United States
                                 Environmental Protection
                                 Environmental Sciences Research ..
                                 Research Triangle Park NC 27711"
                                 Research and Development
                                 EPA-600/S4-81-008  Apr. 1981
Project Summary
                                 Potential  Flow  Model  for
                                 Gaussian  Plume  Interaction
                                 With  Simple  Terrain  Features
                                 A. Bass, D. G. Strimaitis, and B. A. Egan
                                   The theory of turbulent plumes
                                 embedded within potential flow fields
                                 is discussed for flows modified by
                                 special complex terrain situations.
                                 Both two- and three-dimensional
                                 isolated terrain obstacles are consid-
                                 ered. Concentration estimates are
                                 evaluated using a Gaussian solution to
                                 the appropriate diffusion equation;
                                 dispersion coefficients are modified to
                                 account for terrain-induced kinematic
                                 constraints, and plume  centerline
                                 trajectory is obtained from a stream
                                 line of the potential flow.  Specific
                                 limitations to the theory and  its appli-
                                 cability are reviewed.
                                   A computer algorithm is developed
                                 and documented to perform these
                                 calculations. Dispersion estimates
                                 and ground-level concentrations are
                                 given for a variety of meteorological
                                 situations. Parameters of the problem
                                 include obstacle  height,  effective
                                 source height, distance between source
                                 and obstacle, crosswind aspect ratio
                                 of the obstacle,  and atmospheric
                                 stability. The potential flow theory.
                                 originally applicable to neutral flows.
                                 is extended by an empirical  approxi-
                                 mation to slightly stable flows. Addi-
                                 tionally, an interpolation  scheme is
                                 proposed for objects of arbitrary cross-
                                 wind aspect ratio between the limiting
                                 cases of a hemisphere and a half-
                                 circular cylinder. Model computations
                                 are compared to laboratory experi-
                                 mental results and to field measure-
                                   This Project Summary was devel-
                                 oped by EPA's Environmental Sciences
                                 Research Laboratory. Research  Tri-
                                 angle Park, NC, to announce key find-
                                 ings of the research project that is fully
                                 documented in a separate report of the
                                 same title (see Project Report ordering
                                 information at back).
                                  This study has been motivated by the
                                 requirement for  a treatment of plume
                                 dispersion in complex terrain that is
                                 practical for regulatory use, yet retains
                                 much of the essential physics of the
                                 problem. For regulatory purposes, the
                                 modeling approach should emphasize
                                 cases with potential for high ground-
                                 level concentrations. These include:
                                   stable conditions and low wind
                                    speeds, under which direct plume
                                    impact or blocking by nearby terrain
                                    obstacles may occur, and
                                   neutral or slightly stable conditions
                                    and moderate or high wind speeds,
                                    under which the plume centerline
                                    trajectory passes over and close to
                                    the terrain surface.
                                  This report addresses the development
                                 of modeling methods for neutral and
                                 slightly stable conditions. The general
                                 approach employed follows the theory
                                 of turbulent plumes embedded within
                                 potential flow fields. The theory is
                                 applied to the calculation of  ground-
                                 level concentrations using a Gaussian
                                 form of solution  to the diffusion equa-

tion. Streamfunctions proper to potential
flow over a cylinder (aspect ratio = >)
and to potential flow over a sphere
(aspect ratio = 1) form cornerstones of
the model.  These are  extended  to de-
scribe flows  over terrain features of
intermediate crosswind aspect ratio by
a weighting of the two limiting stream-
functions. This weighting scheme was
derived in part using results from wind
tunnel experiments for flows  over ob-
stacles of intermediate aspect ratio.
  In addition, although the model is
strictly applicable only to neutral flows,
an empirical approximation scheme is
included  to define streamline  lowering
caused by increased stratification.  The
empirical basis for this portion  of the
model is derived from stratified tow-
tank experiments.
  Other restrictions in  the use  of the
model have not been addressed. These
limitations to the model arise  from the
neglect of boundary layer phenomena
such as flow separation, unsteady wake
effects, time-dependent effects of  sta-
bility (e.g.,  lee wave generation),  and
surface heating effects. In addition, the
theory is applicable in a strict mathe-
matical sense only for thin plumes.
  The report discusses the rationale for
selecting particular modeling approaches,
provides full technical documentation
for the algorithms developed,  and pre-
sents, for a number of specific test
situations, the results of comparisons
between model calculations and labora-
tory and field observations.

  In complex terrain, moderate or high
wind speeds with neutral or slightly
stable stratifications often result in high
pollutant concentrations because, as
the plume is transported over terrain
features, it is forced to pass close to the
terrain surface. Physical mechanisms
relevant to these conditions include
terrain-induced alteration of the  plume
centerline trajectory and kinematic
constraints on horizontal  and vertical
  The modeling  approach used here
applied potential flow theory to a  Gaussian
point source  model. The  model  incor-
porates  a theory for turbulent plumes
embedded within potential flow fields
based on solutions to the diffusion
equations describing flow fields over
two-dimensional and three-dimensional
axisymmetric terrain obstacles.  Quali-
tatively, these solutions are of Gaussian
form, with crosswind and vertical dis-
persion coefficients evaluated as line
integrals of the velocity field along the
plume centerline trajectory.
  Evaluating the terrain-influenced
dispersion coefficients for this model
requires specifying the crosswind and
the vertical diffusivities. To compare
model calculations with analogous flat
terrain  situations, an approximation
scheme was implemented, using the
PGT dispersion coefficients as a cali-
brating  scale. Qualitatively, the diffu-
sivity at a given  distance  from the
source  along the plume centerline
streamline is taken as that for the same
transit time in flat terrain. The conse-
quence  of this assumption is that model
calculations of dispersion coefficients
reduce to flat terrain values in the limits
of large downwind distances or small
  To account for the effects of stability,
an approximation consistent with labor-
atory observations is adopted to lower
the height of the neutral streamline
within  two obstacle  heights  of the
obstacle center by an amount deter-
mined by the height of the obstacle and
the Froude number.
  A second approximation is derived to
account for an  obstacle with arbitrary
crosswind aspect ratio. In this case,
two- and three-dimensional streamlines
are weighted to provide an intermediate
plume centerline trajectory.

  Model computations indicate that
maximum concentrations vary signifi-
cantly with obstacle size, effective stack
height,  and relative distance between
the stack and the obstacle. Comparisons
of model predictions  with  available
observations test the model performance
for a  limited number of possible com-
binations of these and other factors.
Table 1 summarizes the range of model
parameters involved in the comparisons.
Note that A is the crosswind aspect ratio
of the obstacle, Fr is the Froude number
characterizing the importance of densi
stratification in defining the flow, X/
is the distance between the stack ar
the obstacle normalized by the obstacl
height,  and H,/a is the effective stac
height normalized by the obstacle heigh
   The "smooth tunnel" comparisor
and the "tow tank" comparisons te
the  model under conditions that min
mize the influence of processes ni
contained in the model. They show th.
the model is able to predict the observe
maximum surface concentration with
a factor of two (generally overpredictinc
depending on the interpretation of th
observed plume properties in the al
sence of the obstacle.
   The "rough tunnel" comparisor
include the effects of a strong bounda
layer on flow over obstacles with
triangular cross section. Model predii
tions of maximum surface concentn
tions are again  within a factor of tv\
(overprediction) for obstacles of aspe
ratio 1. However, as the crosswin
aspect  ratio  increases, the concentn
tion predictions fall below the observ:
tions. The data indicate that the plurr
size is significantly enhanced upstreai
and over hills with the larger aspei
ratios. The deformations included in th
potential flow field approximation ai
only partly responsible. A better unde
standing of plume dispersion in a d<
forming boundary layer flow is likely 1
be needed to describe these experiment
more accurately.
   Plume interactions with  two terrai
features, a ridge and an isolated moum
near the Widows Creek Steam Electr
Power  Plant in Alabama  have bee
modeled. Meteorological conditior
used in the model correspond to seve
hours selected from nine months i
hourly  S02 and meteorological dal
collected by the TVA Air Quality Brand
The hours selected for comparison wei
derived by matching hours  of hig
measured SO2 concentrations on th
two terrain features with  neutral-tc
stable atmospheric conditions. In add
Table 1.    Range of Model Parameters Evaluated in Laboratory and Field Tests of th
           Potential Flow Model
Comparison Study
Smooth Tunnel
Tow Tank
Rough Tunnel
Widows Creek



 Table 2.    Comparison of Observed Concentrations (/jg/m3) at Widows Creek and Predicted Concentrations Based on the Potential
            Flow Model with Buoyant Plume Enhancement


Plume Height


Concentration Stability C
Ridge Impact
393 982
550 729
Mound Impact
Terrain Model Predictions
Stability D


Stability E


 tion, only those hours with  nearly
 coincident vertical temperature and
 velocity profiles were considered. Of the
 seven hours selected, four are associated
 with impacts on the ridge, and three are
 associated with impacts on the isolated
   A comparison of observed and calcu-
 lated concentrations for the two most
 appropriate  dispersion parameter
 classes are given in Table 2. Most of the
 observations fall between the model
 predictions for the two dispersion
 parameter classes.
   Uncertainties in the meteorological
 conditions at plume height, and in the
 emissions from  the facility, cloud the
 comparison of model predictions with
 observations. Given the range of data,
 reasonable combinations of assumptions
 can produce good correspondence be-
 tween the concentrations  in six of the
 seven cases. This does not, however,
 constitute an adequate evaluation of the
 model because of the uncertainties
 underlying these assumptions. The
 three greatest uncertainties lie in the
 specification of the dispersion param-
 eters, the final plume  height, and the
 actual emission rate.

  These preliminary assessments sug-
 gest that  with verification and refine-
 ment, the approach may be applicable to
 the following situations:
   isolated, single terrain obstacles of
     arbitrary height, of cross-section
     approximately circular in a plane
     parallel to the wind direction, and
     of arbitrary aspect ratio in the
     crosswind direction; and
   neutral to slightly stable strat-
  A number of limitations arise mainly
from physical effects that are not
described by the potential flow model.
The model should not be applied to the
following situations:
   stable flow cases in which the
    plume may directly impact the hill;
   dispersion cases dominated by
    surface boundary layer effects;
   unstable cases (e.g., strongly
    convective situations) for which
    potential theory is unsuitable; and
   cases dominated by wake effects.
  The range of suitable applications of
the model  is also limited by the
theoretical approximations made, and
by the limited configurations studied
experimentally. These limitations
  the "thin plume" approximation
       A. Bass, D. G. Strimaitis, and B. A. Egan are with Environmental Research and
         Technology, Inc.. Concord, MA 01742.
       J. Clarke is the EPA Project Officer (see below).
       The complete report, entitled "Potential Flow Model for Gaussian Plume Inter-
         action withSimple Terrain Features," (Order No. PB81-171 837; Cost: $17.00,
         subject to change) will be available only from:
              National Technical Information Service
              5285 Port Royal Road
              Springfield, VA 22161
              Telephone: 703-487-4650
       The EPA Project Officer can be contacted at:
              Environmental Sciences Research Laboratory
              U.S. Environmental Protection Agency
              Research Triangle Park, NC 27711
United States
Environmental Protection
Center for Environmental Research
Cincinnati OH 45268
Postage and
Fees Paid
EPA 335
Official Business
Penalty for Private Use $300
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