United States Atmospheric Sciences
Environmental Protection Research Laboratory
Agency Research Triangle Park NC 27711
Research and Development July 1987
V>EPA PROJECT REPORT
OOfR87101
CONTRIBUTIONS OF THE FLUID MODELING
FACILITY TO EPA's COMPLEX TERRAIN
MODEL DEVELOPMENT PROGRAM
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CONTRIBUTIONS OF THE FLUID MODELING FACILITY
TOEPA's COMPLEX TERRAIN MODEL DEVELOPMENT PROGRAM
by
WILLIAM H. SNYDER
Meteorology and Assessment Division
Atmospheric Sciences Research Laboratory
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
Atmospheric Sciences Research Laboratory
Office of Research and Development
U.S. Environmental Protection Agency
Research Triangle Park, NC 27711
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NOTICE
This information in this document has been funded by the United States
Environmental Protection Agency. It has been subject to the Agency's peer and
administrative review, and it has been approved for publication as an EPA
document. Mention of trade names or commercial products does not constitute
endorsement or recommendation for use.
The author, William H. Snyder, is a physical scientist in the Meteorology
and Assessment Division, Atmospheric Sciences Research Laboratory, U.S.
Environmental Protection Agency, Research Triangle Park, NC. He is on
assignment from the National Oceanic and Atmospheric Administration, U.S.
Department of Commerce.
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FORWARD
The Atmospheric Sciences Research Laboratory (ASRL) conducts intramural
and extramural research programs in the physical sciences to detect, define,
and quantify air pollution and its effects on urban, regional, and global
atmospheres and the subsequent impact on water quality and land use. The
Laboratory is responsible for planning, implementing, and managing research
and development programs designed to quantify the relationships between
emissions of pollutants for all types of sources with air quality and
atmospheric effects, and to uncover and characterize hitherto unidentified air
pollution problems. Information from ASRL programs and from the programs of
other government agencies, private industry, and the academic community are
integrated by the Laboratory to develop the technical basis for air pollution
control strategies for various pollutants.
The Complex Terrain Model Development Program is designed to develop
reliable atmospheric dispersion models that are applicable to large pollutant
sources located in complex terrain. The major field studies of this six-year
program were conducted during 1980 at Cinder Cone Butte near Boise, Idaho,
during 1982 at Hogback Ridge near Farmington, New Mexico, and during 1983-84
at the Tracy Power Plant near Reno, Nevada. Data from these field studies
along with measurements of fluid modeling simulations performed in the EPA
Fluid Modeling Facility are being used to quantify the effects of terrain
obstacles on stable plume dispersion. A series of annual milestone reports
has been issued to describe the development of the Complex Terrain Dispersion
Model (CTDM) and to contrast the performance evaluation of the CTDM against
existing complex terrain dispersion models. This report describes the
contributions of the Fluid Modeling Facility to the Complex Terrain Model
Development Program.
A.H. Ellison
Director
Atmospheric Sciences Research Laboratory
in
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ABSTRACT
The contributions of the EPA Fluid Modeling Facility (FMF) to the Complex
Terrain Model Development Program (CTMDP) are described. These contributions
included a wide range of laboratory studies and a limited amount of numerical
modeling of flow and diffusion in neutral and stably stratified conditions in
complex terrain. The goal of the CTMDP is the development of a dispersion
model valid in complex terrain, with emphasis on plume impaction on nearby
hills during nighttime stable conditions. Work at the FMF prior to the
inception of the program provided the basic framework for the model - the
dividing-streamline concept - and the focal point around which the field
program was designed. Throughout the course of the CTMDP, the FMF interacted
vigorously with the model developers by providing support in various ways.
Early work provided direct support as an aid to planning the details and
strategies of the field experiments and testing the limits of applicability of
the dividing-streamline concept. Later work included exercises of "filling in
the gaps" in the field data, furthering the understanding of the physical
mechanisms important to plume impaction in complex terrain and in stably
stratified flows in general, testing various modeling assumptions, providing
data for "calibration" of various modeling parameters, and testing the ability
of the laboratory models to simulate full-scale conditions. Simultaneously,
the FMF responded to the needs of the regulatory arm of EPA, the Office of Air
Quality Planning and Standards (OAQPS), by providing guidance concerning
expected terrain effects and by conducting demonstration studies. Finally,
several supplemental studies were conducted, broadening and expanding upon the
specific requests of the model developers and the OAQPS.
IV
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CONTENTS
Forward ///'
Abstract iv
List of Figures vi
List of Tables vii
List of Symbols and Abbreviations viii
Acknowledgements ix
1. Introduction 1
2. Background 3
3. Description of Experiments and Results 8
3.1 Direct Interactions with the Model Developers 8
The period 1980 through 1981 8
The period 1982 through 1983 19
The period 1984 through 1985 26
The period 1986 through present 32
3.2 Supplemental Modeling of Complex Terrain 37
Neutral-Flow Wind Tunnel Studies 37
Stably Stratified Towing-Tank Studies 42
4. Summary 45
References 47
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LIST OF FIGURES
Number Title Page
1 Oblique view of dye streamers released from a horizontal rake 11
upwind of the CCB model at z//7 = 0.3 under strongly stratified
conditions (F=0.2). Flow is from the left.
2 Top view of dye streamers impinging on CCB under strongly 11
stratified conditions (z/h = 0.3, F = 0.4).
3 Top view of CCB under strongly stratified conditions showing vortex 12
rollup and eddy-shedding in the lee (z/h = 0.6, F = 0.2). Unretouched
sequential photographs cut and pieced together. Building roof
shows in background of center portion.
4 Oblique view of impinging streamers on CCB. Middle dye streamer 14
is released at the dividing-streamline height; others at ±1cm (±6m
full scale).
5 Comparison of predicted dividing-streamline heights with 15
observations as functions of towing speed. Open symbols:
predictions using integral formula; closed symbols: observations.
6 Concentration distributions measured during individual tows of CCB 17
with Hs//7 = 0.31 and HD/h = 0.38; wind direction: 117°,
122°.
7 Scatter diagram comparing superposition of concentration 18
distributions from series of 18 tows of CCB model with field
distributions. Dotted lines denote factor of two on either side of
perfect fit.
8 Deformation of vertical dye line by upstream columnar disturbances. 23
Dye line was formed at a location 16m upstream of starting position
of fence, at time when fence was at x = 12.5m (18.6/7 upstream of
fence). Photograph was taken when fence was at x = 13.8m (11.6ft
upstream of fence). Fence is out of photograph, approaching from
top left.
9 Concentration distributions measured on the hill surface with 28
HD//7 = 0.5 and Hs/ft = 0.6. Top: fully submerged; bottom: half
submerged. Dotted circle indicates half the hill height.
10 Scatter plot comparing concentrations on fully immersed hill with 29
those on half-immersed hill on a port by port basis. Hs/h = 0.6,
VI
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11 Terrain amplification factors measured upwind of axisymmetric CCB 31
model. Heavy lines divide the region into areas where the source
position produced the maximum glc upwind of the hilltop, between
the hilltop and the separation point, and downwind of the hill.
Note that the vertical scale is exaggerated by a factor of 3.
12 Plume cross sections measured in presence ( ) and in absence 36
( ) of axisymmetric CCB model at x = 0 (hill center). Hs/h = 0,
xs/h=-6, ys//7 = 0.
13 Contours of constant terrain amplification factors over (a) 41
axisymmetric hill and (b) two-dimensional ridge. Note that
vertical scale is exaggerated by a factor of 3.
LIST OF TABLES
Number Title Page
1 Summary of Terrain Amplification Factors for Sources in the 39
Vicinity of Hills in Neutral Flow.
VII
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LIST OF SYMBOLS AND ABBREVIATIONS
Symbols
A Terrain amplification factor, Xmx/#mX
F Froude number, U^/Nh
g Acceleration due to gravity
h Hill height
h0 Height of density interface from surface
WD Dividing-streamline height
Hs Source height
L Length of ridge
N Brunt-Vaisala" frequency, [-(c//p)dp/dz]
^oo Towing speed or free-stream velocity
xs Source position in along-wind direction (origin at hill center)
ys Source position in crosswind direction (origin at hill center)
Ap Density difference across interface
p Fluid density
p., Density of fluid between interface and surface
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ACKNOWLEDGEMENTS
Many people have contributed to the work described in this report. I am
particularly grateful to R.E. Lawson for his untiring efforts in the
day-to-day operations of the laboratory, to R.S. Thompson for his unfailing
support and many enlightening discussions, to J.C.R. Hunt for his continual
encouragement, unending infusion of new ideas, and enduring patience in
teaching me so much about stratified flow over obstacles, to R.E. Britter and
I.P. Castro for their many contributions, to G.L Marsh for his dogged
persistence in operating the towing-tank experiments, to M.S. Shipman for his
quiet but solid computer support, to J.C. Smith for his many hours at the
filling station, to G.C. Holzworth for his insistence upon FMF involvement in
the CTMD Program and his acceptance of different viewpoints, and to F.A.
Schiermeier for letting us "do our thing". Finally, I wish to express thanks
to the entire FMF staff, past and present, who do the real work day in and day
out, and whose efforts too often go unrecognized and unrewarded.
IX
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1. INTRODUCTION
In the late 1970's the Office of Air Quality Planning and Standards
(OAQPS) of the Environmental Protection Agency (EPA) identified a crucial need
to develop an improved mathematical model that dealt with plume impaction from
large sources located in mountainous terrain under stable flow conditions. A
workshop was convened (Hovind ef a/., 1979) to focus on complex terrain
modeling problems and to develop recommendations to EPA with respect to the
design of a program of experiments and model development efforts.
Subsequently, Holzworth (1980) outlined the EPA plan to achieve the objective
through an integrated program of model development, fluid modeling experiments
and field studies of plume-terrain interactions on hills of progressively
increasing size and complexity. This multi-year, multi-faceted program is
known as the Complex Terrain Model Development Program (CTMDP). The prime
contractor for this effort is Environmental Research and Technology (ERT),
which has produced a comprehensive series of annual reports, called Milestone
Reports, that describe all phases of the research program. The specific
references are: (1) Lavery ef a/ (1982), (2) Strimaitis ef a/ (1983), (3)
Lavery ef a/ (1983), (4) Strimaitis ef a/ (1985), and (5) DiCristofaro ef a/
(1986); a final report is to be completed in 1987.
The Fluid Modeling Facility (FMF) interacted vigorously with various
groups participating in the CTMDP, and provided direct support and guidance in
many different ways. Whereas the field work and model development effort up
to the present time has been specifically focused on plume impaction under
stable conditions, the work at the FMF has taken a much broader view. The FMF
research program has ranged from the development of broad guidelines (e.g.,
terrain amplification factors) and physical concepts (e.g., dividing-stream-
line height) to modeling of specific sites (e.g., Cinder Cone Butte) and
regulatory applications (e.g., good-engineering-practice stack height). The
FMF has provided laboratory data to "fill in the gaps" in the field data
(e.g., measurements of plume deformations over hills) and tested the validity
of convenient modeling assumptions (e.g., cut-off hill approach).
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This report summarizes the contributions, both direct and indirect, of
the FMF to the CTMDP. The discussion provides a historical perspective and a
comprehensive list of FMF's accomplishments with respect to furthering the
physical understanding of flow and diffusion in complex terrain. In many
cases the early research results were first published as internal documents or
project reports or presented at workshops or conferences in order to speed the
flow of information to the model developers. In most cases, these results
have been published in peer-reviewed journals (which took, in one extreme
case, 8 years to appear in print). For completeness and to provide the proper
perspective, both references are cited at first mention in the text that
follows; thereafter, only the journal publication is cited.
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2. BACKGROUND
Research work conducted at the FMF prior to the inception of the CTMDP
had a strong influence on the directions to be taken in the field work and on
the type of model (i.e., physical concepts) to be developed. The stratified
towing tank was commissioned in 1976 (Thompson and Snyder, 1976) and rather
fundamental studies were begun immediately on the structure of stably
stratified flow over idealized three-dimensional hills and on diffusion from a
point source within a stably stratified field of turbulence.
The first published reports on this work (Hunt ef a/, 1978; Hunt and
Snyder, 1980) described the flow structure observed over a bell-shaped hill
under neutral and stably stratified conditions. Earlier theoretical work by
Drazin (1961), model experiments by Brighton (1978) and Riley ef a/ (1976),
and observations (e.g., Queney ef a/, 1960) all indicated that, when the
stratification is strong enough, the air flows in approximately horizontal
planes around the topography. And this observation had been used by EPA in
estimating the surface concentrations on hills caused by upwind sources of
pollution (Burt and Slater, 1977). Up to that time, however, there had been
little firm laboratory or field data as to how strong the stratification must
be for any given streamline starting below the hill top to pass round the side
rather than over the top of the hill. The Hunt and Snyder (1980) paper
suggested a criterion for this change-over to occur on the basis of the
low-Froude-number theory of Drazin (1961), and confirmed that criterion with
experimental data.
The Drazin (1961) theory is applicable to strongly stratified flows
around three-dimensional hills; indeed, it is asymptotically valid at
zero-Froude-number. In simplistic terms, the theory suggests that the
stratification inhibits vertical motions, so that fluid parcels are
constrained to move in horizontal planes. Hence, the flow may be described in
terms of two-dimensional flow around a cylinder which is not necessarily
circular but, in fact, has the cross-sectional shape of the intersection of a
horizontal plane with the three-dimensional hill. Hunt and Snyder (1980)
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verified that, for a bell-shaped hill, a linearly stratified environment, and
an effectively uniform approach-flow velocity profile, Drazin's theory was
applicable in the range F<0.4, where F is the Froude number (^UJNh, U^ being
the towing speed, A/ the Brunt-Vaisala frequency, and h the hill height).
More importantly, Hunt and Snyder (1980) showed evidence for a dividing
streamline (on the centerplane determined by the flow and the axis of the
axisymmetric hill) of height Hs such that streamlines below Hs would impinge
on the hill surface and follow the surface around the sides, whereas
streamlines above Hs would go over the top. They suggested the simple formula
Hs = h (1 - F) (1)
as the criterion to determine whether a plume embedded in the flow approaching
the hill would impact on the surface or surmount the top, for 0
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The implications of this flow structure with regard to plume impingement
and resulting surface concentrations were amplified by Hunt ef a/ (1979).
This primarily theoretical work described two conceptual models for dealing
with the problem of plume impingement. The first model was applicable to
strongly stratified flow around three-dimensional hills, where vertical motion
and vertical diffusion is negligible. The advective-diffusive equation around
a three-dimensional hill which is axisymmetric about a vertical axis was
solved (using an eddy diffusivity) to show how source positions on and off the
centerline affect the trajectories and splitting of impinging plumes and the
value and position of the maximum surface concentration on the hill. The
results showed that the plume behavior is very sensitive to quite small
changes in wind direction away from the direction that transports the plume
onto a stagnation point, and the model provided a simple way to estimate the
effect of these changes. This model also allowed the computation of
concentrations within the separated, horizontally recirculating wake of the
hill (source upwind of hill).
In the second model, a plume in a neutrally stable potential flow around
a hemisphere was analyzed, also using the diffusion equation. The solutions
showed how, because streamlines approach the surface of a three-dimensional
hill much more closely than that of a two-dimensional hill, the maximum
surface concentration on the hill can become very much greater than in the
absence of the hill (but only for a limited range of source heights).
Prior to the inception of the CTMDP, another complex terrain model was
developed by ERT under contract to EPA. The algorithm developed at that stage
was generally applicable to plume behavior in stability conditions ranging
from neutral to slightly stable. The general approach followed the theory of
turbulent plumes embedded in potential flow fields as developed by Hunt and
Mulhearn (1973), Snyder and Hunt (1984 - original manuscript made available to
ERT in 1978), and Hunt ef a/ (1979). This theory was applied to the
calculation of ground-level concentrations using a Gaussian form of solution
to the diffusion equation. Stream functions appropriate to the potential flow
over a cylinder (aspect ratio, h/L = 0) and to the potential flow over a sphere
(ft/L = 1) form the cornerstones of the model. These solutions were extended to
describe flows over terrain features of intermediate crosswind aspect ratio by
a weighting of the two limiting stream functions. The derivation of this
weighting scheme relied heavily on wind-tunnel experiments of flows over hills
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of various aspect ratios (Snyder and Britter, 1987; data reports made
available to ERT in 1979). Strictly speaking, this algorithm was applicable
to neutral flows, but an empirical approximation was included to define
streamline lowering caused by an imposed stable stratification. This
empirical scheme was derived on the basis of the stratified towing-tank
experiments of Hunt and Snyder (1980). Extensive comparisons of model
predictions with FMF laboratory data were made for both neutral and weakly
stable conditions. A full account of these model-development efforts and the
essential physics of the model are provided by Bass et al (1981). These
algorithms were subsequently incorporated into a routine operational model
called COMPLEX/PFM (Potential Flow Model; Strimaitis ef a/, 1982). In
COMPLEX/PFM, potential flow calculations are performed whenever the plume lies
above the dividing-streamline height and the stability is between neutral and
slightly stable; when the plume is below the dividing-streamline height, the
model reverts to the standard COMPLEX I computation (see Wackter and
Londergan, 1984). The COMPLEX I computation makes the level-plume assumption,
with an effective doubling of surface concentration above the plume centerline
concentration (Burt and Slater, 1977). This particular aspect of the complex
terrain diffusion problem was one of the hotly contested issues that provided
the impetus for the CTMDP.
A "strawman" was proposed by Holzworth and Snyder (1979) for discussion
at the 1979 workshop convened by EPA to make recommendations with regard to
the directions to be taken under the CTMDP. This strawman was hotly debated
at the workshop and, in the end, was largely accepted by the workshop
participants (Hovind et al, 1979). The plan that emerged (Holzworth, 1980)
called for an enlargement of some of the major concepts arising from the
previous work at the FMF, and for a verification of these concepts through the
conduct of a series of field studies on hills of progressively increasing size
and complexity.
Prior to the request for bids on the CTMD contract, a preliminary
one-week field study of the nighttime flow patterns at Cinder Cone Butte was
organized and conducted primarily by FMF personnel (Snyder et al. 1980); the
primary purpose was to assess the suitability of Cinder Cone Butte as the site
for the first small hill study (identified in the ERT Milestone reports as
Small Hill Impaction Study # 1). Numerous observations were made of the flow
structure and plume behavior around the hill, including (1) plumes spread
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broadly in the lateral direction but very thinly in the vertical direction
over the hill in neutral conditions, (2) lee-side separation under
high-wind-speed, neutral conditions, (3) plume impingement under light wind,
strongly stable approach flows, and (4) katabatic winds under light-wind,
neutral approach flow conditions with clear night sky. Cinder Cone Butte was
judged as ideally suited for the first small hill study in several respects.
Finally, numerous suggestions were offered as an aid to the design and conduct
of future field studies at this site (most of which were adopted in the later
studies).
To recap the "state of the science" immediately prior to the contract
award, the dividing-streamline concept had been shown to be a useful
conceptual framework to use in describing the structure of strongly stratified
flow around three-dimensional hills. It had only been shown to be valid,
however, for quite a limited number of hill shapes, all of which were
axisymmetric. It had only been verified under uniform stratification (linear
density gradient) or under a step inversion (sharp density interface), under a
uniform approach-flow velocity profile, and, of course, only under
steady-state, small-scale laboratory conditions (although the preliminary
field study provided reassurances of the validity of the concept).
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3. DESCRIPTIONS OF EXPERIMENTS AND RESULTS
3.1 Direct Interactions with the Model Developers
The period 1980 through 1981
The major CTMDP contract was awarded in June, 1980, and the work plan
called for the small hill impaction study to begin at Cinder Cone Butte (CCB)
in September. Almost immediately, the FMF was called upon to conduct
towing-tank experiments to aid in the detailed planning and design of the
field experiments. The first request was to provide guidance with regard to
the location of the main meteorological tower. The second request was to
provide guidance for smoke- and tracer-release strategies, for preselecting
locations for samplers and cameras, and for choosing in advance several
different sampler strategies to account for variations in flow regimes and
wind fields. The third request was to test the validity of an integral
formula for predicting the dividing-streamline height.
At an early July meeting at ERT headquarters in Boston, MA, the question
arose as to how to predict the dividing-streamline height when the wind
profile was not uniform and the density gradient was not linear. This was of
paramount importance in planning the release scenarios, as the release
locations and heights were to be chosen in real time during the field study
based upon the incoming real-time meteorological data. J.C.R. Hunt
immediately sketched the now well-known integral formula as
(3)
This formula had, in fact, been published 24 years earlier by Sheppard
(1956) as a small note, actually in answer to his own question which arose at
a meeting of the Royal Meteorological Society, although Sheppard's note was
virtually unknown to the modeling community at that time. This integral
formula is based upon simple energy arguments. Sheppard asked the question:
"in a strongly stratified flow approaching a hill, does a particular fluid
parcel at some height upstream possess sufficient kinetic energy to overcome
8
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the potential energy required to lift itself through the potential density
gradient from its upstream elevation to the hill top?" The left-hand side may
be interpreted as the kinetic energy of the parcel far upstream at elevation
Hs, and the right-hand side as the potential energy gained by the parcel in
being lifted from the dividing-streamline height Hs to the hill top h through
the density gradient dp/dz. This integral formula was presumably applicable
to a fluid with any shape of stable density profile and, presumably, with any
shape of approach-flow velocity profile. In practice, it must be solved
'rteratively, because the unknown Hs is the lower limit of integration; the
formula can easily be reduced to the simpler formulae (1) and (2) by using the
boundary conditions applicable to those special cases. The third request to
the FMF was thus to verify this integral formula.
Three studies were conducted in the summer of 1980, and three reports
were prepared in response to these requests. In the first study (Snyder,
1980a), twenty-six separate tows of a model of CCB were made through the tank
in a two-week period. The objective was to assess the suitability of the
particular site chosen for the main (150m) meteorological tower, i.e, was it
close enough to CCB (s100m high and 1km in diameter) to be representative of
the flow approaching the hill, yet far enough away that the measurements were
unaffected by the hill itself? It was impossible, of course, to meet both
these criteria for all wind directions; the question addressed in the
towing-tank studies, then, was whether the flow field at the proposed tower
site would be perturbed by the hill, given the climatological ranges of
prevailing wind directions for light, nighttime winds. Measurements were made
of surface flow patterns, deformation of material lines (instantaneous
crosswind releases of tracer), velocity profiles and streamline patterns over
a model of CCB, and these measurements were compared favorably with
predictions of potential flow theory. The findings from the study suggested
that no significant perturbations to the approach wind field were to be
expected due to the presence of the hill when the wind direction was within
the range of the prevailing wind directions. In addition to the main tower, a
shorter (20m) tower was recommended, to be erected at the trailer site (3km
ESE of the hill). This recommendation was indeed implemented in the field
study.
This was, in fact, the first real-terrain model (i.e., non-idealized
shape) to be studied in the FMF stratified towing tank. As a side benefit,
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therefore, the study provided reassurances that the basic flow features and,
of course, the same physical principles applied to more realistically shaped
hills. Some examples are provided here to illustrate the point. Figure 1
shows an oblique view of the hill, where neutrally buoyant dye streamers were
released from a horizontal rake upstream of the hill under strongly stratified
conditions. The horizontal nature of the flow field is immediately obvious.
Figure 2 shows a top or plan view of the CCB model under roughly similar
conditions. One of the dye streamers obviously impinged on the upwind
shoulder of CCB. Flow separation in the lee of the hill is dramatically
illustrated in Figure 3, where vortex roll-up and eddy-shedding in the lee are
quite vivid. The Karman vortex street was a common occurrence at low Froude
number; a street appeared to form at all elevations below the
dividing-streamline height (at least for small Froude numbers), but the
shedding frequency seemed to vary with elevation and motions at different
elevations were seemingly uncorrelated with one another.
In the second phase of this summer series, eleven tows of the CCB model
were made during which two of the model developers from ERT participated as
observers. In this case, vertical rakes of tubes emitted neutrally buoyant
dye at up to 6 elevations, with different colors of dye being emitted at the
different levels. Each tow was filmed from the side using a camera that moved
with the hill, and from directly below using a fixed camera pointed upward at
the (inverted) model hill. The films were viewed with an analyst's projector,
and the plume paths and envelopes were sketched. These results corroborated
the previous results of Hunt and Snyder (1980) on idealized hills, i.e., that
plumes below the dividing-streamline height Hs and on a stagnation streamline
would impinge on the upwind side of the butte and flow around the sides, and
that plumes released just above Hs may produce maximum ground-level
concentrations on the upwind side as they pass over the top. The results
further emphasized that plumes travelling in a direction only slightly away
from that of the stagnation streamline would tend to pass around CCB without
significant impact, and that plumes released somewhat higher above Hs may be
caught in strong downslope flows and produce maximum ground-level
concentrations on the lee side of the hill. The results were also used, of
course, for the originally intended purpose as a guide for planning of release
and sampler strategies and selection of sampler and camera locations. The
results are described by Bass (1980).
10
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Figure 1. Oblique view of dye streamers released from a horizontal rake
upwind of the CCB model at z//? = 0.3 under strongly stratified conditions (F =
0.2). Flow is from the left.
N
Figure 2. Top view of dye streamers impinging on CCB under strongly
stratified conditions (z/rj = 0.3, F = 0.4).
11
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In the third phase of this summer series, the goal was to test the
validity of the integral formula for the height of the dividing streamline
under density profiles similar to those expected at CCB. A typical nighttime
temperature profile in the Snake River Basin (site of CCB) was found to
consist of a strong, surface-based inversion of depth 50 to 100m and a weaker
inversion above extending to several hill heights. Hence, the stratified
towing tank was filled with a strong density gradient near the surface and a
weaker gradient above. A vertical rake of 3 tubes was positioned well upwind
of the hill, and neutrally buoyant dye was emitted from each tube. For each
tow, a particular stack height (center tube) was chosen and the general
formula was integrated numerically using the measured density profile to
predict the towing speed required such that the center streamer would rise to
the elevation of the saddle point of CCB, i.e., the minimum height of the draw
between the two peaks. If the formula were correct, then, the lower streamer
should go around the side of the hill, the upper streamer should go over the
top, and the center one should split. The height of the break-point between
the two gradients was then reduced and the process repeated. In all, twelve
tows were made, varying the height of the break-point or the
dividing-streamline height (release height) each time.
Figure 4 shows a side view of the impinging streamers during a typical
tow, i.e., the upper streamer going through the draw, the lower streamer going
round the side, and the middle one splitting. Figure 5 shows the results in
quantitative fashion. The density profiles were integrated in accordance with
Equation (3) to find the dividing-streamline heights (based on the height of
the saddle point) as functions of the towing speed. These predictions are
shown in Figure 5 as the continuous lines. The observations of the
dividing-streamline heights made during the twelve tows are also plotted in
the figure; the agreement between the predictions and observations is regarded
as excellent. The error bars result because of some fluctuating behavior of
the streamers, especially at the higher speeds; occasionally, an intermittent
vortex at the top windward side of the hill would engulf all three streamers
and they would all go round the sides temporarily; on other occasions, parts
of the lower streamer could be observed passing through the draw. The results
of this set of experiments (Snyder, I980b) provided confidence in the validity
of the general integral formula for predicting the height of the dividing
streamline for a wide range of shapes of stable density profiles.
13
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' / I \ \
Figure 4. Oblique view of impinging streamers on CCB. Middle dye streamer is
released at the dividing-streamline height; others at ±1cm (±6m full scale).
14
-------
o
t
h-
g
ui
x
UJ
z
-I
<
LU
cc
o
5 10 15 20 25
TOWING SPEED, CM/S
30
Figure 5. Comparison of predicted dividing-streamline heights with
observations as functions of towing speed. Open symbols: predictions using
integral formula; closed symbols: observations.
15
-------
During the six-week field study at CCB, detailed measurements were made
of wind, turbulence, and temperature profiles in the approach flow and at
other positions on the hill. Sulfur hexafluoride (as a tracer) and smoke (for
flow visualization) were released from a platform suspended from a mobile
crane that allowed flexibility in positioning the source (height and
location). One hundred samplers on the hill collected data on surface
concentrations, and lidar was used to obtain plume trajectories and
dimensions.
One particular hour from the field study was selected for simulation in
the towing tank (Snyder and Lawson, 1981). That hour was 0500 to 0600, 24
October 1980 (Case 206), which may be characterized as very stable, i.e.,
light winds and strong stable temperature gradients. Measurements made during
the towing-tank experiments included ground-level concentrations under various
stabilities and wind directions, vertical distributions of concentration at
selected points, plume distributions in the absence of the hill, and visual
observations of plume characteristics and trajectories.
This series of tows showed that the surface-concentration distributions
were extremely sensitive to changes in wind direction. For example, Figure 6
shows that the distribution shifted from the north side of the hill to the
south side with a shift of only 5° in wind direction. Comparisons of
individual distributions with field results showed very much larger maximum
surface concentrations and much narrower distributions in the model results.
To account for the large variability in the winds measured during the hour, a
matrix of 18 tows (three wind directions x six wind speeds) was conducted, and
the concentration patterns were superimposed. A scatter plot of superimposed
model concentrations versus field concentrations (Figure 7) shows a marked
improvement over the single-tow comparisons. The largest model concentrations
were within a factor of two of the highest field values, and 70% of the model
concentrations were within a factor of two of the observed field values.
It was interesting to learn that, whereas the location of the maximum
shifted dramatically with small shifts in wind direction, the value of the
maximum changed very little with changes in wind direction or wind speed.
Maximum surface concentrations approached those at the plume centerline in the
absence of the hill during individual tows, but because of the extreme
sensitivity of the location to wind direction, the plume was "smeared" broadly
across the hill surface as the wind direction changed through only a few
16
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600 M
600 M
SCALE
200M
SOURCE
Figure 6. Concentration distributions measured during individual tows of CCB
with Hs//7 = 0.31 and H0//? = 0.38; wind direction : 117°, 122°.
17
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10000
I 1II I I I III
100
1000
10000
FIELD CONCENTRATION
Figure 7. Scatter diagram comparing superposition of concentration
distributions measured over Cinder Cone Butte with field distributions.
Dotted lines denote factor of two on either side of perfect fit.
18
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degrees. Therefore, short-term averages (*5min) in the field may be expected
to approach plume-centerline concentrations; longer-term averages (*1h) may be
expected to be reduced by factors of five to ten (or more depending upon the
magnitudes of the fluctuations in wind speed and direction).
The period 1982 through 1983
Although considerable work had been done concerning the validity and
limits of applicability of the dividing-streamline concept, several questions
still remained. One question concerned the effects of shear in the
approach-flow velocity profile. Another concerned the effects of the aspect
ratio (ratio of crosswind length of the hill to its height) and, in
particular, its applicability in strongly stable flows to a truly
two-dimensional ridge. A third questioned the effects of the slope of the
hill, and a fourth, the effect of wind angle on a long ridge.
A few earlier studies had shed light on some of these problems. Baines
(1979), for example, had conducted towing-tank studies of low-Froude-number
flows around a barrier with a gap. His results suggested
HJh = 1-2F (4)
for barriers with very small gaps, tending toward Hs/rt = 1-F (Equation 1) for
those with wider gaps. Weil ef a/ (1981) conducted similar towing-tank
studies, extending the work of Baines, and found quite similar results.
However, data from a field study by Rowe ef a/ (1982) of stable air flow over
a "long" ridge showed much better agreement with the data for axisymmetric
hills (Equation 1) than for ridges with gaps (Equation 4).
In the early 1980's, a series of experiments was done by numerous
investigators at the FMF and for a variety of different purposes. The overall
objective was to gain fundamental understanding of flow and diffusion under
stably stratified conditions in complex terrain, but the individual projects
were designed with very specific and limited objectives in mind.
Nevertheless, one aspect of each of the projects was to examine the concept of
the dividing-streamline height, as it obviously had very important
consequences with respect to the CTMDP. The results of most of these projects
were published separately and independently, as will be referenced below, but
the results concerning the validity and applicability of the
dividing-streamline concept were extracted and published as an appendix
(Snyder et a/, 1983) to the Second Milestone Report (Strimaitis ef a/, 1983)
19
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in order to provide timely support and guidance to (1) the mathematical
modelers attempting to expand their models to include a wide variety of
terrain shapes and approach flows and (2) planners of the Second Small Hill
Impaction Study, which was to take place at the Hogback Ridge in northwestern
New Mexico. This paper was subsequently published in a journal (Snyder ef a/,
1985). The individual laboratory experiments included:
1. Towing-tank studies on truncated, steep-sided ridges of various
crosswind aspect ratios. These included examination of upstream
"blockage" regions, surface flow patterns and lee-wave structure
and were reported by Castro ef a/ (1983); those aspects dealing
specifically with the dividing-streamline concept were reported by
Snyder ef a/ (1983) and Snyder ef a/ (1985).
2. Stratified wind-tunnel studies (in Japan) on shear flow over
vertical fences of various crosswind aspect ratios and over a model
of Cinder Cone Butte. (Snyder and Ogawa, 1982; Snyder ef a/,
1985).
3. Towing-tank studies on a truncated sinusoidal ridge with a maximum
slope of 40° positioned perpendicular and at other angles to the
approach wind direction (Lee ef a/, 1984a, 1984b).
4. Towing-tank studies on an "infinite" triangular ridge and a long
sinusoidal ridge to test the validity of the "steady-state"
assumption of flow upwind of an obstacle under strongly stratified
conditions (Castro and Snyder, 1987c).
The conclusion from the studies with truncated triangular and sinusoidal
ridges perpendicular to the wind was that the aspect ratio per se, does not
have a significant influence on the dividing-streamline height Hs. Deviations
from the Hs/h = ~\-F rule were attributed to the combination of shear in the
approach flow and the very steep slope of the triangular ridges, which
resulted in the formation of an upwind vortex with downward flow on the front
faces of the ridges. The "1-F" rule was validated for the sinusoidal ridge
with a length-to-height ratio greater than 16:1; in this case, the shear in
the approach flow was much less pronounced, and the upwind slope was
substantially smaller. Note that these deviations to the "1-F" rule did not
invalidate Sheppard's concept, but required a reinterpretation of the rule as
a necessary but not sufficient condition, i.e., a fluid parcel may possess
sufficient kinetic energy to surmount a hill, but it does not necessarily do
so.
20
-------
In the stratified wind-tunnel studies, reasonably strong shear layers
with depths more than twice the hill heights were developed in conjunction
with strong stable temperature gradients. These approach flows provided
dividing-streamline heights as large as 0.75/7. In the vertical fence studies
with a stratified approach flow, the shear was found to have an overwhelming
influence. The conclusions were: (a) as in the triangular ridge studies, the
aspect ratio was relatively unimportant; the basic flow structure was
independent of aspect ratio; (b) the shear, in conjunction with the steep
slope, created an upwind vortex such that plumes were downwashed on the front
faces; and (c) under strong enough stratification, there was a limit to the
downward penetration of elevated streamlines; the extent of this penetration
appeared to be predictable as a balance between kinetic and potential
energies. However, when these same shear flows approached the much lower
sloped CCB model, there was no evidence of upwind vortex formation. Limited
concentration measurements on the CCB model suggested that Sheppard's integral
formula correctly predicted the height of the dividing streamline.
From the sinusoidal ridge studies with wind angles at other than 90°, it
was concluded that the effect of deviations in wind direction (from 90°) are
relatively insignificant until the wind direction is in the vicinity of 45° to
the ridge axis. At 30°, significant departures from the "1-P rule were
observed; the fluid had sufficient kinetic energy to surmount the ridge, but
found a path requiring less potential energy round the end of the ridge. When
the dye streamers were moved closer to the upstream stagnation streamline
(upwind of the upstream end of the ridge), they behaved according to the "1-P1
rule.
The two-dimensional ridge studies showed that steady-state conditions are
not established in strongly stratified flows (say F<1). Two different
physical mechanisms give rise to this unsteadiness; one is called "squashing",
the other, upstream wave propagation. Brief explanations will be given here;
the interested reader should consult the cited references.
The squashing phenomenon is most easily described in terms of the simple
energy arguments as used in deriving Sheppard's formula (Equation 3). As
discussed there, a fluid parcel with insufficient kinetic energy to overcome
the potential energy requirement to surmount the hill must pass round the
sides of the hill. But a two-dimensional hill has no sides around which to
pass (in a towing-tank, a "two-dimensional" hill is one that spans the entire
21
-------
width of the tank). Hence, the fluid parcel must be brought to rest. In the
towing tank, since the fluid is generally at rest and the hill is towed, this
means that the fluid ahead (upstream) of the hill must be pushed ahead of the
hill, instead of being allowed to surmount the hill top. However, the
upstream endwall of the towing tank, of course, prohibits this fluid from
being pushed. Hence, the fluid between the hill and the upstream endwall is
"squashed" as the hill approaches the endwall; because the fluid is
incompressible, it must rise and spill over the top of the hill, just as the
water in a bucket will rise and spill over the top when the sides are
"squashed".
This squashing phenomenon seems to have no counterpart in the atmosphere.
If true blocking occurred upwind of an "infinite" ridge in the atmosphere, it
seems that the flow would be blocked to infinity upwind (i.e., there is no
"endwall" forcing the flow toward the ridge). In more practical terms,
"blocking" upstream of a very long ridge would imply "upstream influence" to
very large distances, possibly through an upstream-propagating front, which
would imply non-steady-state behavior. From another viewpoint, there are no
infinite ridges in the real world, so that fluid parcels can always be
diverted around the obstacles without changing their elevation.
The results leading to the "1-2F" formula (Equation 4) by Baines (1979)
and Weil ef al (1981) for two-dimensional ridges and ridges with gaps were
surprising because they suggested that fluid parcels could surmount the hills
even though they had insufficient kinetic energy to do so. Snyder ef al
(1983, 1985) suggested that these earlier results were erroneous; that they
were largely due to the squashing phenomenon, i.e., the gaps in their ridges
were insufficiently large to allow a "relief valve" to avoid the squashing.
Upstream wave propagation is also possible in stratified flows. The
introduction of an obstacle in a stratified flow on which lee waves can form
will result in "columnar" disturbances extending upstream (see Turner, 1973);
if such motions are present, they will modify the approaching flow. These
columnar disturbances take a sinusoidal form in the vertical, with the "mode"
(number of oscillations) being dependent upon the Froude number based on the
depth of the tank. An example of an upstream columnar disturbance is shown in
Figure 8. Dye crystals were dropped into the stratified tank at a position
16m upstream of the starting position of an obstacle (in this case, a vertical
fence) which was to be towed along the water surface. These crystals
22
-------
Figure 8. Deformation of vertical dye line by upstream columnar disturbances.
Dye line was formed at a location 16m upstream of starting position of fence,
at time when fence was at x = 12.5m (18.6/7 upstream of fence). Photograph was
taken when fence was at x = 13.8m (11.6/7 upstream of fence). Fence is out of
photograph, approaching from top left.
23
-------
dissolved as they sank to the bottom, leaving behind a vertical dye line. The
dye line was formed after the commencement of the tow, and the photograph was
taken well before the obstacle reached the dye-line position, i.e., the dye
line was deformed by the upstream columnar disturbance into the sinuous curve
shown in Figure 8.
These columnar disturbances, unlike the squashing phenomenon, do have
counterparts in the real atmosphere. They result in "blocking" and "upstream
influence". However, in the laboratory tank, these upstream waves are
reflected from the upstream endwall of the tank and return to modify the flow
locally around the model hill; this reflection from the upstream endwall does
not have a counterpart in the real atmosphere. Baines (1979) argued that
valid observations could be made of the flow over and around the obstacle in
isolation (in the absence of end effects) by making the observations after
steady state was reached (estimated by direct observation), but before
reflected upstream motions arrived. Evidently, he believed that a local
steady state was achieved in that, at some not-too-distant point upstream of
the obstacle, steady-state velocity and density profiles were established
before the reflected motions returned to modify them.
Snyder et al (1983; 1985) showed that steady-state conditions are not
established in strongly stratified flows (say F<1) over two-dimensional
ridges. The squashing phenomenon and reflections of upstream columnar
disturbances continuously changed the shapes of the "approach flow" velocity
and density profiles. Thus, these experiments have no analogue in the real
atmosphere. Further, because long ridges cut by periodic small gaps require
very long tow distances in order for steady state to be established, Snyder ef
al concluded that the previous laboratory studies were not valid models of
atmospheric flows; specifically, the Hs/ft = 1-2F formula proposed for flow about
ridges with small gaps is not expected to apply to the real atmosphere.
Further work was done to better understand the nature and causes of these
upstream motions and lee waves by Thompson and Snyder (1984), Castro (1987)
and Castro and Snyder (1987b, 1987c), but the interpretation of these results
is somewhat controversial. More work is required to establish the precise
relationships between model size and shape, stability, and tank size, shape
and configuration in order to determine the limits of applicability of fluid
modeling and ranges of transferability to the atmosphere.
24
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The second Small Hill Impaction Study was conducted during October 1982
at Hogback Ridge (HBR) (s100m high) near Farmington, NM. In providing input
to the experimental design, the FMF conducted a series of wind-tunnel and
towing-tank flow-visualization experiments prior to the field study. The
laboratory studies were designed to investigate
plume height above the surface over the hill crest and at
the upwind edge of the hill,
apparent size of any plume deformation upwind of the hill,
lee wave importance and structure, and
sensitivity of the plume trajectory to "wind angle".
This information was subsequently used by the field designers to guide the
design of the smoke and tracer-gas release protocols at HBR, and to help
select sampler and camera locations.
Two tests were made in the wind tunnel. One test was done with the ridge
perpendicular to the flow, the other with the ridge rotated by 30°. These
tests suggested that in neutral conditions the streamline patterns were
similar to those expected from potential flow theory; a plume released at a
given height upwind of the ridge should traverse the crest at an elevation of
one-half its initial height. The test with the ridge at an angle to the flow
showed only a very small (<4°) deflection of the plume path as the plume
traversed the ridge.
Eight individual tows of the HBR model were done in the stratified towing
tank, varying the Froude number and wind direction, and each time releasing
dye at eleven different elevations upstream. Heights of these dye streamers
were measured at the upstream base and at the crest of the ridge. These
experiments showed that, during weakly stratified conditions, plumes rose near
the upwind base and fell over the crest to near or slightly lower than their
upstream heights. Low-level releases experienced extensive mixing. More
detailed results are contained in the Third Milestone Report (Lavery ef a/,
1983, p. 117-123).
Around this same time period, the FMF undertook two separate laboratory
experiments that attempted to simulate two specific one-hour periods as
observed in the field at Cinder Cone Butte. The first simulated a neutral
stability period in the Meteorological Wind Tunnel (Thompson et a/, 1983).
25
-------
The second simulated a moderately stable period in the stratified towing tank
(Eskridge ef a/, 1983). [Recall that the simulation of a strongly stable
period was described earlier (Snyder and Lawson, 1981).]
In the summer of 1983, Ben Greene and colleagues from ERT, in cooperation
with the FMF staff, conducted experiments in the Meteorological Wind Tunnel to
characterize the response of the Climatronics UVW propeller anemometers. The
primary objectives of the experiments were to determine the calibration curves
and the non-cosine response corrections, especially at low wind speeds. The
results of these tests are contained in the Fourth Milestone Report
(Strimaitis ef a/, 1985, p. 85-93). The calibration factors and non-cosine
response correction factors were applied to the HBR data base in forming the
Modeler's Data Archive.
In late summer of 1983, discussions were held with ERT concerning
possible contributions of FMF to the Full-Scale Plume Study planned for the
following year at the Tracy Power Plant near Reno, NV. Considerations of
scaling the site for towing-tank studies revealed that, at any reasonable
scale, the model would appear as a two-dimensional ridge with a small gap
(river valley) running through it. Recent work at the FMF as discussed above
had shown that this situation could not be modeled under strongly stable
conditions. Hence, specific site modeling at the Tracy Power Plant was not
undertaken at the FMF. Instead, other studies in direct support of the model-
development effort were undertaken as described below.
The period 1984 through 1985
In September 1983, A. Venkatram, D. Strimaitis and R. Britter from ERT
requested that the FMF conduct two studies in support of their
model-development efforts. The first study attempted to shed light on the
question of the validity of the assumption of a flat dividing-streamline
surface, a key assumption in the model under development. The second study
was to provide a complete set of data on neutral flow and diffusion around a
three-dimensional hill with a shape and slope approximating that of Cinder
Cone Butte. These data were to help ERT to evaluate the separate effects of
plume deformation kinematics and those of increased turbulence around the
hill.
The first study, testing the validity of the flat dividing-streamline
assumption, consisted of a series of 26 tows of a model hill in the stratified
26
-------
towing tank. The model hill was the fourth-order polynomial (45° maximum
slope) used by Hunt et al (1978), except that it was in this case instrumented
with 100 sampling ports located along 8 radial lines. The density gradient
was linear and the dividing-streamline height was fixed at half the hill
height. Effluent was released at three elevations above the
dividing-streamline height. Pairs of tows were made such that, in one tow,
the hill (upside down) was fully immersed in the water and the towing speed
was adjusted to provide a "natural" dividing-streamline surface. In the
second tow of the pair, the model (baseplate, hill, and source, as a unit) was
raised out of the water to the point where only the top half of the hill was
immersed, thus, forcing a flat dividing-streamline surface, while all other
conditions remained identical. Concentration distributions were measured on
the hill surface (and in the absence of the hill). Concentration
distributions from each pair of tows were compared to ascertain any
differences between the "natural" dividing-streamline surface and the (forced)
flat dividing-streamline surface. A comparison of surface-concentration
patterns from a typical pair of tows is shown in Figure 9, and a scatter plot
comparing concentrations on a port by port basis is shown in Figure 10. These
results showed that the assumption of a flat dividing-streamline surface is a
reasonable assumption to make, at least with regard to predicting the
locations and values of the maximum surface concentrations and areas of
coverage on the windward side of the hill. The results are contained in an
appendix to the Fourth Milestone Report (Snyder and Lawson, 1985a) and were
presented at the Third International Symposium on Stratified Flows (Snyder and
Lawson, 1987).
The second study, providing a relatively complete set of data on flow and
diffusion around a three-dimensional hill, was conducted in the Meteorological
Wind Tunnel. The primary objective was to determine the influence of the hill
on the maximum ground-level concentration (glc) and to locate the source
positions where this influence was greatest. All measurements were made with
an approach flow that simulated the neutral atmospheric boundary layer
measured at Cinder Cone Butte. However, the nearly axisymmetric CCB shape was
replaced by a truly axisymmetric hill represented by a simple mathematical
formula, and having a maximum slope of 24° (the same as CCB).
The measure of the hill's influence on the maximum glc was the "terrain
amplification factor" A. This factor is defined as the ratio of the maximum
27
-------
Figure 9. Concentration distributions measured on the hill surface with
HD//i = 0.5 and Hs/h = O.Q. Top: fully submerged; bottom: half submerged. Dotted
circle indicates half the hill height.
28
-------
100
.1
10
100
CONCENTRATION, HALF SUBMERGED
Figure 10. Scatter plot comparing concentrations on fully immersed hill with
those on half-immersed hill on a port by port basis. Hg//? = 0.6, H0/h = 0.5.
29
-------
glc observed in the presence of the hill to the maximum observed in the
absence of the hill. The locations of the maxima are not considered in this
evaluation; the maxima may be found at entirely different places in the
presence and in the absence of the hill.
A matrix of source locations was used covering the range from 4 to 16
hill heights (h) upstream of the hill center and to 1.25r» in the vertical. A
map of terrain amplification factors is shown in Figure 11. The presence of
the hill was found to influence the transport and dispersion of the plume and
to increase the maximum glc in three ways. For low sources at moderate
distances from the hill, the reduction in mean wind speed and increase in
turbulence allow the plume to reach the ground surface closer to the source,
thus producing higher concentrations than in the absence of the hill. Plumes
from higher sources may be thought of as being intercepted by the hill, that
is, the hill penetrates the plume to where the concentrations are greater than
those that would occur at ground-level farther downstream over flat terrain.
For yet higher sources, the streamline convergence over the hill top and the
corresponding downward flow and much enhanced turbulence in the lee of the
hill again bring the plume to the ground more rapidly than over flat terrain.
Terrain amplification factors ranged from near 1.0 to 3.63, and the range of
source locations that produced an amplification factor greater than 1.4
extended to an upwind distance of 14 hill heights. These results were
reported in an appendix to the Fourth Milestone Report (Thompson and Snyder,
1985b).
In the fall of 1984, ERT requested a list of data sets available from
previous complex terrain studies that had been conducted at the FMF. A report
was prepared by Thompson et al (1985) listing 24 separate complex terrain
studies. Each project was synopsized with a brief description of the project,
the name of the principal investigator(s), the facilities used, types of data
collected, names of data reports available, major conclusions reached, listing
of published results from the project, and a listing and description of the
data files available.
An earlier request (prior to summer 1983) from the modelers at ERT had
been to provide data on streamline trajectories in neutral and stratified flow
over a three-dimensional hill, i.e., to provide data to use in developing
algorithms for predicting lateral and vertical streamline displacements over a
hill as functions of source location and stratification. Earlier work on this
30
-------
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31
-------
project had been set aside because of experimental difficulties and because of
the more urgent requests described immediately above. Having completed those
studies, work commenced again on the streamline trajectories.
In attempting to predict the maximum glc from a source upwind of a hill,
the most important feature of the flow is the displacement of the mean
streamline through the source, because that displacement determines how near
to the surface the "centerline" of the plume will reach. The exact path taken
by the plume in circumventing the hill and the plume's closeness of approach
to the hill surface are critical in determining the location and magnitude of
the glc's. These displacements are known to be strongly affected by the hill
shape and especially by the stratification in the approach flow. The purpose
of this study was thus to characterize the effects of stability on the
horizontal and vertical deflections around an isolated hill. A large set of
streamline trajectories over the axisymmetric CCB model was measured using the
stratified towing tank. Three-dimensional coordinates of the streamlines (86
independent trajectories) were determined through stereographic analysis of
photographs of dye streak lines released at a matrix of source positions
(heights and lateral offsets from the hill/flow centerline), and at
stabilities ranging from strongly stable to neutral (Froude numbers of 0.6,
1.0, 2.0, and <»). These measurements provided a relatively complete data set
for testing mathematical models and algorithms of the detailed structure of
stratified flow over hills. The results were presented in an appendix to the
Fifth Milestone Report (Snyder ef a/, 1986).
As an example use of the data set, a mathematicai model using linear
theory and a Fast Fourier Transform (FFT) technique to predict these
streamline trajectories was evaluated and described in the above appendix by
Snyder et at (1986) and, with some additional work and computations, by
Thompson and Shipman (1986). The calculated results agreed well with the
experimental results for neutral flow. In the stable flow (Fr=2.0), however,
lateral deflections were underpredicted and vertical deflections were
overpredicted using the FFT model.
The period 1986 through present
In February 1986, ERT conducted a Complex Terrain Workshop at Research
Triangle Park, NC (Lavery ef a/, 1986). Each participant was beforehand
provided a diskette containing the Complex Terrain Dispersion Model (CTDM)
32
-------
code and a draft User's Guide and was asked to exercise the model to assess
its overall effectiveness and validity in whatever way he chose. The purpose
of the workshop, then, was to exchange information on the results of these
exercises and to make recommendations to the model developers concerning
further refinements of the CTDM model.
The present author exercised the CTDM by comparing is predictions with
previous laboratory measurements of flow and diffusion over hills made in the
FMF. This was accomplished in four phases. In phase 1, CTDM calculations
were compared with wind-tunnel simulations of plumes released upwind of two-
and three-dimensional hills in a neutral atmospheric boundary layer. Terrain
amplification factors were compared for a matrix of source locations upwind of
the hills. This phase was intended to test the LIFT module of CTDM, where the
stratification was neutral and the potential flow calculations of LIFT should
be most applicable. In phase 2, CTDM calculations were compared with stably
stratified towing-tank observations, where plumes were released above the
dividing-streamline height upwind of a three-dimensional hill. This phase was
intended to again test the LIFT module, but this time under strongly
stratified conditions. In phase 3, CTDM calculations were compared with
strongly stratified towing-tank observations wherein plumes were released
below the dividing-streamline height upwind of the Cinder Cone Butte model.
This phase was intended to test the WRAP module exclusively. In phase 4, CTDM
calculations were made for one selected hour of field conditions, and were
compared with results of towing-tank observations. This phase was intended to
exercise both the LIFT and WRAP modules of CTDM.
The results, made available in a detailed report that was distributed to
the workshop participants (Snyder, 1986), may be summarized as follows:
1. From the neutral flow simulations (phase 1), the hill effects (as
exemplified through computations of terrain amplification factors)
appeared to be much too small. Reasons speculated for this
discrepancy included: (a) plume trajectories were too far from the
hill surface, (b) potential flow calculations did not properly
handle the deep boundary-layer flow approaching the hill, or, more
likely (c) the plume centerline did approach the hill surface
closely enough, but the plume did not mix to the the surface through
the hill-surface boundary layer.
2. From the stable flow simulations with releases above the
dividing-streamline height (phase 2), it appeared that the plume
trajectories were again too far from the hill surface. Vertical
deflections of streamlines appeared to be strongly overestimated and
lateral deflections appeared to be strongly underestimated. In the
33
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towing tank, plumes released slightly above the dividing-streamline
height spread broadly but thinly to cover the entire hill surface
above the dividing-streamline height, whereas the CTDM plume was
apparently deformed only slightly - it "hung together" in going over
the top of the hill. An apparent shortcoming of LIFT at that time
was its lack of appropriate treatment of the stratification effects
in the flow that surmounted the hill, i.e., streamline (hence,
plume) deformations under quite strongly stratified flows (Frs1)
were treated the same as those for neutral flow (Fr=w).
3. From the stable flow simulations with releases below the
dividing-streamline height (phase 3), the WRAP module yielded rather
poor results except when the input parameters (primarily
-------
an upstream source with height such as to obtain a plume that just "grazed"
the hill top. The postulate here was that the roughness on the surface would
maximize the effects of a rapid-mixing layer near the hill surface, thus
mixing material from this elevated plume to the surface, whereas the smooth
surface would minimize the effects of this mixing layer. The results showed
that the postulate of an "inner hill-surface boundary layer" was untenable;
extremely steep concentration gradients remained near the hill surface, even
when the hill was roughened, so that rapid mixing was not induced by the
hill-surface boundary layer.
To satisfy the second goal, a series of measurements was made of plume
characteristics in flat terrain and over a three-dimensional hill. Effluent
was released at a number of elevations, upwind distances, and positions
laterally offset from the centerplane determined by the wind direction and the
center of the hill. Sufficient concentration measurements were made to enable
the construction of plume cross sections at the downwind position of the hill
center and, in a few cases, at the upwind base of the hill. These data were
analyzed to provide the desired information on horizontal and vertical plume
deflections and deformations effected by the hill. One of the more dramatic
examples is shown in Figure 12. In this case, the source was on the
centerplane at ground level, 6 hill heights upwind of the hill center (the
skirt of the hill extended to 5h). Plume cross sections measured at the
position of the center of the hill, both in the presence and in the absence of
the hill, are shown. The hill effected a 91% increase in the lateral plume
width. In this case, the maximum surface concentration (at the same downwind
distance) was decreased by a factor of 2 but, of course, the area of coverage
by large concentrations was greatly increased. Detailed data reports were
provided to ERT in March 1986, and the results were published by Snyder and
Lawson(1986).
Subsequent to the CTMD Workshop (and as a result of the rather poor
comparisons of the CTDM predictions of terrain amplification factors with
wind-tunnel data), refinements were made to CTDM. Specifically, the strain
inferred or measured over the crests of two- and three-dimensional hills in
the wind tunnel were used in the calculations, i.e., the T-factors in the
model were adjusted in accordance with wind-tunnel data. Substantial
improvements in the CTDM predictions of terrain amplification factors were
obtained, as described by Strimaitis and Snyder (1986).
35
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2 r
Z
H
1 -
-2
.05
-1
Y/H
-) and in absence
Figure 12. Plume cross sections measured in presence (
( ) of axisymmetric CCB model at x = 0 (hill center). Hs/h = 0, xs/rt = -6,
/.//) = 0.
36
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3.2 Supplemental Modeling of Complex Terrain
In addition to the modeling done in direct support of the CTMDP, numerous
other complex terrain studies were conducted at the FMF, primarily in response
to envisioned needs of and direct requests from the OAQPS, the regulatory arm
of EPA. These ranged from generic studies attempting to understand the
fundamental physics of flow and diffusion in neutral and stable environments
to a practical demonstration to determine the good-engineering-practice stack
height for a specific power plant located in complex terrain. Whereas the
studies done in direct support of the CTMDP were primarily concerned with
plume impingement from upwind sources and focussed primarily on strongly
stable conditions, the supplemental studies were broader ranging, for example,
including sources on the tops and lee sides of hills, perhaps a broader range
in stability from strongly stable to neutral, and investigation of similarity
criteria - rules to ensure that the behavior of the flow in the laboratory
simulates that in the real world. An example of the latter is the Guideline
for Fluid Modeling of Atmospheric Diffusion, prepared by Snyder (1981) in
response to a request from the OAQPS. In several cases, studies that were
initiated through the CTDM developers were subsequently enlarged upon and
expanded so as to be useful to the modeling community at large. Hence, in
many cases, studies could have been described as supplemental (this section)
or in direct support of the CTMDP (Section 3.1). The choices have been
somewhat arbitrary.
One of the important overall goals in this effort was to ascertain what
circumstances lead to the largest ground-level concentrations, i.e., are
larger glc's expected when the plume from an upwind source impinges on a hill
or when the source is downwind of that hill such that the plume is caught in a
recirculation region and downwashed to the surface? Which are likely to lead
to larger glc's, two-dimensional or three-dimensional hills? Stable
conditions or neutral conditions? In each of these circumstances, what order
of magnitude of surface concentrations may be expected?
Neutral-Flow Wind-Tunnel Studies
A simple method used to intercompare effects of terrain on the maximum
glc and to determine worst-case conditions is through the terrain
amplification factor, as mentioned in Section 3.1. Again, the terrain
37
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amplification factor, A, is defined as the ratio of the maximum ground-level
concentration occurring in the presence of the terrain feature, xmx, to the
maximum that would occur from the same source located in flat terrain, x£x,
i.e., A=Xmx/Xnx- Tnis definition is useful only for elevated sources, of
course, because for ground-level sources, the maximum surface concentration
occurs at the source itself.
Numerous neutral-flow wind-tunnel studies have been conducted at the FMF
on diffusion over two-dimensional terrain features: (a) a ramp with a slope
of 14° followed by a plateau (Snyder and Pendergrass, 1980; Pendergrass and
Arya, 1983; Pendergrass and Snyder, 1987), (b) a bell-shaped hill with a
maximum slope of 12° (Courtney, 1979; Courtney and Arya, 1980), (c) a steep
triangular ridge with a slope of 63° (Arya and Shipman, 1981; Arya et al,
1981), (d) a series of smooth shaped hills of various slopes (Khurshudyan et
al, 1981; Capuano, 1983; and Lawson and Snyder, 1985, 1987) and (e) a valley
formed between two ridges of sinusoidal cross section (Lee et al, 1981).
Three studies have been performed to determine the effects of the crosswind
aspect ratio of a triangular ridge on dispersion from nearby sources. As
mentioned in Section 2, Snyder and Britter (1987) investigated surface
concentrations on the ridges from upwind sources. (Note that the work was
done in 1979, much earlier than the publication date, so that the results were
available, indeed, used in the development of a forerunner to CTDM.) Castro
and Snyder (1982) extended the study by measuring the sizes and shapes of the
recirculation regions downwind of these hills of various crosswind aspect
ratio, and by measuring the concentration fields resulting from sources placed
at various downwind locations. Recently, Castro and Snyder (1987a) have
further extended this work to include the case when the approaching wind is
not perpendicular to the long axis of the hill. This allows one to use the
wind-tunnel data to estimate the effects of long-time-scale wind meander.
Other generic three-dimensional hill studies included: (a) conical hills with
slopes of 26.5° and 17.5° with sources located at the hill top or at the
downwind base (Gadiyaram, 1984; Arya and Gadiyaram, 1986) and (b) the
axisymmetric CCB model with downwind sources (Lawson and Snyder, 1985,1987).
These various studies were summarized through publications at various stages
by Thompson and Snyder (1981, proceedings published 1985a) and Snyder (1983a,
1983b, 1984). Only a broad overview and a few typical results will be
presented here.
38
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Table 1 shows the terrain amplification factors for the cases listed
above, in order of decreasing A. From the standpoint of a fixed stack height,
the worst location for a source appears to be just downwind of a
two-dimensional ridge. Downwind sources generally result in larger glc's
because of the excess turbulence generated by the hills and because the
effluent is generally emitted into a low speed region where the streamlines
are descending toward the surface. Maximum As are considerably larger than
those downwind of three-dimensional hills. A probable cause of this effect is
that, in three-dimensional flows, lateral and vertical turbulence intensities
are enhanced by roughly equal factors, whereas in two-dimensional flows, the
lateral turbulence intensities are not enhanced as much as are the vertical
turbulence intensities (because of the two-dimensionality). Since the maximum
glc depends upon the ratio
-------
They do not provide practical estimates for use by, say, an air pollution
meteorologist in determining the maximum glc resulting from a particular power
plant or for determining the best location for that plant. For that purpose,
the concept of a "window" of excess concentrations, as introduced by Hunt ef
a/ (1979) is more useful. For any given plant location (say, upwind of the
hill), there is a limited range of stack heights Hs for which a significant
amplification of the glc will occur. (For sake of argument, we will here
define significant as a factor of 2.) This amplification can occur only if
the position of the maximum glc lies on or near the hill surface. For small
Hs, xmx will occur upwind of the hill and thus be little influenced by the
hill, so that A (s*mx/*mx) wi" approach unity. If Hs is too large (for
example, Hs»/7, the hill height), xmx will lie well beyond the hill and A will
again approach unity. In either case, there is little amplification. These
"windows" of critical Hs values have been measured by Lawson and Snyder (1985,
1987) for two typical hill shapes that might be found in the real world, one
axisymmetric, the other two-dimensional. The results are shown in Figure 13.
The 1.4-window, for example, extends to about 14/7 upstream, 10/7 downstream,
and as high as 1.8/7 in the vertical for the axisymmetric hill. For the
two-dimensional hill, this 1.4-window extends about Bh upstream, 15/7
downstream, and as high as 2.2/7 in the vertical.
Such contour maps as provided in Figure 13 can be very useful for the
practitioner. Once an acceptable terrain amplification factor (or "excess
concentration") is decided upon, it is a simple matter to trace the window on
the contour map to determine the area (plant location and/or stack height) to
be avoided. Conversely, from such maps, the likely maximum glc for a
potential site and stack height can be estimated. The use of terrain
amplification factors simplifies the application of these data to full-scale
situations. The expected maximum glc in flat terrain is calculated (from
mathematical models or standard curves), then the concentration in the
presence of the hill is simply the product of this quantity and the TAF. This
study was initiated through a request from the EPA Office of Air Quality
Planning and Standards (OAQPS) to aid in the decision-making process with
regard to the promulgation of the Stack Height Regulations under the Clean Air
Act, and the data were provided to OAQPS much earlier than the publication
dates shown.
40
-------
H
.2
g «
eo
w o
o r
«
.2 o
£ Z
o.
*8 0)
O)
c S
_^
2 c
o
g 'co
CO m
E 2
E|S>
l^SP
.S3 x x
U. 03 (D
41
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Subsequent to the idealized study described above, the OAQPS requested
the FMF to conduct a study demonstrating the application of the fluid modeling
approach to the determination of good-engineering-practice (GEP) stack height
for a power plant in complex terrain, i.e., to provide an example study/report
for industry to follow in the conduct of a GEP determination. The site chosen
for this demonstration was the Clinch River Power Plant in southwestern
Virginia, and a 1:1920 scale model of the surrounding terrain was constructed.
Measurements were presented (Snyder and Lawson, 1985b) that described the
simulated atmospheric boundary layer structure, plume-dispersion
characteristics in that boundary layer, and the maximum glc of effluent
downstream from the plant, both in the presence of all significant terrain
surrounding the plant and in the absence of "nearby" upwind terrain. Analysis
of the maximum glc showed that, in this case, a stack height of 326m met the
GEP criteria under 50% load conditions, i.e., the nearby upwind terrain
effected an increase of 40% in the maximum ground-level concentration. This
study followed the general guidance set forth in the Guideline for Fluid
Modeling of Atmospheric Diffusion (Snyder, 1981) and the specific
recommendations set forth in the Guideline for Use of Fluid Modeling to
Determine Good Engineering Practice Stack Height (EPA, 1981) and the Guideline
for Determination of Good Engineering Practice Stack Height (Technical Support
Document for the Stack Height Regulations, Revised Draft) (EPA, 1985).
Stably Stratified Towing-Tank Studies
Lamb and Britter (1984) conducted a combined numerical and laboratory
study of so-called shallow water flow over an isolated hill. They showed how
certain geometrical and flow parameters affect the tendency of a fluid to flow
around rather than over an obstacle in the case of a homogeneous single layer
fluid, i.e., simulating the atmospheric condition of an elevated step
inversion. A series of numerical experiments was conducted using a
finite-difference model. Measures were suggested for quantitative assessment
of the tendency of the fluid to flow around the obstacle as a function of the
relative hill height and the Froude number. The laboratory experiments
examined the motions of two superposed homogeneous layers of fluid past a
conical hill in the towing tank. The resulting motions were found to agree
with the results of the numerical experiments and extended the understanding
42
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gained from them. Flow visualization techniques were used to demonstrate the
impingement of the interface on the obstacle, and its dependence on flow speed
and hill height.
Another numerical model was acquired and implemented at the FMF for
comparison with laboratory results. The numerical model was originally
developed by Mason and Sykes (1979); it integrates the Navier-^Stokes equations
for incompressible stratified flow using a finite-difference scheme. Direct
comparisons were made between the results of this model and laboratory
experiments for density-stratified flow around the idealized axisymmetric CCB
model by Rottman ef a/ (1987) for three specific experimental arrangements.
First, a small towing tank was used in which both the Reynolds number and
Froude number were matched exactly with the numerical model. This provided an
overall assessment of the accuracy of the approximations made in the numerical
model. Second, the large towing tank was used in which mean plume
trajectories were measured and compared with particle paths computed through
the numerical model. Third, some comparisons were made with wind-tunnel
measurements of the flow structure over the hill. In general, the numerical
model qualitatively reproduced the experimental results on the flow structure.
Whereas the following area of investigation is not directly related to
complex terrain, it is included here because it played an important (and
somewhat controversial) role in the CTDM formulation. This is the area of
describing the effects of stable stratification on turbulent diffusion or, put
another way, estimating vertical plume growth in the nighttime stable boundary
layer. Experiments were conducted (Britter et a/, 1983) in which a grid was
towed horizontally along the stratified towing tank. The vertical velocity
fluctuations produced near the grid were reduced under strong stratification
by up to 30%, but the decay rates of the turbulent velocity fluctuations were
found to be unaffected by the stratification over a considerable distance
downstream. Turbulent diffusion from a point source located downstream of the
grid was also measured. The lateral plume widths were found to be largely
unaffected by the stratification and grew with the 1/2-power of time. The
vertical plume growth, however, was found to reach an asymptotic limit. These
results were largely in agreement with the theoretical models of Csanady
(1964) and Pearson ef a/ (1983), but in contradiction to the theory and
limited data of Venkatram ef a/ (1984). The latter data suggest a continuous
43
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vertical plume growth (for large times), but the measurements did not, in
fact, extend very far downwind (maximum downwind distance of about 1 km).
Further grid-turbulence studies were done in the towing tank with the aim
of investigating internal wave effects and providing guidance on the
partitioning of wave and turbulence energies in stably stratified flows
(Rottman and Britter, 1986). The results suggested that the fraction of
available turbulent kinetic energy that is converted to potential energy,
commonly referred to as the mixing efficiency, increases monotonically with
increasing stability, and there is some indication that this mixing efficiency
approaches a constant as the flow becomes strongly stable.
A cooperative project was completed with the Los Alamos National
Laboratory to examine the conditions under which flushing of a valley between
two ridges will occur, i.e., to answer the question of when a stable crosswind
will sweep the valley clean and when the flow will separate from the top lee
side of the first ridge, reattach at the top windward side of the second
ridge, and thus form a nearly stagnant region in the valley beneath. In this
series of towing-tank studies, three experimental parameters were varied: the
steepness of the ridge/valley slopes (40°, 27° and 13°), the separation
distance between the ridges, and the Froude number that characterizes the
stability of the crosswind. In broad terms, the characteristics of the flow
between the ridges may be explained using criteria for boundary-layer
separation from the lee side of a single ridge. The downstream ridge appears
to induce separation from the lee side of the upstream ridge only when it is
steep-sided (Lee er a/, 1984a,b, 1986, 1987). As an offshoot of this work,
the conditions conducive to the onset of severe downslope winds on the lee
sides of mountains was investigated (Rottman and Smith, 1987). The results
showed that an intrusion (breaking wave - associated with severe downslope
winds) existed when the Froude number based on the ridge height was in the
range 0.2 ^ F < 0.6 for a steep-sloped ridge (maximum slope 40°) and 0.2 ^ F ^
1.1 for a low-sloped ridge (13°).
An overview of fluid modeling of pollutant transport and diffusion in
stably stratified flows over complex terrain was provided for Annual Review of
Fluid Mechanics by Snyder (1985).
44
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4. SUMMARY
The EPA Fluid Modeling Facility has conducted a wide range of laboratory
studies and a limited amount of numerical modeling of flow and diffusion in
association with the Complex Terrain Model Development Program. The goal of
the CTMDP is the development of a dispersion model valid in complex terrain,
with emphasis on plume impaction on nearby hills during nighttime stable
conditions. Work at the FMF prior to the inception of the program provided
the basic framework for the model - the dividing-streamline concept - and the
focal point around which to design the field program.
Throughout the course of the CTMDP, the FMF interacted vigorously with
the model developers by providing support in various ways. Early work
provided direct support in planning the details and strategies of the field
experiments and solidifying and testing the limits of applicability of the
dividing-streamline concept. Later work included exercises of "filling in the
gaps" in the field data, furthering the understanding of the physical
mechanisms important to plume impaction in complex terrain and in stably
stratified flows in general, and testing the ability of the laboratory models
to simulate full-scale field conditions. And, as the needs arose, the FMF
tested various modeling assumptions, concepts, and hypotheses and provided
data for "calibration" of various parameters within the CTDM model.
Simultaneously, the FMF responded to the needs of the regulatory arm of
EPA, the Office of Air Quality Planning and Standards, by providing guidance
concerning expected terrain effects and by providing a demonstration study -
an example for industries to follow in conducting good-engineering-practice
stack height determinations in complex terrain. Also, a broad range of
supplemental studies was conducted, expanding and enlarging upon the specific
requests of the OAQPS and the CTDM model developers to provide information of
general use to the scientific and air pollution modeling communities. Many of
the data sets generated in the course of this program have been provided to
and used by various groups (nationally and internationally) in the
development, testing and evaluation of complex terrain dispersion models.
45
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The most significant contributions included (1) the conceptual framework
for the mathematical model (i.e., the division of the flow-field into two
regimes, a lower layer below the dividing-streamline height which flows in
essentially horizontal planes around the hill, and an upper layer above the
dividing-streamline height which is treated as modified potential flow over a
cut-off hill) and the detailed experimental validation and establishment of
limits of applicability of these concepts, (2) verification of the integral
formula for the height of the dividing streamline - this allowed computations
of the dividing-streamline height under arbitrary approach-flow conditions,
including shear in the approaching wind-speed profile and nonlinear
temperature gradients, (3) demonstration of the extreme sensitivity of surface
concentration patterns to wind direction under strongly stratified conditions,
(4) measurements of plume deflections and deformations over hills in neutral
flow - these permitted adjustment of the T-factors in CTDM and resulted in
substantial improvements in the CTDM predictions, and (5) the introduction of
the concept of "windows of excess concentration" and measurements of terrain
amplification factors - these provided simple and practical methods for
estimation and intercomparison of effects of terrain and source locations on
maximum ground-level concentrations that may result from sources placed in the
vicinities of hills.
46
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REFERENCES
* Arya, S.P.S. & Gadiyaram, P.S. 1986 An Experimental Study of Flow and
Dispersion in the Wakes of Three-Dimensional Low Hills. Atmos. Envir.,
20, 729-40.
* Arya, S.P.S. & Shipman, M.S. 1981 An Experimental Investigation of Flow
and Diffusion in the Disturbed Boundary Layer over a Ridge, Part I:
Mean Flow and Turbulence Structure. Atmos. Envir., 15, 1173-84.
* Arya, S.P.S., Shipman, M.S. & Courtney, LY. 1981 An Experimental
Investigation of Flow and Diffusion in the Disturbed Boundary Layer over
a Ridge, Part II: Diffusion from a Continuous Point Source. Atmos.
Envir., 15, 1185-94.
Baines, P.O. 1979 Observations of Stratified Flow Past Three-Dimensional
Barriers. J. Geophys. Res., 84, no. C12, 7834-8.
* Bass, A. 1980 Towing Tank Studies in Support of Field Experiments at Cinder
Cone Butte, Idaho, Part II: Plume Behavior with Froude Number and
Incident Wind Direction. Rpt. by Envir. Res. & Tech. on cooperative
work with Fluid Mod. Facility, Envir. Prot. Agcy., Res. Tri. Pk., NC.
Bass, A., Strimaitis, D.G. & Egan, B.A. 1981 Potential Flow Model for
Gaussian Plume Interaction with Simple Terrain Features. Rpt. under
Contract No. 68-02-2759, Envir. Prot. Agcy., Res. Tri. Pk., NC, 201 p.
Brighton, P.W.M. 1978 Strongly Stratified Flow Past Three-Dimensional
Obstacles. Quart. J. Roy. Meteorol. Soc., 104, 289-307.
* Britter, R.E., Hunt, J.C.R., Marsh, G.L & Snyder, W.H. 1983 The Effects of
Stable Stratification on Turbulent Diffusion and the Decay of Grid
Turbulence. J. Fluid Mech., 127, 27-44.
Burt, E.W. & Slater, H.H. 1977 Evaluation of the Valley Model. AMS-APCA
Joint Conf. on Appl. of Air Poll. Meteorol., Salt Lake City, UT, Amer.
Meteorol. Soc., Boston, MA.
* Capuano, M.E. 1983 The Effects of Hill Slope on Flow and Dispersion over
Two-dimensional Hills - A Wind Tunnel Study. M.S. Thesis, Dept.
Marine, Earth, Atmos. Sci., NC State Univ., Raleigh, NC, 153p.
* Castro, I.P . 1987 A Note on Lee Wave Structures in Stratified Flow over
Three-Dimensional Obstacles. Tellus, 39A, 72-81.
* Castro, I.P. & Snyder, W.H. 1982 A Wind Tunnel Study of Dispersion from
Sources Downwind of Three-Dimensional Hills. Atmos. Envir., 16,
1869-87.
* Castro, I.P. & Snyder, W.H. 1987a Wind Direction Effects on Dispersion from
Sources Downwind of Steep Hills. Atmos. Envir. (to be submitted).
* Publications generated from research conducted within the Fluid Modeling
Facility.
47
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* Castro, IP. & Snyder, W.H. 1987b Obstacle Drag and Upstream Motions in
Stratified Flow. Proc. Third Int. Symp. Stratified Flows, Cal. Inst.
Tech., Pasadena, CA, Feb. 3-5 (general session).
* Castro, IP. & Snyder, W.H. 1987c Upstream Motions in Stratified Flow. J.
Fluid Mech. (submitted).
* Castro, IP., Snyder, W.H. & Marsh, G.L 1983 Stratified Flow over Three-
Dimensional Ridges. J. Fluid Mech., 135, 261-82.
* Courtney, LY. 1979 A Wind Tunnel Study of Flow and Diffusion over a Two-
Dimensional Low Hill. M.S. Thesis, Dept. of Meteorol., NC State Univ.,
Raleigh, NC, 134p.
* Courtney, LY. & Arya, SP.S. 1980 Boundary Layer Flow and Diffusion over a
Two-dimensional Low Hill. Preprints Vol., 2nd Jt. Conf. Appl. Air Poll.
Meteorol., Mar. 24-28, New Orleans, LA, 551-8. Amer. Meteorol. Soc.,
Boston, MA.
Csanady, G.T. 1964 Turbulent Diffusion in a Stratified Fluid. Atmos. Sci.,
21,439-47.
DiCristofaro, D.C., Strimaitis, D.G., Greene, B.R., Yamartino, R.J.,
Venkatram A., Godden, D.A., Lavery, T.F. & Egan, B.A. 1986 EPA Complex
Terrain Model Development Fifth Milestone Report - 1985. Rpt. No.
EPA/600/3-85/069, Envir. Prot. Agcy., Res. Tri. Pk., NC, 277p.
Drazin, P.G. 1961 On the Steady Flow of a Fluid of Variable Density Past an
Obstacle. Te//us, 13, 239-51.
EPA 1981 Guideline for Use of Fluid Modeling to Determine Good Engineering
Practice Stack Height. Rpt. No. EPA-450/4-81-003, Envir. Prot. Agcy.,
Res. Tri. Pk., NC, 47p.
EPA 1985 Guideline for Determination of Good Engineering Practice Stack
Height (Technical Support Document for the Stack Height Regulations).
Rpt. No. EPA-450/4-80-023R (Revised June 1985), Envir. Prot. Agcy.,
Res. Tri. Pk., NC, 102p.
* Eskridge, R.E., Lawson, R.E. Jr. & Marsh, G.L 1983 Simulation of an
Atmospheric Tracer Experiment in Complex Terrain Using a Stratified
Towing Tank: A Case Study. 6th Symp. Turb. & Diffusion, Boston, MA,
Mar. 22-25, Amer. Meteorol. Soc., Boston, MA.
* Gadiyaram, P.S. 1984 Flow and Dispersion over Three-Dimensional
Axisymmetric Hills: A Wind Tunnel Study. M.S. Thesis, Dept. Marine,
Earth, Atmos. Sci., NC State Univ., Raleigh, NC, 126p.
Holzworth, G.C. 1980 The EPA Program for Dispersion Model Development for
Sources in Complex Terrain. 2nd Jt. Conf. Appl. Air Poll. Meteorol.,
March 24-27, New Orleans, LA, Amer. Meteorol. Soc., Boston, MA.
* Holzworth, G.C. & Snyder, W.H. 1979 Program Plan for Development of a
Mathematical Air Quality Assessment System for Use in Complex Terrain.
Rpt. No. EPA-600/9-79-041, Workshop on Atmos. Disp. Models in Complex
Terrain, 137- 50. Envir. Prot. Agcy., Res. Tri. Pk., NC.
Hovind, E.L, Edelstein, M.W. & Sutherland, V.C. 1979 Workshop on
Atmospheric Dispersion Models in Complex Terrain. Rpt. No.
EPA-600/9-79-041, Envir. Prot. Agcy., Res. Tri. Pk., NC, 213p.
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Hunt, J.C.R. & Mulhearn, P.J. 1973 Turbulent Dispersion from Sources Near
Two-Dimensional Obstacles. J. Fluid Mech., 61, 245-74.
* Hunt, J.C.R., Puttock, U.S. & Snyder, W.H. 1979 Turbulent Diffusion from a
Point Source in Stratified and Neutral Flows around a Three-Dimensional
Hill: Part I: Diffusion Equation Analysis. Atmos. Envir., 13, 1227-39.
* Hunt, J.C.R. & Snyder, W.H. 1980 Experiments on Stably and Neutrally
Stratified Flow over a Model Three-Dimensional Hill. J. Fluid Mech.,
96, 671- 704.
* Hunt, J.C.R., Snyder, W.H. & Lawson, R.E. Jr. 1978 Flow Structure and
Turbulent Diffusion around a Three-Dimensional Hill: Fluid Modeling
Study on Effects of Stratification; Part I: Flow Structure. Rpt. No.
EPA-600/4-78-041, Envir. Prot. Agcy., Res. Tri. Pk., NC..
* Khurshudyan, L.H., Snyder, W.H. & Nekrasov, I.V. 1981 Flow and Dispersion
of Pollutants over Two-Dimensional Hills: Summary Report on Joint
Soviet-American Study. Rpt. No. EPA-600/4-81-067, Envir. Prot. Agcy.,
Res. Tri. Pk., NC, 143p.
* Lamb, V.R. & Britter, R.E. 1984 Shallow Water Flow over an Isolated
Obstacle. J. Fluid Mech., 147, 291-313.
Lavery, T.F., Bass, A., Strimaitis, D.G., Venkatram, A., Greene, B.R.,
Drivas, P.J. & Egan, B.A. 1982 EPA Complex Terrain Modeling Program:
First Milestone Report - 1981. Rpt. No. EPA-600/3-82-036, Envir. Prot.
Agcy., Res. Tri. Pk., NC, 304p.
Lavery, T.F., Strimaitis, D.G. & Egan, B.A. 1986 A Workshop Report on the
Complex Terrain Model Development Project (February 4-6, 1986). Rpt.
under Contract 68-02-3421, Envir. Prot. Agcy., Res. Tri. Pk., NC, 75p.
Lavery, T.F., Strimaitis, D.G., Venkatram, A., Greene, B.R., DiCristofaro,
D.C. and Egan, B.A. 1983 EPA Complex Terrain Model Development: Third
Milestone Report - 1983. Rpt. No. EPA-600/3-83-101, Envir. Prot.
Agcy., Res. Tri. Pk., NC, 271 p.
* Lawson, R.E. Jr. & Snyder, W.H. 1985 Stack Heights and Locations in Complex
Terrain. Preprints Vol: 7th Symp. Turb. Diff., Nov. 12-15, Boulder, CO,
223-6. Amer. Meteorol. Soc., Boston, MA.
* Lawson, R.E. Jr. & Snyder, W.H. 1987 Estimation of Pollutant Concentration
from Sources Near Complex Terrain in Neutral Flow. Atmos. Envir., (to
be submitted).
* Lee, J.T., Barr, S., Lawson, R.E., Jr., Snyder, W.H. & Marsh, G.L 1984a
Towing Tank Studies of Stratified Flow over Ridges and Valleys. Rpt.
No. LA-UR-84-1314, Los Alamos National Laboratory, Los Alamos, NM, 29p.
* Lee, J.T., Barr, S., Lawson, R.E., Jr., Snyder, W.H. & Marsh, G.L. 1984b
Towing Tank Studies of Stratified Flow over Ridges and Valleys.
Preprints Vol. 3rd Conf. Mtn. Meteorol., Portland, OR, 37-41. Amer.
Meteorol. Soc., Boston, MA.
* Lee, J.T., Barr, S., Snyder, W.H. & Lawson, R.E. Jr. 1981 Wind Tunnel
Studies of Flow Channeling in Valleys. Preprint Vol. 2nd Conf. Mtn.
Meteorol., Nov. 9-12, Steamboat Springs, CO, Amer. Meteorol. Soc.,
Boston, MA.
49
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* Lee, J.T., Lawson, R.E. Jr. & Marsh, G.L 1986 Flow Visualization
Experiments on Stably Stratified Flow over Ridges and Valleys. Proc.
3rd Int. Workshop on Wind and Water Tunnel Modeling of Atmos. Flow and
Dispersion, Sept., Lausanne, Switzerland.
* Lee, J.T., Lawson, R.E. Jr. & Marsh, G.L. 1987 Flow Visualization
Experiments on Stably Stratified Flow Over Ridges and Valleys: Final
Report. Rpt. No. LA-UR-87-127, Los Alamos National Laboratory, Los
Alamos, NM.
Mason, P.J. & Sykes, R.I. 1979 Three-Dimensional Numerical Integrations of
the Navier-Stokes Equations for Flow Over Surface-Mounted Obstacles. J.
Fluid Mech., 91, 433-50.
Pasquill, F. 1974 Atmospheric Diffusion. 2nd Ed., Chichester, Ellis
Horwood Ltd., John Wiley & Sons, NY, NY, 429p.
Pearson, H.J., Puttock, J.S. & Hunt, J.C.R. 1983 A Statistical Model of
Fluid-Element Motions and Vertical Diffusion in a Homogeneous Stratified
Turbulent Flow. J. Fluid Mech., 129, 219-49.
* Pendergrass, W.R. & Arya, S.P.S. 1983 Vortex Development in Boundary Layer
Flows over Two-Dimensional Ramps. Preprint Vol. 6th Symp. Turb. &
Diff., Mar. 22-25, Boston, MA, Amer. Meteorol. Soc., Boston, MA.
* Pendergrass, W.R. & Snyder, W.H. 1987 Wind Tunnel Measurements of Terrain
Amplification Factors for Sources Upwind of Two-Dimensional Ramps of
Various Slopes. Atmos. Envir. (to be submitted).
* Queney, P., Corby, G.A., Gerbier, N., Koschmieder, H. & Zierep, J. 1960 The
Airflow over Mountains. World Meteorol. Org., Tech. Note No. 34,
Geneva, Switz.
Riley, J.J., Liu, H.T. & Geller, E.W. 1976 A Numerical and Experimental
Study of Stably Stratified Flow Around Complex Terrain. Rpt. No.
EPA-600/4-76-021, Envir. Prot. Agcy., Res. Tri. Pk., NC, 41 p.
* Rottman, J.W. & Britter, R.E. 1986 The Mixing Efficiency and Decay of Grid-
Generated Turbulence in Stably Stratified Fluids. Proc. 9th
Australasian Fluid Mech. Conf., Dec. 8-12, Univ. Auckland, Auckland, New
Zealand.
* Rottman, J.W., Lawson, R.E. Jr. & Snyder, W.H. 1987 A Comparison of
Numerical and Laboratory Experiments on Density-Stratified Flows around
a Three-Dimensional Hill. Proc. Third Int. Symp. Stratified Flows, Cal.
Inst. Tech., Pasadena, CA, Feb. 3-5.
* Rottman, J.W. & Smith, R.B. 1987 Tow-Tank Simulations of the Severe
Downslope Wind. Proc. Third Int. Symp. on Stratified Flows, Cal. Inst.
Tech., Pasadena, CA, Feb. 3-5.
Rowe, R.D., Benjamin, S.F., Chung, K.P., Havlena, J.J. & Lee, C.Z. 1982
Field Studies of Stable Air Flow over and around a Ridge. Afmos.
Envir., 16, 643-53.
Sheppard, P.A. 1956 Airflow over Mountains. Quart. J. Floy. Meteorol. Soc.,
82, 528-9.
50
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* Snyder, W.H. 1980a Towing Tank Studies in Support of Field Experiments at
Cinder Cone Butte, Idaho, Phase I: Influence of Hill on Wind Field at
the Meteorological Tower Site. Fluid Modeling Facility Internal Rpt.,
July 30, 20p. Envir. Prot. Agcy., Res. Tri. Pk., NC.
* Snyder, W.H. 1980b Towing Tank Studies in Support of Field Experiments at
Cinder Cone Butte, Idaho, Phase III: Verification of Formula for
Prediction of Dividing Streamline Height. Fluid Modeling Facility
Internal Rpt., Aug. 29, Envir. Prot. Agcy., Res. Tri. Pk., NC, 12p.
* Snyder, W.H. 1981 Guideline for Fluid Modeling of Atmospheric Diffusion.
Rpt. No. EPA-600/8-81-009, Envir. Prot. Agcy., Res. Tri. Pk., NC, 200p.
* Snyder, W.H. 1983a Fluid Modeling of Terrain Aerodynamics and Plume
Dispersion - A Perspective View. Invited Presentation, AMS Workshop on
Dispersion in Complex Terrain, Keystone, CO, May 17-20.
* Snyder, W.H. 1983b Fluid Modeling of Terrain Aerodynamics and Plume
Dispersion - A Perspective View. Preprint Vol. 6th Symp. Turb. & Diff.,
March 22-25, Boston, MA, 317-20. Amer. Meteorol. Soc., Boston, MA.
* Snyder, W.H. 1984 Terrain Aerodynamics and Plume Dispersion: A Perspective
View Gained from Fluid Modeling Studies. Proc. Symp. Tibetan Plateau &
Mtn. Meteorol., Beijing, P.R.C., March.
* Snyder, W.H. 1985 Fluid Modeling of Pollutant Transport and Diffusion in
Stably Stratified Flows over Complex Terrain. Ann. Rev. Fluid Mech.,
17, 239-66.
* Snyder, W.H. 1986 Comparisons of CTDM Calculations with Fluid Modeling
Observations. Complex Terrain Workshop, Research Triangle Park, NC,
Feb. 4-6, 45p.
* Snyder, W.H. & Britter, R.E. 1987 A Wind Tunnel Study of the Flow Structure
and Dispersion from Sources Upwind of Three-Dimensional Hills. Atmos.
Envir., 21, 735.
* Snyder, W.H., Britter, R.E. & Hunt, J.C.R. 1980 A Fluid Modeling Study of
the Flow Structure and Plume Impingement on a Three-Dimensional Hill in
Stably Stratified Flow. Proc. Fifth Int. Conf. on Wind Engr. (J.E.
Cermak, ed.), 1, 319-29. Pergamon Press, NY, NY.
* Snyder, W.H. & Hunt, J.C.R. 1984 Turbulent Diffusion from a Point Source in
Stratified and Neutral Flows around a Three-Dimensional Hill, Part II:
Laboratory Measurements of Surface Concentrations. Atmos. Envir., 18,
1969-2002.
* Snyder, W.H. & Lawson, R.E. Jr. 1981 Laboratory Simulation of Stable Plume
Dispersion over Cinder Cone Butte: Comparison with Field Data.
Appendix: EPA Complex Terrain Model Development First Milestone Report -
1982, Rpt. No. EPA-600/3-82-036, p. 250-304. Envir. Prot. Agcy., Res.
Tri. Pk., NC.
* Snyder, W.H. & Lawson, R.E. Jr. 1985a Stable Plume Dispersion over an
Isolated Hill: Releases above the Dividing-Streamline Height. Appendix
A: EPA Complex Terrain Model Development Fourth Milestone Report - 1984,
Rpt. No. EPA/600/3-84/110, 233-68. Envir. Prot. Agcy., Res. Tri. Pk, NC.
51
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* Snyder, W.H. & Lawson, R.E. Jr. 1985b Fluid Modeling Demonstration of Good-
Engineering-Practice Stack Height in Complex Terrain. Rpt. No.
EPA-600/3-85/022, Envir. Prot. Agcy., Res. Tri. Pk., NC, 89p.
* Snyder, W.H. & Lawson, R.E. Jr. 1986 Laboratory Observations of Plume
Deformations in Neutral Flow over a Three-Dimensional Hill. Preprint
Vol. AMS 5th Jt. Conf. Appl. Air Poll. Meteorol. with APCA, Nov., Chapel
Hill, NC. Amer. Meteorol. Soc., Boston, MA.
* Snyder, W.H. & Lawson, R.E. Jr. 1987 Stable Plume Dispersion over an
Isolated Hill: Releases above the Dividing-Streamline Height. Proc.
Third Int. Symp. Stratified Flows, Cal. Inst. Tech., Pasadena, CA, Feb.
3-5.
* Snyder, W.H., Lawson, R.E. Jr., Thompson, R.S. & Holzworth, G.C. 1980
Observations of Flow around Cinder Cone Butte, Idaho. Rpt. No.
EPA-600/7-80-150, Envir. Prot. Agcy., Res. Tri. Pk., NC, 30p.
* Snyder, W.H. & Ogawa, Y. 1982 Simulation of Flow and Diffusion over Cinder
Cone Butte in a Stratified Wind Tunnel. Data Report, National Inst.
for Envir. Studies, Tsukuba, Japan.
* Snyder, W.H. & Pendergrass, W.R. Ill 1980 Ramp Study: Idealized Widows
Creek. Unpublished Data Rpt., Fluid Modeling Facility, Envir. Prot.
Agcy., Res. Tri. Pk., NC.
* Snyder, W.H., Thompson, R.S., Eskridge, R.E., Lawson, R.E., Jr., Castro,
I.P., Lee, J.T., Hunt, J.C.R. & Ogawa, Y. 1983 The Structure of
Strongly Stratified Flow over Hills: Dividing-Streamline Concept.
Appendix: EPA Complex Terrain Model Development Second Milestone Report
- 1982, Rpt. No. EPA-600/3-83-015, p. 319-75. Envir. Prot. Agcy., Res.
Tri. Pk., NC.
* Snyder, W.H., Thompson, R.S., Eskridge, R.E., Lawson, R.E., Jr., Castro,
I.P., Lee, J.T., Hunt, J.C.R. & Ogawa, Y. 1985 The Structure of
Strongly Stratified Flow over Hills: Dividing-Streamline Concept. J.
Fluid Mech., 152, 249-88.
* Snyder, W.H., Thompson, R.S. & Shipman, M.S. 1986 Streamline Trajectories
in Neutral and Stratified Flow over a Three-Dimensional Hill. Appendix:
Rpt. No. EPA/600/3-85/069, EPA Complex Terrain Model Development Fifth
Milestone Report - 1985, 240-277. Envir. Prot. Agcy., Res. Tri. Pk.,
NC.
Strimaitis, D.G., Lavery, T.F., Venkatram, A., DiCristofaro, D.C., Greene,
B.R. & Egan, B.A. 1985 EPA Complex Terrain Model Development: Fourth
Milestone Report - 1984. Rpt. No. EPA-600/3-84-110, Envir. Prot.
Agcy., Res. Tri. Pk., NC.
Strimaitis, D.G., Scire, J.S. & Bass, A. 1982 COMPLEX/PFM Air Quality Model
User's Guide. Rpt. (awaiting printing), Envir. Prot. Agcy., Res. Tri.
Pk., NC, 114p.
* Strimaitis, D.G. & Snyder, W.H. 1986 An Evaluation of the Complex Terrain
Dispersion Model Against Laboratory Observations: Neutral Flow over 2-D
and 3-D Hills. Preprint Vol. AMS 5th Jt. Conf. Appl. Air Poll.
Meteorol. with APCA, Nov., Chapel Hill, NC, Amer. Meteorol. Soc.,
Boston, MA.
52
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Strimaitis, D.G., Venkatram, A., Greene, B.R., Hanna, S., Heisler, S.,
Lavery, T.F., Bass, A., & Egan, B.A. 1983 EPA Complex Terrain Model
Development: Second Milestone Report - 1982. Rpt. No. EPA-600/3-83-015,
Envir. Prot. Agcy., Res. Tri. Pk., NC.
* Thompson, R.S. & Shipman, M.S. 1986 Streamlines in Stratified Flow over a
Three-Dimensional Hill. Preprint Vol. AMS 5th Jt. Conf. Appl. Air Poll.
Meteorol. with APCA, Nov., Chapel Hill, NC, Amer. Meteorol. Soc.,
Boston, MA.
* Thompson, R.S., Shipman, M.S. & Snyder, W.H. 1985 Synopses of FMF Projects
in Complex Terrain. Rpt. to ERT on CTMD Program, Envir. Prot. Agcy.,
Res. Tri. Pk., NC, 24p.
* Thompson, R.S. & Snyder, W.H. 1976 EPA Fluid Modeling Facility. Proc.
Conf. on Modeling & Simulation, Rpt. No. EPA-600/9-76-016, Envir. Prot.
Agcy., Wash. D.C., July.
* Thompson, R.S. & Snyder, W.H. 1981 Air Pollution and Terrain Aerodynamics:
A Review of Fluid Modeling Studies at the EPA Fluid Modeling Facility,
ASCE Fall Conv., St. Louis, MO, Oct.
* Thompson, R.S. & Snyder, W.H. 1984 Fluid Modeling of Blocking and Upstream
Influences of Stable Flow over Two-Dimensional Hills. Proc. 2nd
Workshop Wind/Water Tunnel Dispersion Modeling, Oxford, England, Sept.
26-28, C3.1-3.7.
* Thompson, R.S. & Snyder, W.H. 1985a Air Pollution and Terrain Aerodynamics:
A Review of Fluid Modeling Studies at the EPA Fluid Modeling Facility.
J. Wind Engr. & Indus. Aerodyn., 21, 1-19.
* Thompson, R.S. & Snyder, W.H. 1985b Dispersion from a Source Upwind of a
Three-Dimensional Hill of Moderate Slope. Appendix B: EPA Complex
Terrain Model Development Fourth Milestone Report - 1984, Rpt. No.
EPA/600/3-84/110, 269-86. Envir. Prot. Agcy., Res. Tri. Pk., NC.
* Thompson, R.S., Snyder, W.H. & Lawson, R.E. Jr. 1983 Laboratory Simulation
of Neutral Plume Dispersion over Cinder Cone Butte: Comparison with
Field Data. Appendix: EPA Complex Terrain Model Development Third
Milestone Report -1983, Rpt. No. EPA-600/3-83-101, p. 212-51. Envir.
Prot. Agcy., Res. Tri. Pk., NC.
Turner, J.S. 1973 Buoyancy Effects in Fluids. Cambridge Univ. Press,
Cambridge, England, 368p.
Venkatram, A., Strimaitis, D. & DiCristofaro, D. 1984 A Semiempirical Model
to Estimate Vertical Dispersion of Elevated Releases in the Stable
Boundary Layer. Atmos. Envir., 18, 923-8.
Wackter, D.J. & Londergan, R.J. 1984 Evaluation of Complex Terrain Air
Quality Models. Rpt. under Contract No. 68-02-3514, Envir. Prot.
Agcy., Res. Tri. Pk., NC, 233p.
Weil, J.C., Traugott, S.C. & Wong, O.K. 1981 Stack Plume Interaction and
Flow Characteristics for a Notched Ridge. Rpt. No. PPRP-61, Martin
Marietta Corp., Baltimore, MD, 92p.
53
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