency,  nor does mention of trade names of cormiercial products constitute en-
dorsement or recommendation for use.

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                               PREFACE

     Flow Research has been under contract with the Environmental
Protection Agency (Contract No. 68-02-1293) to continue investigation
of plume dispersion in stably stratified flows over complex terrain.   Two
tasks are involved:
Task I - Laboratory simulation of plume dispersion in stably stratified
flows over complex terrain.
Task II - Development of a numerical model using a small-Froude-number
asymptotic expansion to simulate strongly stratified flows over complex
terrain.
     The final report consists of two task-oriented parts, each of which
is an individual report.  The first is entitled "Plume Dispersion in
Stably Stratified Flows Over Complex Terrain:  Phase 2," and the second
is entitled "A Numerical and Experimental Study of Stably Stratified Flow
Around Complex Terrain."  In addition, a 16mm color film entitled
"Laboratory Simulation of Stratified Flows Over Complex Terrain," in which
most of the visualization results for both tasks are summarized, is
included as an essential supplement to this final report.
                                  iii

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                                ABSTRACT
     Laboratory experiments were conducted in a stratified towing tank
to investigate plume dispersion in stably stratified flows.   First, plume
dispersion over an idealized terrain model with simulated elevated inver-
sions was investigated.   These results were compared with those of experiments
previously conducted for simulated ground inversions.   Second,  plume
dispersion in 1-layer stably stratified flows over a realistic  terrain
was modeled.   The plume  dispersion patterns showed a strong interaction
between the stratified flow and the rugged terrain features.   The third
experiment was a simulation of plume dispersion during inversion breakup.
Results indicated that pollutants were stirred and carried to the ground
as soon as the convective layer reached the plume that was originally
trapped in the inversion layer.
                                  IV

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                               CONTENTS

Preface	iii
Abstract	iv
List of Figures	vi
List of Tables	viii
List of Symbols	ix

    I.   Introduction  	  1
   II.   Summary	4
  III.   Conclusions 	  5
   IV.   Laboratory Facilities	8
    V.   Plume Dispersion in 3-Layer Stratified Flows  	   19
   VI.   Plume Dispersion From the Kennecott Smelter Stack ....   29
  VII.   Plume Dispersion During Inversion Breakup 	   36

References	46
Appendices

    A.   The Effect of an Absorptive Layer on Plume Dispersion .  .   48
    B.   The Effect of an Exaggerated Stack on Plume Dispersion  .   51
    C.   The Response of a Hot-Film Probe to a Variation of Fluid
          Density	53

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                             LIST OF FIGURES
Number                                                                 Page

   1   A Contour Map of the Idealized Terrain Model .........   10

   2   Terrain Model in the Vicinity of the Kennecott Copper
         Smelter in Garfield,  Utah	   12

   3   A Block Diagram of the Effluent Injection Device 	   14

   4   Calibration Curves of a Thermistor Probe 	   16

   5   A Typical 3-Layer Stratification Profile Measured With a
         Conductivity Probe in the Towing Tank (Runs Ila and lib) .   .   18

   6   3-Layer Stratification Structure for the Simulation of
         Plume Dispersion Into an Elevated Inversion Layer  	   20

   7   Plume Dispersion Into an Elevated Inversion Layer Over the
         Idealized Terrain Model.  FQ = 3.08	   21

   8   Mean Velocity Profile at the Location of the Stack in Run
         lib.  The Ambient Fluid Was Stratified with a 3-Layer
         Structure.  The Idealized Terrain Model Was That Described
         in Section 5.9	   25

   9   Dye Visualization of Plume Dispersion From a Stack Located
         at the Kennecott Copper Smelter in Garfield, Utah, Under
         Stable Conditions.  Wind Direction = 315°.  F  = 2.02   ...   31

  10   Mean Velocity Profiles at the Location of the Stack in the
         Kennecott Smelter Model.  Wind Direction = 315°  	   34
                                                      
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                         LIST OF FIGURES (CON'T)
Number
  15   Temperature Profiles During the Growth of an Unstable Layer
         Adjacent to a Surface in a Stratified Fluid (N = .095 Hz).
         The Growth of the Unstable Layer Was Generated by Cooling
         the Surface With Dry Ice	   45

  16   Dye Visualization of Plume Dispersion in a Stratified Flow
         Over the Idealized Terrain Model.  An Absorptive Layer Was
         Installed To Reduce Internal-Wave Reflection.  F  = 3.11.
         See Figs. 17 and 18 in  [l] for Comparison	   50
                                    vii

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                             LIST OF TABLES
Number                                                                 Page

   1   Summary of Experiments 	 .........     2

   2   Simulation Conditions for the Sharp Inversion
         Experiments  	 ....... 	    11

   3   Ground Concentrations Data of the Sharp Inversion
         Experiments	•	    27

   4   Simulation Conditions for Plume Dispersion From
         the Kennecott Copper Smelter Stack 	    30

   5   Simulation Conditions for the Inversion Breakup
         Experiments	    38
                                  Vlll

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                             LIST OF SYMBOLS

SYMBOL                         DESCRIPTION                DIMENSION*
B
—
C
	
C
a

"c
s
D
F
FD
JJ

FH


F,
n
Ffcl
a buoyancy number defined in eq. (B.I)

mean pollutant concentration

ambient pollutant concentration

source pollutant concentration
stack diameter
buoyancy flux of a plume
W
stack Froude number, s
\fe&
V ps
internal Froude number based on the stack
height, °°
NH
internal Froude number based on h, — 7-
' N/z-
internal Froude number based on the Brunt-
_
-2 -2
ML T
_o _7
ML ^T *
-2 -2
ML T
L
L4T-3
_



-




             Vaisala frequency at the icn layer,
              U
              i
                                                               _2
  g          gravitational acceleration                      LT
  H          stack height                                    L
  h          characteristic height, such as that of a
             mountain                                        L
  K          ratio of effluent velocity to free-stream
                       W
             velocity,  s
                       Ucc
  L          exaggeration factor of the stack diameter
                                       i   /    ,—               _i
             Brunt-Vaisala frequency, —  /_§_ A£              T
                                             dz
                                    W D
  R          stack Reynolds number,  s
                                     V
  R,          Reynolds number based on the ridge height,
   72         u h
              CO                                              —
                                         2                    -2
  s          a stability parameter, (2irN)                    T
  T          a time scale defined as the ratio of the
             length scale to the velocity scale              T
 L = length, T = time, T = temperature, M = mass
                                     ix

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                              LIST OF SYMBOLS
SYMBOL                         DESCRIPTION                        DIMENSION*
  T.           time required for the unstable layer to                T
              reach its maximum height
  t           time                                                   T
  U(z)        mean velocity component in x direction                 LT
                                                                       _i
  U           free-stream velocity                                   LT
   =°                             '                                     _1
  w           vertical velocity component                            LT
  w^          a convective velocity scale                            LT
  W           stack effluent velocity                                LT
   s
  x.y.z       Cartesian coordinate axes in longitudinal,
              lateral and vertical directions,  respectively          L
  Z           plume trajectory above the stack  exit                  L
  Z,           elevation of a lower boundary in  the towing            L
              tank
  Z           final height of the top of a plume in a calm           L
              environment
  Z           elevation of an upper boundary in the                  L
              atmosphere
  z.           the height of the penetrative layer                    L
                                  i        i                             —3
  Ap          density difference, |p  - p |                           ML
                                    S    a
  9           fluctuating temperature                                T
  8           mean temperature                                       T
  S           mean effluent temperature                              T
   S                                                                   _o
  p           density of the ambient fluid at stack exit              ML
              level
                                                                       _o
  p           stack effluent density                                 ML
  L =  length, T =  time,  T =  temperature, M = mass

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                                 SECTION  I

                               INTRODUCTION
       The objective of this study is to investigate plume dispersion over
complex terrain in stably stratified flows under several conditions which
might lead to serious pollution episodes.  This study is a continuation of
the laboratory investigation of plume dispersion over an idealized terrain
in a 1-layer stratified flow, which simulates a ground inversion (Lin, et
al., 1974 - hereafter referred to as  llj  ).  References to  ll  are made
frequently to ensure continuity, to provide cross-examination and to
minimize unnecessary duplication.
       The present study consists of three (3) subtasks,. which are summarized
in table 1.  A brief description of each subtask is given in the following.
       The first subtask is the investigation of the plume dispersion over
an idealized terrain model  (used in  [Ij ) in a 3-layer stratified flow.
The three layers consisted of a neutral layer next to the ground, a neutral
or a stable layer far above the ground, and an extremely stable layer or
inversion layer in between.  We then compare the results with those obtained
in  III  in a 1-layer stratified flow.
      Under the second subtask, we conducted experiments of plume dispersion
over a realistic terrain model in a 1-layer stable flow.   The realistic
terrain chosen was the Kennecott Copper Smelter vicinity including part of
Great Salt Lake and part of Oquirrh Mountain.   The terrain features
are highly rugged and asymmetric, compared to those of the idealized terrain.
We selected one of the existing smelter stacks as the pollutant source in
the experiment.  Results are compared with those obtained by Veenhuizen, et
al. (1973), who modeled the same terrain under neutral conditions.
       The third subtask is the development of a method which simulates plume
dispersion during inversion breakup.  Pollutants once aloft and trapped in
the inversion layer are subsequently mixed and brought to the ground by the
convective motion which develops in the growing unstable layer adjacent to
the ground.  Using either mass or heat released from a surface into a
stratified fluid, we conducted several tests in an attempt to simulate the
growth of the unstable layer, and we concluded that heat release provided
a more natural and realistic simulation than mass release.

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                                               Table  ].   Summary  of  Uxpev imen t.s
                                                a.   Plume  Dispersion  Experiments
Run Number
la
Ib
] la
fib
I Tic.
Illb
Desc r i pt i on
Simulation of Plume Dispersion
into an F.levated Inversion
S iiiml at ion of P] nine Dispersion
into tin Klevaled inversion
Simulation of Plume Dispersion
into an Ulcvcitocl Inversion
Simulation oi: Plume Dispersion
Into an Klevated In very Jon
Simulation of Plume Dispersion
in Stably Stratified Flows
Over Complex Terrain
Simulation of Plume Dispersion
in Stably Stratified Flows
Over Complex Terrain
Terrain Model
Idealised Terrain Model
(e<|. 3.J)
Idealized Terrain Model
(eq. 3.1)
Idealized Terrain Model
(eq. 3.1)
Ideal i/.ed Terrain Model
(ec,. 3.1)
Kennccott Copper Smelter
(figs. 2 and 9)
Kennecott Copper Smelter
(fijjs. 2 and 9)
Stratification
Profile
*
3-layer (N-S-H)
3-layer (N-S-N)
3-layer (N-S-S)
3-layer (N-S-S)
1-layer (S)
1-layer (S)
K
(..8
3.4
6.8
3.4
2.0
1.0
F,
'(
•", .92, <»
v, 1.85, ™
•», .68, 1.54
«>, 1.37, 3.08
1.04
2.08
Fu
3.08
3.08
3.07
3.07
2.02
2.02
                                                          b.   Inversion Breakup

-



Desc r i pt ion
Simulation of Plume Dispersion
During Inversion breakup
(Prototype Condi cion-TVA
Paradise Plant 9-13-1966)
Terrain Model
Flat Surface



Stratification
Profile
1-layer (S)



K
°°, 3.76



F,
n
oo, 6.10



FD
3.15



*  N = neutral, S = stable
*" Based on tbe stacK height

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       Section III summarizes the important findings of this investigation
Section IV of this report describes the laboratory facility.  Sections V,
VI and VII present, respectively, the results of the three subtasks
described above.  The visualization results are also presented in a 16mm
color film entitled "Stably Stratified Flows Over Complex Terrain."

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                               SECTION II

                                SUMMARY

       Laboratory experiments in a stratified towing tank were conducted to
investigate plume dispersion over a complex terrain for various inversion
conditions.  The existence of strong vertical shear with alternating over-
shooting and blocked regions characterized the flow field.
       For plume dispersion over an idealized terrain model with simulated
elevated inversions, pronounced impingement of pollutants onto the mountain
slopes was observed.  In this case, more pollutants were carried around
the model than in previous experiments conducted under weaker ground inver-
sions.
       When the idealized model was replaced by a realistic model in a
1-layer stably stratified flow, which was highly rugged and asymmetric,
the dispersion pattern of the latter showed a strong interaction between
the stratified flow and the rugged terrain features.   The plume axis of
the latter showed a lateral diversion of 20  from the free-stream wind
direction because of upstream blocking.
       Lastly; the feasibility of simulating plume dispersion inversion
breakup was successfully demonstrated by cooling a simulated ground surface
Pollutants were stirred and carried to the ground as soon as the convective
layer reached the plume originally trapped in the inversion layer.

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                               SECTION III
                               CONCLUSIONS

3.1    Plume Dispersion in 3-Layer Stratified Flows
       (i)    The bent-over plumes level off and are trapped within the
              middle inversion layer.  Upstream of the mountain, the
              vertical spread of the plume is larger than that in a 1-
              layer stable flow as a result of the relatively large
              spreading rate in the bottom neutral layer.
       (ii)   For all the cases, the wind carries the pollutants in the
              plume at least partially around the mountain.   For the
              cases with a more stable middle-inversion layer, most
              pollutants are carried around the mountain.
       (iii)  Direct impingement of pollutants on the mountain slopes
              is evident from both visualization results and probe
              measurements.  For the cases with a less stable middle
              layer and a neutral upper layer, the measurement made
              on the mountain ridge along the center line of the
              model has the maximum concentration.   For the  cases with
              a more stable middle layer, ground concentrations on the
              ridge are low because most pollutants are carried around
              the mountain.
       (iv)   For the low internal-Froude-number, F^9, cases, the pollutants
              remain aloft both upstream and downstream of the mountain.
              The vertical spreads are small.  For the high internal-Froude-
              number cases, the wind forces pollutants downward as it carries
              them around the mountain.  Downstream of the mountain,
              pollutants appear to be stirred and carried to the ground.
       (v)    Downslope wind is not as strong as that in a linearly strati-
              fied case because the lee wave cannot penetrate into the
              bottom neutral layer.
       (vi)   At the stack location,  the velocity profile (Run lib), U(z),
              shows a minimum wind-speed region in the middle inversion layer,
              where the flow is blocked by the mountain ridge.  Pronounced
              shear regions are present in the regions near the interfaces of
              layers.  Strong overshooting occurs in the upper layer.

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3.2    Plume Dispersion From the Kennecott  Smelter Stack
       (i)    Under the simulated conditions,  the plumes for both cases
              (F  = 1.04 and 2.08)  are  quite close to the ground.  The
                n
              vertical and lateral  spreads,  especially far downstream of
              the stack, increases  with the  internal  Froude number.
       (ii)   For the low internal-Froude-number  case (F^ = 1.04), the
              plume is aloft throughout the  entire length of the model.
              The overall plume shape conforms closely with the under-
              lying terrain features.   When  the internal Froude number
              increases (F,  = 2.08),  the thickness of the turbulent
                          n
              boundary layer (TBL)  increases to include  the plume.   As a
              result, pollutants are  stirred and  carried to the ground.
              For both cases, however,  the  ground concentrations are low.
       (iii)  The wind carries  the  plumes around  Oquirrh Mountain.   The
              plume was trapped  within  Little  Valley.  We observe a  20
              initial diversion  for both cases.   For  the high  internal-
              Froude-number case, the wind forces  the  plume slightly
              farther away from  the foothill of Oquirrh  Mountain.
       (iv)   Velocity profiles show  that large overshooting occurs  at a
              level high above the  terrain  surface and is a result of the
              blocking by the tall  and  massive mountain ridge.  The  plumes
              level off and remain  in the blocked region.
3.3    Plume Dispersion During Inversion Breakup
       (i)    Simulation of inversion breakups have been successfully per-
              formed by cooling a model surface using dry ice as the coolant.
              The shadowgraph records have  shown  many interesting features,
              such as the developments  of the growing domes, the receding
              cusps, the sharp interface, etc., which actually occur in
              the atmosphere.
       (ii)   Both the penetration  height and  the duration of occurrence have
              been realistically scaled. The initial penetration height
              increases with t1 2,  in agreement with other data.

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(iii)   From the visualization results,  we have clearly demonstrated
       the capability of simulating the sequential  occurrence  of
       the entrainment of pollutants into the unstable layer.

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                               SECTION IV

                          LABORATORY FACILITIES

4.1    The Stratified Towing Tank
       All experiments,  except those concerning  inversion breakup, were
conducted in a stratified towing tank,  18.3  m long,  1.2 tn wide and .9m
deep.  A detailed description of this facility appears in a previous FRI
report (Pao, et al.,  1971).   Several features of the towing tank system
which are pertinent  to the present investigation are described briefly in
the following:  (i)  It has a specially-designed  filling system,  which
facilitates the preparation of a stratified  fluid having a predetermined
density profile.  (ii) It has transparent side and bottom walls, which
allow visualization  experiments from several directions.  (ill)  It has a
smooth, oil-lubricated carriage, which has a noise level that is approxi-
mately 0.3% of the towing speed.  The low noise  level permits accurate
measurements of the  velocity, temperature and salinity fluctuations with
hot-film probes, thin-film and/or thermistor probes,  and single-electrode
conductivity probes.   (iv) It has a minicomputer system for direct, on-line,
multiple-channel,  data acquisition and  subsequent,  statistical,  data analysis.
       In addition,  we installed an absorptive layer made of 7-layer nylon
netting on the bottom of the towing tank to  reduce internal wave reflection.
The nylon netting is knitted with .12-cm braided threads and has diamond-
shaped openings (1.3 cm x 1.3 cm).  The distance between layers  was approxi-
mately .6 to 1.2 cm.   As an internal wave travels through the absorptive layer,
we observed, from shadowgraph pictures, turbulence generated in  the wakes
of the nylon threads.   The generation of turbulence,  which is finally damped
by the stable stratification, dissipates the energy of the internal wave.
To compare the overall dispersion patterns of two plumes released in a stable
flow, with and without the absorptive layer  in place, we conducted several
experiments.  The results showed no significant  difference between the
corresponding cases  (see appendix A).
       The inversion breakup experiment took place in a stratified towing
tank, which was 7.3m long,  .20 m wide, and  .71  m deep.   This towing tank
has the same special features as the larger  one, except the tracks of the
smaller tank are not oil lubricated.

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4.2    Terrain Models
       During the experiment, we mounted the terrain models and the stack
upside down on an oil-lubricated carriage in the stratified towing tank.
To simulate a buoyant plume in the atmosphere, we injected a heavy plume
from the inverted stack into the ambient fluid.  The plume was traced with
dye, and 35mm still-picture cameras and 16mm movie cameras recorded the
dispersion patterns.  We presented the flow visualization results in such
a way that the plume appeared to be injected upward,  as in the prototype.
       In the sharp inversion experiments (Run la, Ib, Ila and lib), we
used the idealized model described in [ij.  Figure 1 shows a contour map of
the model.  The characteristic lengths of the model and the stack are
summarized in table 2.
       The vicinity of the Kennecott Copper Smelter in Garfield,  Utah was
modeled for the experiments of plume dispersion over realistic terrain
under stable conditions.  Figure 2 is a topographic map of the area in the
vicinity of the smelter.  The stack under investigation is located about
1 km west of Smelter Peak.  The  surrounding terrain features are extremely
rugged.  The terrain model, with a scale of 1/10,000 was designed to
include terrain features for a far-field simulation of the stack plume.
The model covered an area roughly 11 km wide and 30 km long (extending
10 km into Salt Lake in the north and northwest directions, and 11 km in
the south and southeast directions).  The modeled area includes Kessler Peak
(elev. 2689 m) and Coon or Farnsworth Peak (elev. 2760 m) of Oquirrh Mountain.
We chose the characteristic height h for the internal Froude number to be
the difference between the elevations of Coon Peak and Salt Lake (elev.
1280 m).  The model was 1.1 m wide and 3 m long and simulated a wind
direction of 315°.  The model surfaces were intentionally stepped with
vertical steps of .31 cm, corresponding to 30.5-m contour intervals in the
prototype.
4. 3    The Effluent  Injection Device
       The effluent was a concentrated dye solution (brilliant-blue food dye)
with a predetermined density.  The injection device consisted of a heated
flask containing the effluent fluid, a temperature controller (YSI Model 72),
a veristaltic pump (Monostat Model 72-895-05) with insulated Tygon tubing,

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X
i
X

ta
CJ
2
<
r-1
CO
c
       • Stack  and  Sraricn for
         Velocitv Measurement
                                        O Stations for Surface
                                          Temperature Measurement
      60
      50
      30
       10
      -10
      -30
      -50
      -6C
                                          i = 13 (cm)
            -40   -30   -2Q   -10   0    10   20


                       LATERAL  DISTANCE y(cm)
                                                  30   40
       1—I ^ ^^  T
                A Contour  Map  of the Idealized Terrain Model
                                 1C

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                 Table 2.  Simulation Conditions  for the
                           Sharp Inversion Experiments
         a.  Characteristic Length of  the  Idealized Terrain Model

                           Length Scale:   1/2,500
Descriptions
Stack Diameter, D
Stack Height, H
Mountain Peaks Height, h
o
Mountain Peaks Separation
Mountain Ridge Height, h
Prototype [m]
7.94
127.0
609.6
941.0
406.4
Model [cm]
.32
5.08
24.38
37.64
16.26
                         b.   Simulation Conditions

                            Velocity  Scale:  1/100
Run Number

la


Ib


Ha


lib

Uoo[cm/s]

3


6


3


6
-i — '
K

6.8


3.4


6.8


3.4

FD

3.08


3.08


3.07


3.07

Layer
1
2
3
1
2
3
1
2
3
1
2
3
Top of Layer
[cm]
9.7
17.8
40.6
9.7
17.8
40.6
8.6
19.3
55.9
8.6
19.3
55.9
N [HZ]
0
.20
0
0
.20
0
0
.27
.12
0
.27
.12
7h
CO
.92
oo
CO
1.85
OO
CO
.68
1.54
oo
1.37
3.08
-36 pc/lOOml
~5"z~ L J
(prototype)
-.98
6.23
-.98
-.98
6.23
-.98
-.98
12.22
1.59
-.98
12.22
1.59
pg = 1.175
[gm/cm J
                                    11

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                                                          Smoke Stack

                                                                   Copper Smelter

                                                           Smelter Peak
                                                             Thermistor Probes
Fig.  2    Terrain Model in the Vicinity of  the Kennecott  Copper
          Smelter in  Garf.ield, Utah.

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an accumulator, and a heated hose  (Technical Heaters, Inc., Model 352)
connected to the stack.  Figure 3  is a block diagram of the device.  After
preheating the dye solution to 80°C in the flask, we pumped it through the
stack into the ambient  fluid and,  just upstream of the stack, reheated the
effluent in the heated  hose, which maintained the temperature at 90 + 2°C.
Fine temperature control was essential since thermistor probes measured the
temperature at the terrain surface downstream of the stack to indicate
ground concentration.   Prior to each experiment, we calibrated the effluent
discharge rate with a stopwatch and a graduated cylinder.
       To ensure a turbulent plume at the stack exit, we installed a sapphire
nozzle ranging from  .13 mm to  .38  mm in diameter about .5 cm upstream of the
stack exit.  The size of the nozzle is dependent upon the flow rate and the
stack diameter.  As  the effluent passed through the nozzle, it expanded to
the designed size at the stack exit.  At a constant discharge rate, the
stack Reynolds number is inversely proportional to the nozzle diameter.
4.4    Instrumentation
       Two, 10-channel, constant-temperature anemometers (Models 1051-10
and 1053-B, Thermo Systems, Inc.)  using fourteen (14) conical and cylindrical
hot-film sensors  (TSI Models 1230S and 1290 AK) measured the mean and fluctu-
ating velocities of  the approaching flow near the stack.  The sensors were
insulated with two coats of quartz for use in conductive fluid.  The system
has a frequency response of up to  1 kHz.  Hot-film sensors mounted on a
strut measured the vertical velocity profiles.  These sensors covered a
vertical distance of 30 cm, and the spacing decreased between sensors toward
the terrain surface.  We calibrated the sensors either before or after each
velocity measurement with the strut lowered to a distance (the model was
upside down) at which no sensors were within the turbulent boundary of the
terrain model.  For  the extreme cases (Runs Ila and lib), the maximum
specific gravity change was about  .03 and the corresponding corrections
required for the sensor were -8% and +6% for the mean and fluctuating
measurements, respectively (appendix C).  Five towing speeds were used for
the calibration, and the data points were least-squares fitted with second-
degree polynominals.
       The plumes used  in the study were basically turbulent although they
tended to relaminarize  far downstream of the stack under extremely stable
                                    13

-------
  Temperature
  Controller
(YSI  Model  72)
   Preheated  Dye
     Solution
      (80°C)
Veristaltic Pump
 (Manostat Model
  72-895-05)
Ceramic  Stack
    Heated  Hose

(Technical  Heaters,
 Inc.,  Model  352)

       90°C
   Accumulator
          Fig.  3   A  Block  Diagram of  the Effluent Injection Device

-------
conditions.  In a turbulent flow, the ratio of the turbulent diffusivity of
salinity to that of heat is approximately unity.  Therefore, the temperature
concentration measured in the model can be directly extrapolated to the
field (see eq.  (4.1)).  Using the temperature as a tracer, we measured
ground concentrations with the thermistor probes (Fenwal Electronics
GC32SM2).  The  thermistor probes have a nominal resistance of 2000 ft and a
temperature coefficient of -3.4%/°C at room temperature.  The probe tip is
0.76 mm in diameter, and the time constant (3db point) of the thermistor
probes in still water is about .07 sec.  A 10-channel gauge with the
thermistor probe as one arm of the wheatstone bridge measured the temperature
of the fluid.   The sensitivity of the system is typically 10 volt/ C.  The
output of the gauge went directly into the minicomputer system for on-line
calibration and data acquisition.  Signal conditioners increase the overall
sensitivity of  the temperature gauge to 30 volt/ C with a noise level
equivalent to 1.4 x 10    C, and  the thermistor probe has long-term stabil-
ity  (a typical  drift of  .01 C/year).  The probes are pre-calibrated against
a precision thermometer with  .01  C divisions  (Brooklyn Thermometer Company,
Inc.) in a constant-temperature bath, which is equipped with a temperature
controller (YSI Model 72) of  .01  C repeatability.  In the range of tempera-
ture differences of interest  (0~.5 C), the calibration curves appear to be
quite linear.   We used second-degree polynominals to best fit the calibration
data.  Before each experiment, we measured a reference temperature in the
towing tank and 'fed it into the computer.  The computer shifted the recorded
calibration curve so that is was  parallel to the pre-calibrated curve.
Figure 4 is two typical calibration curves of the thermistor probes.  For
ground concentration measurements, we installed the probes in the terrain
model with the  probe tips exposed to the ambient fluid at a distance
approximately .2 cm above the terrain surface.  We then measured and recorded
the coordinates of the probes, in reference to the stack.  When extrapolated
to the field, the following analogy can be made
o-ea
0-0
s a

m
C - C
a
"c - "c
s a
                                                                          (4.1)
                                               JP
                                    15

-------
-9
                                       20. 'J
            TEMri.'IRATUUb'.  (  C)




             a.   liiyh  Gain
                                                 -1
                                                 -3
                                                 -7
  I	I
j	I
       8    10   12    14  16
                                                                               °
TEMPERATURE (C)



 b.   Low Gain
                   Pig.  4   Calibration Curves of  a Thermistor  Probe

-------
where  C  is the mean pollutant  concentration,  C   is the ambient concen-
             _                                   a
tration and  C   is  the  source concentration.
       A conductivity gauge  (Model 1110) developed by Flow Research, Inc.,
measured the density profiles in the  tank.  This gauge has a frequency
response of from DC  to 1 kHz.  The sensor was a single-electrode conduc-
tivity probe, which  has  a .025-mm stainless-steel tip platinized with
platinum black  solution.   The sensitivity of  the conductivity gauge is about
                      3
1 volt per 0.025 gm/cm  .   The probe was  calibrated in jars of salt solution
of known density,  and the calibration data were least-squares fitted with
a second-degree polynominal.  Figure  5 shows  a 3-layer stratification profile
measured with a conductivity probe in the towing tank.
                                    17

-------
                                         Terrain Surface
                                          Mountain Ridqe
                                          Mountain  Peaks
    70
     1.00
                                                      1.05
                     SPECIFIC GRAVITY
ig.  3   A  Typical  3-Layer  Stratification  Profile  Measu^^cl Wi^h
       a  Conductivity  Probe  in the Towing Tank  (Runs  Ila and lib)
                          13

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                                 SECTION V
                 PLUME DISPERSION IN 3-LAYER STRATIFIED FLOWS

       For the experiments,  a  3-layer  stratified  fluid was  prepared  in
the towing tank  to  simulate  an elevated inversion layer in  the atmosphere.
Figure 6 shows two  sketches  of the  structure  of the  3-layer fluid.   Figure
5 corresponds to the  actual  density profile of fig.  6b (upside down  model).
The 3-layer  fluid consists of  a neutral layer (constant density) adjacent
to the ground, a neutral  (fig. 6a)  or  a stable  (fig.  6b)  layer high  above
the ground layer, and an  extremely  stable or  inversion layer between the
two.  Figure 6 also shows the  reference elevations of the idealized
terrain model and of  the  stack.   We purposely arranged the  top of  the
middle inversion layer at a  level above the mountain ridge  so the  plume
would not rise above  the  mountain.
       In the experiment, we conducted two (2) runs  for each of  the  two  3--
layer stratified cases (fig.  6).  Table 2 lists the  experimental conditions
for all four (4) runs.  The  free-stream wind  speed is denoted by U , and
the ratio of the effluent speed W  to  U  is denoted  by K.  The stack Froude
number, F  ,  is defined as F   = W / ^/gDAp/p ,  where D is the  stack diameter,
         D                 D    S         S
Ap is the difference  in the densities  of  the  effluent  and the ambient fluids
at the stack exit,  g  is the gravitational  acceleration  and  p  is the effluent
                                                             S
density.  The internal Froude  number,  F, .,  is defined  as  F,  .  = U^/N./j, where
F, . = U^/N.Tz, N.  is the Brunt-Vaisala  frequency of the  i    layer, and h is
the height of the mountain ridge.
5.1    Flow  Visualization
       Figure 7  shows the side and plan views of the plumes in 3-layer
stratified flows over the idealized terrain model.   The side views (figs.
7a through 7d) indicate that  the overall dispersion  patterns resemble,  to
some degree, those  observed  in 1-layer stratified flows (figs. 15  through
18 in  [ij),   especially in the  region upstream of  the mountain.
       In the near  field, the  turbulent motion in the plume dominates the
plume dispersion.   The plumes  released into the bottom neutral layer rise
into the middle  inversion layer.  Overshooting of the plumes, in the in-
version layer for the  low internal  Froude number  (figs.  7a  and 7c) is evident
                                     19

-------
             W, = 20.4 cm/s
                              F0= 308
    Mountain Peaks
    Mountain -tidge
   Layer 3. N, = 0 Hz

       (Neutral)
                               Layer 2. N; - 2 Hz

                                  (inversion)
                                Layer 1  N, = 0 Hz

                                   (Neutral)
                                                   r-30 cm
                                                   r-20
               a.    Runs  la  and  Ib
                cm/sec
     Mountain Peaks
     Mounta.n
                                = 3.07
Layer 3. N,= .12 Hz

   (Stable)
                              Layer 2, N, - .27 Hz


                                (inversion)





                                 Layer 1. N, = O H

                                   (Neutral)
                                                    30 cm
                                                   h20
              b.    Runs Ila and lib
3-Layer  Stratification  Structure  for  the  Simulation
of  plume Dispersion Into an Elevated  Inversion  Layer
                         20

-------
                                       . 5 m
         a.    Run la,  U^ = 3 cm/s, K = 6.8,  F   = .92
 I
b.   Run Ib, U^ = 6 cm/s, K = 3.4,
                                                   1.85
         c.    Run Ha,  U  = 3 cm/s,  K = 6.8,  F
         d.    Run lib,  U  = 6 cm/s,  K = 3.4,  F,0 = 1.37
Fig. 7   Plume Dispersion Into an Elevated Inversion Layer  Over
         the Idealized Terrain Model.  F  = 3.08
                             21

-------
         e.  Run la, UOT = 3 cm/s, K =  6.8,  F
         f.  Run Ib, U^ = 6 cm/s, K =  3.4,  F, „  =  1.85
          g.   Run Ha, Uro = 3 cm/s, K = 6.8, F,  =  . 68
        h.   Run lib, U  = 6 cm/s, K = 3.4, F, .  =  1.37
Fig. 7  (Cont'd) Plume Dispersion  Into  an  Elevated Inversion
         Layer Over the Idealized  Terrain  Model.   F  = 3.08
                        22

-------
The bent-over plumes  level  off  and  are  trapped within  the  inversion layer.
The vertical spreads  of  the leveling  plumes  increase with  an  increase in
internal Froude number,  F^.  Compared  with  the corresponding cases in  [l],
the vertical and  lateral spreads  of all the  present cases  are quite large
as a result of the  relatively large spreading rate in  the  bottom neutral
layer.
       Farther downstream,  the  mountain blocks the flows in the inversion
layers.  For all  the  cases,  the pollutants in the plumes are carried by
the wind, at least  partially, around  the mountain.  Direct impingement of
the plume onto the  mountain slope is  evident.  For the low internal-Froude-
number cases (figs. 7a and  7c), the plumes are aloft upstream and down-
stream of the mountain.   The wind carries the pollutants around the mountain
at the same level as  those  upstream and downstream of  the mountain.  This
phenomenon implies  that  the vertical  displacements of  the  streamlines around
the mountain are  small.   When the internal Froude numbers are doubled (figs.
7b and 7d), the wind  forces the pollutants carried around  the mountains
downward to the ground.   This complicated dispersion pattern apparently
results from the  interaction of the stratified flow with the terrain and
from the vertical pressure  gradient developed as the fluid flows around
the mountain slope  (see  Task II report).  Downstream of the mountain,
the pollutants which  were once  aloft  at  small Froude numbers,  are stirred
intensively until they reach the  ground.  As a result, we expect high
concentrations on the ground.   The  tops  of the pollutant layer do not
show significant  differences in the elevation upstream and downstream
of the mountain,  as opposed  to  the  cases observed in figs.  16  and 18 in
[ ll .   In the present  experiment,  lee  waves cannot penetrate into the
bottom neutral layer; and,  therefore, the strength of the downslope wind
(the descending portion  of a lee  wave) which tends to carry the pollutants
toward the ground, decreases considerably.
       Figures 7e through 7h show the plan views of the plumes.  The plumes
released from the stacks (right)  were advected toward  the mountain.  The
I-shaped, white portion  shown in  fig. 7h corresponds to the peaks and the
ridge between the peaks  (see, also, fig. 1).  For all  cases, the plan views
(figs.  7e through 7h) show  that the wind carries the plumes, at least partially,
around the mountain.  For the cases with a less stable inversion layer  (figs.
                                     23

-------
7e and 7f), the plumes are carried over and around the mountain while, for
the cases with a more stable inversion layer (figs.  7g and  7h),  the plumes
are carried mainly around the mountain.   This result demonstrates that the
plume rise decreases while the upstream blocking increases  with increasing
stability.  Comparing the individual cases with the  same stratification
profile, we find the initial lateral spread decreases  while the  plume rise
increases with an increasing internal Froude number, F^ (fig-  7e vs. 7f
and 7g vs. 7h).
       The two cases with a more stable,  middle inversion layer  (figs. 7g
and 7h) are strikingly different.   For the low internal-Froude-number case,
the valley just downstream of the  mountain ridge is  practically  free of
pollutants (fig. 7g).   The pollutants, which are carried by the  wind around
the mountain, are transported downstream along the outside  contour of the
mountain.  On the other hand, for  the high internal-Froude-number case (fig.
7h),  the valley is filled with pollutants.   In this  case, a strong reverse
flow, which carries pollutants from the  sides into the valley,  appears to
develop in the lee of the mountain.   A small portion of the pollutants
trapped in the downstream valley is contributable to those  carried over the
mountain ridge (see, also, the movie).
5.2    The Velocity Profile
       Hot-film  probes  on  the  x-z  plane at  the  stack location measured  the
mean  velocity profile,  U(z),  of Run  lib.   Figure  8 shows these measurements.
A dotted line in fig.  8 denotes the free-stream wind or towing  speed, U .
The profile shows several interesting features, which  are the consequences
of the interaction between the stratified flow and the topography.  The
wind  speed in the middle inversion layer,  where the  flow is blocked by the
mountain ridge (upstream blocking),  appears to be at a minimum.   In the
bottom neutral layer,  the velocity is higher than that in the middle layer
because upstream blocking does not occur in a neutrally stable  flow.  In the
upper stable layer, where no major obstacle blocks the flow, we  measured
strong overshooting from the mean  wind or towing speed.   Overshooting is
an established characteristic of stably  stratified flows (Long,  1959 and
Pao,  1968).  The profile displays  several regions of high vertical shear.
The most pronounced shear region occurs  just above the mountain  ridge, between
                                    24

-------
 Ei
 o
N


O
H
C-H

>
P

w
     50
     40
     30
     20
     10
         Muntaxn Peaks
         Mounbain
         Ridqe
         Stack Exit
                                                  N3=.12 Hz
                               U(cm/s)


Pig. 8   Mean Velocity Profile at the Location of the Stack in Run
         lib.  The Ambient Fluid Was Stratified With a 3-Layer
         Structure.  The Idealized Terrain Model Was That Described
         in Section 5.9

-------
the blocked and the overshooting regions.   The visualization results  (fig.  7)
show that the plume levels off at an elevation slightly below that of the
mountain ridge, where the flow is noticeably blocked.
5.3    Concentration Measurements
       Ten (10) thermistor probes that were installed in the terrain model
measured the ground concentration on the mountain slope.  Their positions
are indicated on the contour map shown in fig. 1.  Table 3 summarizes the
results of Runs la, Ib, Ila and lib.
       For Run la where F7 9 = .92, the wind carries the plume over and around
the mountain, and maximum ground concentrations occur on the top of the
mountain ridge between the peaks (probes nos.  1 and 3) and have values as
high as 4,400 ppm relative to the effluent concentration.   High ground con-
centrations were also present at other locations on the mountain slope
(probes nos. 4, 5, 9 and 10) at the level where a portion of the pollutants
in the plume are carried around the mountain.   These measurements further
support the observation (Lin, et al.,  1974) that direct impingement of a
plume onto a mountain slope occurs under stable conditions.  The maximum
root-mean-square concentration occurred on the mountain ridge (probe no.
3).   This location corresponds to that of  the  plume edge,  where the con-
centration signal is highly intermittent.
       When the internal Froude number increases (Run Ib,  F,   = 1.85), the
plume rise tends to increase slightly, and the ground concentrations on
the mountain ridge decrease considerably.   The measurement of the highest
concentration still occurred at probe no.  1.
       In Run Ila, the wind carries the pollutants around  the mountain (fig.
7a),  and ground concentrations on the ridge are low.   The  vertical spread is
so limited that the plume is not in direct contact with any of the probes.
When the internal Froude number increases (Run lib, F7„ =  1.37), the
plume rise increases, and a small portion of the pollutants are carried over
the mountain ridge.  As a result, measurement  of concentrations on the ridge
were slightly higher (probe no.  1).  The vertical spread also increases and
high concentrations were measured at other locations on the mountain slope
(probes nos.  2, 4, 7 and 10).
                                    26

-------
                 Table 3.  Ground Concentrations Data of  the Sharp Inversion Experiments

Thermistor

1
2
3
4
5
6

7
8
9
10

x [cm]

61.00
57.47
61.00
57.47
67.00
64.77

36.83
38.74
44.45
57.47

y lcml

0.00
0.00
6.35
6.35
0.00
0.00

19.69
19.69
19.69
13.97

z [cm]

16.26
8.89
16.50
11.68
12.95
14.48

10.29
12.09
14.10
13.97
Ambient Conditions
Run Number
la
ePc]
20.75
20.37
20.62
20.44
20.65
20.37

20.35
20.37
20.48
20.42
20.35
(6-6 )/(6 -9 )
a s a
5.74 x 10~3
2.87 x 10~4
3.87 x 10~3
1.29 x 10~3
4.31 x 10~3
2.87 x 10~4

0.0
2.87 x 10~4
1.87 x 10~3
1.01 x 10~3
-
J7 PC]
3.82 x 10~2
1.36 x 10~3
1.04 x 10"1
4.44 x 10~2
1.39 x 10~2
5.89 x 10~3
_2
1.07 x 10
2.82 x 10~2
8.06 x 10~2
2.31 x 10~2
1.0 x 10~3
Ib
Q [°c]
20.56
20.42
20.36
20.45
20.44
20.41

20.28
20.33
20.38
20.32
20.28
(e-ea)/(es-ea)
4.02 x io~3
2.01 x 10~3
1.15 x 10~3
2.44 x 10~3
2.29 x 10"3
1.86 x 10"3

0.0
7.17 x 10"4
1.43 x 10"4
5.74 x 10"4
-
J7[°d
2.71 x 10~2
2.32 x 10~2
4.72 x 10~2
5.04 x 10"2
3.69 x 10~2
3.62 x 10~4
2
1.12 x 10
4.83 x 10"2
5.21 x 10~2
1.69 x 10~2
3.0 x 10~4
Effluent Temperature  9  = 90 + 2 C
                       S

-------
                           Table 3.   (Cont'd)  Ground Concentrations Data of the
                                     Sharp Inversion Experiments


Thermistor
Probe No.

1
2
3
4
5
6

7
8
9

10


x [cm]

61.00
57.47
61.00
57.47
67.00
64.77

36.83
38.74
44.45

57.47


Y [cm]

0.00
0.00
6.35
6.35
0.00
0.00

19.69
19.69
19.69

13.97


z [cm]

16.26
8.89
16.50
11.68
12.95
14.48

10.29
12.09
14.10

13.97
Ambient Conditions
Run Number
Ila


e L°c]
19.93
19.91
19.92
19.90
19.91
19.92

19.91
19.91
19.92

20.01
19.90

(6-6 )/(6 -6 )
a s a
4.28 x 10~4
1.43 x 10~4
2.85 x 10~4
0.0
1.43 x 10"4
2.85 x 10~4
-4
1.43 x 10
1.43 x 10~4
2.85 x 10~5
-3
1.57 x 10 J
-
	
Je2 [°c]
2.65 x 10~3
1.70 x 10~3
4.42 x 10~3
4.30 x 10~3
2.02 x 10"3
1.01 x 10~3
-3
3.82 x 10
2.13 x 10~3
4.80 x 10~3
-3
5.57 x 10
1.0 x 10~3
lib


¥ [°c]
20.00
20.12
19.95
20.29
19.96
19.93

20.20
19.93
19.92

20.05
19.90

(6-6 )/(8 -6 )
a s a
1.43 x 10~3
3.14 x 10~3
7.13 x 10~3
5.56 x 10~3
8.56 x 10"4
4.28 x 10~4
T
4.28 x 10
4.28 x 10"4
3.14 x 10"4
0
2.14 x 10
-
	
>2 PC]
7.46 x 10~2
5.12 x 10~2
8.92 x 10~3
6.93 x 10~3
3.51 x 10~2
2.32 x 10~3
i
1.17 x 10
9.42 x 10"3
6.36 x 10~3
T
2.14 x 10
1.0 x 10"3
Effluent Temperature  6   =  90 + 2  C

-------
                               SECTION VI

            PLUME DISPERSION FROM THE KENNECOTT SMELTER STACK
       To simulate plume dispersion  in 1-layer stratified flows over a
realistic terrain, we selected one of the stacks at the Kennecott Copper
Smelter in Garfield, Utah and the surrounding terrain.  Table 4 summarizes
the simulation conditions for both the prototype and the model.
       The terrain model, whose features are more rugged and asymmetric than
the idealized model, had a scale of  1/10,000.  To ensure a turbulent plume,
we enlarged the stack diameter by a  factor of two (1/5,000 scale).  According
to the discussion in appendix B, the effect of the diameter exaggeration on
plume dispersion in the far field is insignificant under given neutral or
stable conditions, as long as the buoyancy number in the model remains
the same as that in the prototype.   The buoyancy number in the exaggerated
stack was preserved by reduction of  the speed ratio, K, by 21% (see appendix
B).
6.1    Flow Visualization
       Figure 9 show plumes in stably stratified flows (1-layer) over the
rugged terrain model southeast of the Kennecott Copper Smelter in Garfield,
Utah.  The plumes in both cases (Run Ilia and Illb), with F,  = 1.04 and 2.08,
respectively, are quite close to the ground.  The vertical and lateral spreads
of the plumes, although quite different in the two cases, are small compared
to the vertical and horizontal extents of the area modeled.
       For the low internal-Froude-number case (fig. 9a) , where F,  = 1.04,
the overall shape of the plume conforms closely to the underlying terrain
features.  The plume is aloft over the entire length of the model.  Far
downstream of the stack, the plume tends to relaminarize.  This relam-
inarization indicates that the turbulence intensity at the plume level,
although quite close to the ground,  is low and the turbulent boundary layer
(TBL) is very thin.
       When the internal Froude number increases by a factor of two (fig. 9c)
and F  =2.08, the overall shape of  the plume tends to smoothen out.  The
vertical and lateral spreads increase considerably, and the wind carries the
pollutants in the plume downward to  the ground.   No tendency of relaminarization
                                    29

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           Table 4.   Simulation Conditions for Plume Dispersion From
                     the Kennecott Copper Smelter Stack
                           a.   Characteristic Length

                               Length Scale:   1/10,000
Description

Stack Diameter, D
Stack Height, H
Elevation of Coon Peak
Characteristic Height, h
Prototype [m]

8.23
124
2,760
1,480
Model [cm]
*
.17
12.4
27.6
14.8
Enlarged by a factor of two
                               Simulation Conditions
Description
Free-Stream Wind Speed, U^ [m/s]
Effluent Speed, Ws [m/s]
Brunt-Vaisala Frequency, N [Hz]
Internal Froude Number, F,
' n
Speed Ratio, K
Stack Froude Number, F
Lapse Rate, - -^ [°C/100m]
Ambient Temperature, 9 \_ CJ
3.
Effluent Temperature, 6 [°cj
r s -,
3
Effluent Density, p gin/cm
Prototype
Run Ilia
6.1
15.24
.004
1.04
2.5
2.11
.78
0
177
—
Run I lib
12.2
15.24
.004
2.08
1.25
2.11
.78
0
177
—
Model
Run Ilia
.02
.04
.13
1.04
2.0
2.02
—
20.6
90
1.035
Run I lib
.04
.04
.13
2.08
1.0
2.02
—
20.6
90
1.035
                                     30

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                     5km
  a.  Run Ilia, Side View, U  =  2 cm/s, K  =  2.0,  F,  =  1.04
                                                Mean Wi-nd
   b.   Run Ilia,   Plan View, U  = 2 cm/s, K = 2.0, F  - 1.04
                     5 km,
    c.   Run Illb, Side View, U   =  4  cm/s,  K  = 1.0,  F,  =  2.08
                                                Mean  Wind
    d.   Run  IIlc,  Plan View, U^ = 4 cm/s, K  =  1.0, F, =  2.08
Fig. 9   Dye Visualization of Plume Dispersion  From a  Stack
         Located at the Kennecott Copper  Smelter  in Garfield,
         Utah, Under Stable Conditions.   Wind Direction = 315°,
         F  = 2.02
                          31

-------
of the plume is observable, and the plume edges are relatively ill-defined.
This phenomenon indicates that the thickness of the TBL has increased to
include the plume and that the turbulence intensity at the plume level
increases.
       The importance of terrain effects on plume dispersion in stably strati-
fied flows are unambiguously demonstrated by the plan views of  the  plumes
(figs. 9b and 9d).   The wind definitely carries the plumes around Oquirrh
Mountain and diverts it into Little Valley, which is northeast of the
mountain.  In the near field, the terrain effects are so dominant that the
initial diversion (—20° from the free-stream wind direction)  of the plume
is independent of the internal Froude number.   For both cases, the plumes
are carried into Little Valley avoiding the steep mountain slope on the
southwest of Oquirrh Mountain,   For the low internal-Froude-number flow,
F7 = 1.04,  the wind seems to carry the plume into the valley along the
foothill of Oquirrh Mountain.  Farther downstream,  in the lee  of the
mountain, the plume tends to turn back to follow the mean wind.   When the
internal Froude number is double, the plume is carried slightly farther
away from the mountain toward the northeast.
       In the near field, the lateral plume spread of the high internal-
Froude-number case is slightly smaller than that of the low internal-Froude-
number case.   This reduction is present because the turbulent  motion in the
plume dominates the plume dispersion.  In the experiment, we increased
the internal Froude number for the same stratification by increasing the
towing speed.  The plume in  the low internal-Froude-number case, therefore,
has a relatively long time to spread before the wind advects it to a
fixed downstream location.  As the plume is advected farther downstream,
however, the role of the background turbulence becomes increasingly
important.   In the far field, the lateral plume spread in the high
internal-Froude-number case becomes considerably larger than that in
the low internal-Froude-number case because the turbulence intensity
at the plume level is higher in the former than that in the latter.
       Under neutral conditions,  a plume rises considerably higher with a
larger vertical spread and a much smaller lateral diversion than under stable
conditions  (Veenhuizen,  et al.,  1973).  These distinctive differences are
not surprising because the vertical motion in a neutral flow is not inhibited
                                    32

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and because the buoyant plume  tends  to rise above rather than around the
mountain.  The large lateral diversion observed in the stable cases is the
result of upstream blocking, which does not occur in the neutral cases.  The
generation and maintenance of  a thick TBL with high turbulence intensity
further disperses the plume as the neutral fluid flows over the rugged
terrain.
6.2    Probe Measurements
6.2.1  Velocity Profiles
       Figure 10  shows  the mean velocity profiles, U(z), of Runs Ilia and
Illb, which we measured with hot-film probes at the stack location.  The
dotted lines denote  the free-stream  speed for the respective runs.  Both
profiles  show blocked regions  at  low levels and overshooting regions high
above the blocked regions.  The abnormally large overshooting from the
mean wind speed is the  result  of  blocking induced by the tall and massive
mountain  ridge on the southwest of the smelter.  This ridge includes
Kessler Peak  (elev.  2689 m) and Coon Peak (elev. 2760 m) of Oquirrh
Mountain.  From the  visualization results, the plumes were released in
and appear to remain in the blocked  regions.
6.2.2  Concentration Measurements
       Based on the  visualization results, locations were selected to
install  ten  (10)  thermistor probes for the measurement of ground concen-
trations  (see fig. 2).  The probes were  installed to cover an area large
enough that  the distribution of ground concentrations could be inferred from
the data.  The background  concentrations were measured with probes installed
outside  the  plumes.
       For both Runs Ilia  and  Illb,  the  results show no appreciable ground
concentrations at any of  the locations inside and outside the plumes.  The
measured  temperatures were all comparable with  the thermal noise level
(.01°C)  in the towing tank.  If a source S02 concentration of 2000 ppm is
assumed,  the noise level  of  .01°C is equivalent to a full-scale noise level
of  .28 ppm, which is lower than  the  Federal  Secondary Ambient Air Quality
Standard  of  .5 ppm  (3-hr  average).   In the experiment,  the sampling time
was about 60 seconds, which is equivalent to a  sampling time of 1/2 hour in
the full-scale case  (time  scale = 1/33).  Note  that the experiment was
designed  to  simulate a  steady  wind condition.

                                     33

-------
e
o
o
H

e-<
K


W
      0
                        U  (cm/s)


   10  Mean Velocity Profiles  at  the  Location of the Stack
        in  the Kennecott Smelter  Model.

        315°
Wind Direction =

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       From the visualization results, we expect the ground concentrations
in Run Ilia to be low because the plume is aloft throughout the entire length
of the model.  In Run Illb, however, pollutants in the plume appear to be
stirred and carried to the ground.  Apparently, the turbulent motion enhances
the plume spread, and the pollutants have been diluted greatly.
                                     35

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                               SECTION VII

                PLUME DISPERSION DURING INVERSION BREAKUP
       After a nocturnal inversion is formed, a plume released into the  stable
layer is transported downwind in the form of a flat ribbon with variable
lateral spreading and minimum vertical dispersion.  Subsequently, as the
result of surface heating, a growing unstable layer below replaces the
nocturnal inversion.  As the thermally induced vertical mixing develops and
builds to include the plume, pollutants in the plume are entrained into  the
unstable layer and are uniformly stirred and carried to the ground.  Thomas,
et al. (1970) measured maximum ground concentrations in a narrow band along
the plume axis during the inversion breakup period.   The unsteady, convective
motion, also termed penetrative convection, has been the subject of some
full-scale study (Lenschow and Johnson, 1968 and Thomas, et al., 1970)
and of some theoretical modeling (Lilly,  1968).   In the laboratory, Deardorff,
et al. (1969) investigated the penetrative convection in a tank filled with
thermally stratified distilled water.  Subsequently,  Willis and Deardorff
(1974) conducted experiments to study the rate of dispersion of nonbuoyant
particulates released from a near-ground source into the convective layer.
       In this study, we attempted to develop a method of simulating the
penetrative convection in the atmosphere by releasing either heat or mass
from a surface to initiate and to maintain the growth of the unstable layer
adjacent to the ground.   Pollutants are released from a stack to alloxv in-
vestigation of the dispersion characteristics during the unsteady inversion-
breakup period.   For realistic simulation of the unsteady inversion-breakup
phenomena,  several conditions, in addition to those described in [I I must be
satisfied.   Geometric similarity requires that the maximum height of the
unstable layer,  z.,  be simulated correctly, i.e.,
                                          m
                                                                        (7.1)
where the subscripts m and p refer to the model and the prototype, respectively,
Kinematic similarity requires
                             U
                              c<
                             W,
U
 cc
W,
(7.2)
                                 m
                                   36

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where w^  is  a  convective velocity scale  (Deardorff  and Willis,  1975).   In
the present  study,  however,  we made no attempt  to satisfy  eq.  (7.2).
       When  simulating any unsteady phenomena,  one must define  the
characteristic time scale, T,  which is the ratio of the length  scale
to the velocity scale.   Correct  simulation of the unsteady inversion-
breakup phenomenon requires
                                     IT I
                                                                         (7.3)
where T± is the time required for the unstable layer to reach its
maximum height.
       We conducted  several  tests to develop  a method  to  simulate inversion
breakup.  First, we  generated the growth  of the unstable  layer adjacent to
a surface by  allowing  a heavy salt  solution to infiltrate slowly through
the surface  (an upside-down  model).  Although we  could easily control the
penetration height by  varying the density of  the  salt  solution, the observed
convective motion lacked the large-scale  components  (the  growing "dome" as
described by  Deardorff,  et al.,  1969) observed in the  field.  These large-
scale components are responsible for the  fumigation  of a  plume in an
unstable layer.  Second,  we  used ice in an attempt to  generate the convective
motion, but because  the heat flux was not sufficiently large (the
stable fluid  was at  a  temperature of 20 C), the penetration height was too
small to include the plume.  Finally, we  tested dry  ice and obtained satis-
factory results.
       A special device was  designed by FRI to facilitate the experiment.
First, we filled two aluminum channels  (6.1 m x 7.6  cm x  .32 cm) with dry
ice and then  placed  them into the towing  tank.  The  bottom of the channels
were in direct contact with  the  water surface.  Between the channels was
a gap of 1.3  cm, through which we would tow the stack  to  simulate plume
dispersion in a crosswind.
       The field conditions  at the  TVA Paradise Power Plant on 13 September
1966 (Thomas,  et al. ,  1970)  were simulated at FRI in this experiment.  Two
183-m stacks  are located  in  the  Paradise  Plant, but  only  one of them was
in operation  on that day.  Table 5  lists  all  the  experimental and the
                                    37

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                    Table 5.   Simulation Conditions for the
                              Inversion Breakup Experiments


                            a.   Characteristic Length

                               Length Scale:   1/5000
  Description
     Prototype [mj
(TVA Paradise Power Plant)
Model  [cm]
Stack Diameter,  D

Stack Height,  H
          7.92

          183
   .158

   3.66
                            b.   Simulation Conditions
Description
Free-Stream Wind Speed, U [m/sl
Effluent Speed, Ws [m/s]
Ambient Temperature, 6 [ Cj
a
Stack Effluent Temperature, 0 1 Cj
5
Lapse Rate Before Breakup, - -^ [°C/100m]
Lapse Rate After Breakup, - ^- [°C/'100m]
Brunt-Vaisala Frequency Before Breakup, N [HZ]
Effluent Density, p gm/cm
Ambient Fluid Density, p gm/cm
3. 1— -J
Internal Froude Number, F
Stack Froude Number, F
iJ
Speed Ratio, K
Prototype
(TVA Paradise Power
Plant 9/13/1966)
0, 4.88
18.0
20.6
144
-1.2
.98
.0043
;;;
0, 6.20
3.15
», 3.69
Model
0, .020
.075
23.0
23.0
	
	
.09
1.043
1.005
0, 6.10
3.15
00 , 3.76
                                      38

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simulated prototype  conditions.   Figure 11 shows  the  actual  and  idealized
profiles of  the  temperature soundings  before and  after  the inversion breakup
The atmosphere adjacent  to the ground  was  stably  stratified  and  was nearly
isothermal at 0658.   It  finally became neutrally  stratified  (adiabatic) at
0934.   The terrain surrounding the plant site is  relatively  flat, as shown
on the  USGS  topography map.   The terrain effect on  the  plume released  from
the 183-m stack  under stable conditions will probably be  insignificant
except  very  close  to the ground.   Field observations  of the  Keystone plume
(Schiermeier and Niemeyer,  1968  - figs.  11 and 12), where the terrain
features appear  to be more rugged than those of the Paradise plant, have
substantiated, at  least  qualitatively,  the above  statement.  For a
feasibility  study  of the simulation of the inversion  breakup, representa-
tion of the  surrounding  terrain  by a flat  surface is  therefore sufficient.
7.1     Flow  Visualization
        To visualize the  structure of the growing  unstable layer, we used
the shadowgraph  method described in III.  Figure  12  is  a  plot of the
penetration  height z.(t).  The average of  z.  was  measured from shadowgraph
pictures.  The  initial slope of the data indicates  that z. is proportional
    1/2                                                  1
to t    before  the convection stablizes, which agrees with the observation
of Turner  (1968).   In the present experiment, we  cooled the  fluid by a
constant temperature rather than by a  constant heat  flux.  This  cooling
process explains the leveling off of the curve at large times, as the
temperature  in  the fluid approaches that of the cooling surface.  The  time
required for z.  to reach its maximum of 10.5 cm  ( 1700  m  in  the  prototype)
is about 8 minutes (3 hours in the prototype), which  is in the same range as
the simulated conditions given in table 5  and fig.  11.
        Figure 13 is  a series of shadowgraph pictures  which show  the growth
of the  unstable  layer with time.   A plume  released  into the  calm (no cross-
wind),  stable layer  is also shown in each  picture.
        The interface between the  unstable  and stable  layer is distinctive,
but irregular, as  shown  in  fig.  13.  Frequently,  individual  thermals with
well-defined boundaries  form and  rise  into  the stable layer.  The larger
the size of  the  thermal,   the higher  it  rises.  Penetration of large
thermals into the  stable  layer occurs  frequently  and  randomly at the
interface.   The  frontal boundaries of  these  large thermals in the
                                    39

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   900 -
   300 •-
   7 0 0 ' ~
   500
   500
O  400
H
E-
   300
DJ
   200
   100--
                      Paradise ?o
                         9-13-196
                             Time
     .- 0653
     +- 0934
                       Adiabatic
        I-.To? of
          Stack
/\
             «/er Plant
       1C
   20
15 10
                                          Before
                                         Breakup
15
                           TEMPERA'

         a.  Actual Profiles
              :URS(°C)
                                After
                               Breakup
:o
25
                   b.   Idealized Profiles
   Fig. 11 Typical and  Idealized Temperature Profiles for the
           Inversion Breakuo Experiment  (see Thoruas,  et al.,
           1970)

-------
   10 -
e
u
 •H  5
M
U
M
EH
&
H
O

EH
M
O
M
H
ffi
                       I	I
                                 I  1  l  i
      10
100
                                                                500
                                  1000
                                       TIME  t(sec)
    Fig.  12  Penetration Height z.(t) of  an  Unstable Layer Generated by Cooling  a  Surface

             With Dry Ice in a Stratified Fluid  (N ~.1 Hz)

-------
                                        t =r 90 s
                                        t = 120 s
                                        t = 200 s
                                        t = 270 s
Fig. 13  Shadowgraph Pictures of Entrainment of Pollutants  in a

         Growing Unstable Layer During Inversion Breakup
       U  = 0, N =  .09 Hz, K = 0°, Fu  =  0,  Fn  =  3.15
        00                                   JJ

-------
stable layer take the shape of a dome  (Deardorff, et al., 1969).
Individual domes always overshoot  the  interface and then subsequently
recede.  The repetition of the overshooting and receding motions of
the large thermals appear to contribute  efficiently to the growth of
the unstable layer.  Between domes,  cusp-shaped regions, through which
the undisturbed fluid is entrained  into  the unstable layer, are observed.
The intensity and frequency of the  generation of large thermals decrease
with time.  A sharp and relatively  smooth  interface develops as the
penetrative motion becomes less vigorous.  The sharp interface observed
in the shadowgraph pictures corresponds  to the "super" stable region
measured by Deardorff, et al.  (1969).
       When simulating a crosswind,  we towed the stack as soon as we
secured the channels filled with dry ice.  Figure 14 is a series of
pictures, in sequence, which show,  by  tagging the same patch of pollutants
in the plume (the camera was stationary  to the towing tank), the evolution
of the entrainment process.  Before the  unstable layer builds to reach the
plume levels, pollutants in the plume  remain aloft.  As soon as the top
of the growing unstable layer reaches  the  plume level, pollutants begin
to become entrained in the unstable layer  (fumigation).  As the convective
motion continues to penetrate the  stable layer, it stirs the entrained
pollutants within the unstable layer,  and  a well-mixed layer adjacent to
the ground is finally established.
7.2    Temperature Profile During  Inversion Breakup
       Ten (10) thermistor probes mounted  on a strut measured the temperature
profile, 6(z,t), adjacent to the surface (the bottom of the channels) where
the growth of the unstable layer began.  The gain of the thermistor gauge
was modified to cover a temperature range  of 25 C.   Figure lib shows a
typical calibration curve of a thermistor  probe.
       The vertical temperature profiles,  6(z,t), adjacent to the ground
are plotted in fig. 15.  The temperature profiles tend to stablize in about
10 minutes, which is slightly longer than  the time required for z± to reach
its maximum (fig. 12).  The initial  cooling at t-tQ = 0 is the result of
radiation which came from the bottom of channels before they were secured
in place.   Note that a kink on the  temperature profile at z ^ 3 cm tends
to develop after t-tQ exceeds 600 seconds.
                                    43

-------
                  0
                   I
1 km
                                                            2 .
                                                             1
                        t = 4 0 s

                        t = 300 s
                                                            z .
                                                             i
                        t = 400 s
                        t = 720 s

Fig.  14   Dye Visualization of the Sequential Entrainment
          of Pollutants (Fumigation)  in a Growing Unstable
          Layer During Inversion Breakup.  The Pictures Were
          Taken With the Camera Stationary to the Towing Tank
          (Following the Same "Patch" of the Plume)
                          44

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     30
  0
2
O
 W
     25
     20
     15
     10
          Symbols
             O
             *
             x
             a
             •
             v
             -2
t-t [sec]
   o L   J
    0 +
   50
  200
  400
  600
 1000
 1400
                        4   6   3  10  12   14   16   13   20   22

                          TEMPERATURE(°C)
Fig. 15  Temperature  Profiles  During  the Growth of  an Unstable
         Laver Adjacent  to  a Surface  in  a Stratified Fluid
         (>f=  .095  Hz).   The Growth of  the Unstable Layer '--7as
         Generated  by Cooling  the  Surface With Dry  Ice.

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                              REFERENCES


Briggs, G. A. (1969) Plume Rise, U.S. Atomic Energy Commission Critical
    Review Series, TID-25072.

Deardorff, J. W. and Willis, G. E. (1975) "A Parameterization of Diffusion
    into the Mixed Layer," Manuscript No. 0201-75-9 (to be published  in
    JAM), National Center for Atmospheric Research, Boulder, Colorado.

Deardorff, J. W.,  Willis, G. E. and Lilly, D. K. (1969) "Laboratory
    Investigation of Non-Steady Penetrative Convection," J. Fluid Mech.
    3J5, 7-32.

Defant, A.  (1961) Physical Oceanography, vol. 1, Pergamon Press, New  York.

Ippen, A. T. (1966) Estuary and Coastline Hydrodynamics, McGraw-Hill,
    New York.

Lenschow, D. H.  and Johnson, W. B. (1968) "Concurrent Airplane and Balloon
    Measurement of Atmospheric Boundary-Layer Structure Over a Forest,"
    J_. Appl.' Meteor. 1_, 79-89.

Lilly, D. K. (1968) "Models of Cloud-Topped Convection Layer Under a  Strong
    Inversion," Quart.  J. R. Meteor.  Soc. 94, 292-309.

Lin, J. T.,  Liu, H. T., Pao, Y. H., Lilly, D. K.,  Israeli, M. and Orszag,
    S. A. (1974) "Laboratory and Numerical Simulation of Plume Dispersion
    in Stably Stratified Flow Over Complex Terrain," Report No. EPA 650/4-
    74-044,  USEPA, Research Triangle Park, North Carolina.

Liu, H. T.,  Lin, J. T., Pao, Y. H., Veenhuizen,  S.  D., Peecher, D. W. and
    Hiatt, G. L. (1974) "The Plume Dispersion in Stably Stratified Flow
    Over a Flat Plate and a Three-Dimensional Terrain," Flow Research
    Film No. 6.

Long, R. R.   (1959) "The Motion of Fluids With Density Stratification,"
    J. Geophys.  Res. _64_, 2151-2163.

Martin, S. (1966)  "The Slow Motion of a Finite Flat Plate Through a Viscous
     Stratified Fluid," Tech. Report No. 21 (ONR Series), The Johns Hopkins
     University.

Pao, Y. H.  (1968) "Laminar Flow of a Stably  Stratified  Fluid Past  a  Flat
    Plate,"  J.  Fluid Mech. _34_, 795-808.

Pao, Y. H.,   Lin, J. T., Carlson, R. L.  and Smithmeyer,  L. P. C.  (1971)
    "The Design and Construction of a Stratified Towing Tank With  an
    Oil-Lubricated Carriage,"  Flow Research Report No.  4  (APL/JHU
    POR-3530).

Sanborn, V.  A.  (1972) Resistance Temperature Transducers. Metrology  Press
     Fort Collins, Colorado.                                              '
                                   46

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                         REFERENCES  (CONT'D)
Schiermeier, F. A. and Niemeyer, L. E.  (1968)  "Large Power  Plant Effluent
     Study," (LAPPES), Vol. 1 - Instrumentation, Procedures, and Data
     Tabulations, National Air Pollution Control Administration Publication
     No. APTD70-2.

Thomas, F. W., Carpenter,  S. B. , Leavitt,  J. M. , Montgomery, T. L., Colbaugh,
    W. C. (1970) "Report on Full-Scale  Study of  Inversion Breakup at Large
    Power Plants," Tennessee Valley Authority, Div. of Environ. Research
    and Development, Muscle Shoals, Alabama.

Turner, J. S.  (1968) "The  Behavior of a Stable Salinity Gradient Heated
    From Below," J. Fluid  Mech. 33>, 182-200.

Veenhuizen,  S. D. , Lin, J.-T.,  Pao, Y.-H.,  Peecher, D. W. and Hiatt, G. L.
    (1973) "Laboratory Simulation of Plumes From Kennecott  Copper Smelters
    in Garfield, Utah:  Neutral Atmosphere," Flow  Research  Report No. 9.

Willis, G. E.  and Deardorff, J. W.  (1974)  "A Laboratory Model of the Unstable
    Planetary  Boundary Layer,"  J. Atmos. Sci.  31,  1297-1307.

Wunsch, C.  (1969) "Progressive  Internal Waves  on Slopes," J. Fluid Mech.
    35,  131-144.
                                    47

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   APPENDIX A.  THE EFFECT OF AN ABSORPTIVE LAYER ON PLUME DISPERSION

       In the atmosphere, the upper boundary is nonreflective.  Internal
waves generated near the ground propagate upward and finally disperse and
dissipate into the upper atmosphere.  Partial reflection is possible,
however, if the outgoing waves encounter sharp inversion layers.  In general,
we can write the upper boundary condition in the atmosphere as
3w
3z
                                         0,                              (A.D
where w is the vertical fluid velocity and Z  is the elevation of the upper
boundary considered.  In a stratified towing tank,  the bottom of the tank
imposes a reflective upper boundary condition (since the model is upside
down), i.e.,

                             Is        =0,                             (A.2)
                                Z = Zb
where Z  is the elevation of the tank bottom in reference to the terrain-
       b
model surface.
       The reflective boundary condition might cause the formation of un-
realistically strong downstream blocking and prevent full penetration of
downslope winds toward the leeward surface of the mountain.   To resolve
this  speculation, one could install an absorption layer on the bottom of
the towing tank to absorb, at least partially, the internal energy generated
by the towed terrain model.  We could then observe, with the absorptive
layer in place, whether the flow pattern would be more asymmetric and the
pollutants would be carried further toward the ground and into the turbulent
boundary layer in the lee of the mountain.  Absorbers of various types have
been applied in the laboratory to reduce reflection of surface and internal
waves from tank walls,  by Ippen (1966) and Wunsch (1969).   The present
experiment,  however, requires revisions to design an absorptive layer
for effectively reducing the reflection of internal waves from the
bottom of the towing tank.
                                    48

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       Figure 16 shows two plumes in a 1-layer stratified flow over the
idealized terrain model.  In this experiment, we installed an absorptive
layer made with nylon nettings  (section 5.1) on the bottom of the towing
tank to reduce internal wave reflection.  Other experimental conditions
were the same as those shown in  figs. 17 and 18 in  III.  For the overall
dispersion pattern, we observed  no  significant difference between the
corresponding figures, with or without the absorptive layer in place.  The
direct interaction between the  stratified flow and the terrain is so
strong, especially close  to the  terrain surface where plume dispersion is
heavily influenced, that  the effect of the reflection from the solid bottom
becomes insignificant.
                                     49

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                                         5 m
         a.   Side View,  U^ = 3 cm/s, K = 6.8, F,  = 1.37
         b.  Side View, UOT =  6 cm/s, K =  3.4,  F,  =2.
73
                                       . 5 m
         c.   Plan View,  UOT = 6 cm/s, K = 3.4, F, = 2.73
Fig. 16   Dye Visualization of Plume Dispersion  in  a Stratified
          Flow Over the Idealized Terrain Model.  An Absorptive
          Layer Was Installed To Reduce  Internal-Wave Reflection.
          FD ••  3.11.  See Figs. 17 and 18 in  [l]  for Comparison.
                             50

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   APPENDIX B.  THE EFFECT OF AN EXAGGERATED STACK ON PLUME DISPERSION

       Under neutral conditions, the application of a stack with an exaggerated
diameter in simulated plume dispersion has been investigated by Veenhuizen,
et al, (1973).  The main advantage of this approach is that the flow field is
not distorted or disturbed.  In the following, we attempt to examine the
possible errors involved with the use of an exaggerated stack.
       Let a buoyancy number be defined as

                                              "
                        B -
                     /Z\  _    B   x               2 /D\/x
                     U)  -
where D is the stack diameter, F is the buoyancy flux of the plume, H is
the stack height, F  is the stack Froude number, K is the speed ratio, U
is the ambient wind speed  (assumed to be uniform), and p  and p  are the
                                                        a      s
ambient fluid and effluent density, respectively.  By using eq. (B.I), we
can rewrite the second equation on p. 33 in Briggs (1969) in a dimensionless
form as
                         3     -   'x\2
                                   ,HJ   -  4\par  WW           (B-2)

where Z is the plume trajectory above the stack exit.  In the near field
when x/H is small, both terms on the right-hand side (r.h.s) of eq. (B.2)
are significant.  In the  far field, where the ratio of the stack diameter
to the stack height, D/H  is small, we can neglect the second term on the
r.h.s of eq. (B.2) except  for the very large speed ratio, K.  Under neutral
conditions, the speed ratio, K, is of order 1.  Therefore, if we consider
the plume dispersion in the far field, the plume rise depends only on the
buoyancy number, B, defined in eq. (B.I).
       Under stable conditions, the final height of the tops of plumes Zfc
under calm and stable conditions with a constant density gradient is given
by Briggs (1969) as
                               5F1/4 s-      .                            (B.3)
Using eq.  (B.I) with s =  (2irN)2, we can rewrite eq.  (B.3) as
                                   =  1.26B174 F3/4    .                 (B.4)
                                   51

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Equation (B.3) or (B.5) is also applicable to cases with a light crosswind
(Lin, et al., 1974).   With the presence of a crosswind, an empirical
formula for predicting the final rise of a bent-over plume is also given
by Briggs (1969) as
                           Z  = 4.0 (F/Us)1/3 .                           (B.5)

Again, with the use of eq. (B.I), eq. (B.5) can be rewritten as

                          -^  =  1.17B173 F^'3  .                         (B.6)

Equations (B.2), (B.4) and (B.6) all show that the plume rise in the far field
is preserved under a given stable condition,  i.e., when F  is constant,
as long as the buoyancy number, B,  is identical  for the model and the proto-
type.
       Consider plume dispersion experiments which use an exaggerated stack.
According to eq. (B.I), there are two ways to preserve the buoyancy number,
B.  One can reduce the speed ratio  (K~L   ) if  F  remains unchanged, or
                                                                       1/3
if K remains unchanged, one can increase the stack Froude number (F ~ L
where L  is the exaggeration factor of the stack diameter).   For example,
when we exaggerate the stack diameter by a factor  of two, i.e., L  = 2,
then we can preserve B, by reducing K by 21% or  by increasing F  by 21%.
The optimum choice, however, depends on which regime of the plume we wish to
investigate.  In the near field, the ratio K is  more significant while, in
the far field, the stack Froude number is the more important factor.
                                   52

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 APPENDIX C.  THE RESPONSE  OF A HOT-FILM PROBE  TO A VARIATION OF FLUID DENSITY

     During the calibration of  the  hot-film probes, the probe strut was
lowered about 30 cm  to  avoid disturbance from the terrain  surface.  As a
result, the probes encountered  fluids  of different  densities during measure-
ment and calibration.   In the following,  the response  of the hot-film probes
to the variation of  fluid density is examined,  and  the required correction
is evaluated.
     Consider an extreme case when  a hot-film probe is used to measure the
velocity at a level  where the fluid density,  p,  =1.01 and then is cali-
brated at a different level where   p = 1.04.  Neglecting the heat loss to
the supports, the rate  of production of Joulean heat   Q  attributable to
the current  I = E/R   is equal to  the heat loss to the surrounding fluid,
that is,
                        E2/R   = hTTD£(T  - T),                      (C.I)
                             w            w
where  E  is the supply voltage, R   is the film resistance,  h  is the
                                    w
heat transfer coefficient,   D   is the  diameter  of the  cylindrical hot-film
probe,  £  is the length of the sensor,   T  is the film temperature and
T  is the ambient fluid temperature.
     Equation (C.I)  can be  written  to  include the Nusselt  number  N  = -r- ,
                                                                   U    K,
where  k  is the thermal conductivity,  as
                        E2   = TTD£R  (T   - T)kN .                      (C.2)
                                  w w      u
Note that only  k  and  Nu   in  the  right-hand side  of  eq.  (C.I) depend on
the fluid density.   After differentiation and normalization, the sensitivity
of the hot-film output  to density is

                      f  - k   (f + £) •                      (c'3)
                                 \            '
     According to King's relation (Sandborn, 1972), we have
                        N    =  .318  +   .69 \/Re  ,                     (C.4)
                        u
where  Re = —  is the  Reynolds number.   The respective kinematic viscos-
ities for  p = 1.01  and  p = 1.04  are (Martin, 1966)

      v|           =  .00953   and vl      .  _,  = -00990 cm /sec.
       'p  = 1.01                 'p =  1.04
                                   53

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For  U = 6 cm/sec  and  D = .002 in.,  the Nusselt numbers are
            Nu|p = 1>Q1 = 1.552  and  Nu p= ^^ = 1.529.

The thermal conductivity for  p = 1.01  and  p = 1.04  are (Defant,  1961)
       k|p = 1.01   1-355 x 10    and  k|p = 1.04   1>3  X          Q
                                                        (cal/cm sec  C)
Substituting the above values in eq. (3), we have

               ^          = | (-.023 - .015}
                  Ap = .03
                           = -.02.
According to King's law,  the velocity-voltage relation is
                               E2 ~ U5.                                (C.5)
Therefore, the corresponding correction for the mean velocity is
                                     - -.08.                           (C.6)
As a reference, the experimental error is approximately 10% for mean velocity
measurements.
     The turbulent velocity is proportional to the local slope of the E-U
curve, i.e.,
                                    dE
                                u~dU '
                                                             AE
The correction for  u,  by using eq. (C.5) and the value of  —  .
                                                              E Ap — .Uj
is, therefore,
                    u     /dE\

for the extreme case considered.
      A/dE\
Au     -dU^ _3 (M)= +.
                                            06
                                  54

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                                   TECHNICAL REPORT DATA
                            (Please read instructions on the reverse before completing)
1. REPORT NO.
  EPA-6QQ/4-7fi-n??
             3, RECIPIENT'S ACCESSIOIVNO.
  i ITLE AND SUBTITLE
  PLUME  DISPERSION IN STABLY  STRATIFIED FLOWS OVER
  /"" /"*i I j r*» f \i  -w ^ _. _ . — .,
  COMPLEX  TERRAIN
  Phase  2
             5. REPORT DATE
              May  1976
             6. PERFORMING ORGANIZATION CODE
7. AUTHOR(S)
  H. T.  Liu  and J. T. Lin
                                                           8. PERFORMING ORGANIZATION REPORT \O.
              Flow  Research  Report No. 57
9. PERFORMING ORGANIZATION NAME ANO ADDRESS

  Flow  Research, Inc.
  1819  South Central Avenue
  Kent,  Washington   98031
             10. PROGRAM ELEMENT NO.

              1AA009
             11. CONTRACT/GRANT NO.
                                                             68-02-1293
 12. SPONSORING AGENCY NAME AND ADDRESS
  Environmental  Sciences  Research Laboratory
  Office  of Research and  Development
  U. S.  Environmental Protection Agency
  Research  Triangle Park,  NC    27711
             13. TYPE OF REPORT AND PERIOD COVERED
              Final Reoort.  5/74-.V75	
             14. SPONSORING AGENCY CODE
              EPA - ORD
 15. SUPPLEMENTARY NOTES
 16. ABSTRACT
        Laboratory experiments  were conducted in a  stratified  towing tank to
   investigate plume dispersion in stably stratified  flows.   First,  plume dispersion
   over  an  idealized terrain  model with a simulated elevated  inversion in the
   atmosphere was investigated.  These results were compared with  those of experiments
   previously conducted under simulated ground inversions.  Second,  plume dispersion
   in  1-layer stably stratified flows over a realistic  terrain was also modeled.  The
   plume dispersion patterns  showed a strong interaction  between  the stratified flow
   and the  rugged terrain  features.  Third, plume dispersion during  inversion breakup
   was simulated.  Results  indicated that as soon as  the  convective  layer built to
   reach the plume, pollutants  were stirred and carried to  the ground.
17.
                                KEY WORDS ANO DOCUMENT ANALYSIS
                  DESCRIPTORS
                                              b.IDENTIFIERS/OPEN ENOE3 TERMS
                             :OSATI Field/Group
  *Tests
  *Plumes
  *Atmospheric diffusion
  *Stratification
  *Terrain
   Air pollution
                                 148
                                 21B
                                 04A
                                 14G
                                 08 F
                                 136
13. DISTRIBUTION STATEMEN"

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                                              55

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