United States EPA-600/7-82-037d
Environmental Protection
Agency May 1982
MPA Research and
Development
VERIFICATDN AND TRANSFER OF
THERMAL POLLUTJDN MODEL
Volume IV. User's Manual for
Three-dimensional Rigid-lid Model
Prepared for
Office of Water and Waste Management
EPA Regions 1-10
Prepared by
Industrial Environmental Research
Laboratory
Research Triangle Park NC 27711
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EPA-600/7-82-037d
May 1982
VERIFICATION AND TRANSFER
OF THERMAL POLLUTION MODEL
VOLUME IV: USER'S MANUAL FOR THREE-DIMENSIONAL
RIGID-LID MODEL
By
Samuel S. Lee, Subrata Sengupta,
Emmanuel V. Nwadike and Sumon K. Sinha
Department of Mechanical Engineering
University of Miami
Coral Gables, Florida 33124
NASA Contract No. NAS 10-9410
NASA Project Manager: Roy A. Bland
National Aeronautics and Space Administration
Kennedy Space Center
Kennedy Space Center, Florida 32899
EPA Interagency Agreement No. 78-DX-0166
EPA Project Officer: Theodore G. Brna
Industrial Environmental Research Laboratory
Office of Environmental Engineering and Technology
Research Triangle Park, North Carolina 27711
Prepared for:
U. S. Environmental Protection Agency
Office of Research and Development
Washington, D. C. 20460
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PREFACE
The three-dimensional rigid-lid model is intended to be used for
hydrothermal predictions of closed basins subjected to a heated discharge
together with various other inflows and outflows. This volume has been
written in order to assist any prospective user in applying the mode! to
specific sites. Derivation of the governing equations and various other
details have been omitted. The programs are fairly general and only
one subroutine and a data file has to be rewritten for specific cases.
This work was sponsored by the National Aeronautics and Space
Administration (NASA-KSC) and the Environmental Protection Agency
(EPA-RTP).
ii
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ABSTRACT
The three-dimensional rigid-lid model was developed by the thermal
pollution group at the University of Miami and verified for accuracy at
various sites. The model results have been found to be fairly accurate
in ail the verification runs. The mode! is intended to be used as a
predictive tool in future sites and this manual has been written to enable
any user to be able to apply it without difficulty.
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CONTENTS
Preface H
Abstract Hi
Figures v
Tables vi
Symbols vii
Acknowledgments viii
1. Introduction 1
2. Recommendations 2
3. Program Description and Flow Chart 3
Description of program algorithm „ 3
Flow chart 3
Subroutine descriptions 3
4. List of Program Symbols Used in Main Program 6
Description of main variables 6
Marker matrices 11
5. Preparation of Runs 13
6. Input Data 14
7. Plotting Programs 15
Description of plot programs 15
Subroutines 15
References 16
Appendices 17
A. Example Case 18
Introduction 18
Problem statement 18
Calculations of parameters and input data 20
Sample input 22
Lake Keowee execution deck 24
B. Fortran Source Program Listing 45
List of main program and subroutines 46
List of plot programs 97
Sample run 120
Sample plots 138
iv
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FIGURES
Number
1 Flow chart 'main program) 30
2 Coordinates and arid system 32
3 Map of Lake Keowee 37
4 Lake Keowee (region of interest) 38
5 MAR matrix 39
6 MRH matrix 40
7 Keowee hydro discharge, February 27, 1979 **3
8 Jocassee-pumped storage station discharge, February 27,
1979 W
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TABLES
Number
1 Governing Equations 5
2 Subroutines for Calculations 26
3 Input Data to Main Program 33
4 Subroutines for Plots 36
5 Meteorological Data for Lake Keowee, February 27, 1979 .. 41
6 Summary of Inflows and Outflows to Lake Keowee,
February 27, 1979 42
vi
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SYMBOLS
AV
A
ref
B
JH
JV
ref
Eu
f
g
h
H
K
Pe
Q
Re
Ri
Horizontal kinematic: eddy
viscosity
Vertical kinematic eddy
viscosity
Reference kinematic eddy
viscosity
Ay/A f
Horizontal eddy thermal
diffusivity
Vertical eddy thermal
diffusivity
Reference eddy thermal
diffusivity
BV /EW
Specific heat at constant
pressure
Euler number
Coriolis parameter
Acceleration due to gravity
Depth relative to the mean
water level
Reference depth
Grid index in x-direction or
ct-direction
Grid index in y-direction or
0-direction
Grid index in z-direction or
y-direction
Surface heat transfer coefficient
Horizontal length scale
Pressure
Surface pressure
Turbulent Prandtl number,
Peciet number
Heat sources or sinks
Reynolds number (turbulent)
Richardson number
.ref
.e
v
w
X
y
z
xz
Temperature
Reference temperature
Equilibrium temperature
Surface temperature
Time
Reference time
Velocity in x-direction
Velocity in y-direction
Velocity in z-direction
Horizontal coordinate
Horizontal coordinate
Vertical coordinate
Greek Letters
Horizontal coordinate in
stretched system, = x
Horizontal coordinate in
stretched system, = y
Vertical coordinate in
stretched system
Constant in vertical diffusi-
vity equation, or vertical
coordinate in stretched sys-
tem, = Z/H
Transformed vertical velocity
Density
Surface shear stress in
x-direction
Surface shear stress in
y-direction
Dimensional quantity
Dimensional mean quantity
Dimensional quantity
Dimensional quantity
Reference quantity
vii
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ACKNOWLEDGMENTS
This work was supported by a contract from the National Aeronau-
tics and Space Administration (NASA-KSC) and the Environmental Pro-
tection Agency (EPA-RTP).
The authors express their sincere gratitude for the technical and
managerial support of Mr. Roy A. Bland, the NASA-KSC project manager
of this contract, and the NASA-KSC remote sensing group. Special
thanks are also due to Dr. Theodore G. Brna, The EPA-RTP project
manager, for his guidance and support of the experiments, and to Mr.
S. B. Hager, Chief Engineer, Civil-Environmental Division, and Mr.
William J. McCabe, Assistant Design Engineer, both from the Duke Power
Company, Charlotte, North Carolina, and their data collection group for
data acquisition. The support of Mr. Charles H. Kaplan of EPA was
extremely helpful in the planning and reviewing of this project.
viii
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SECTION 1
INTRODUCTION
The need for mathematical modeling in predicting and monitoring
thermal pollution was discussed in previous reports by Veziroglu et ai.
(1973, 1974). Predictive studies of ecosystems can only be made by
mathematical models. A prior knowledge of the effects of disturbances
is essential for environmental impact studies. Thus, the mathematical
model is a crucial tool in decisions involving power plant siting, land
development, etc.
The University of Miami team undertook development of a methodology
using remote sensing and numerical modeling to study thermal pollution.
The use of remotely-sensed data in modeling has been discussed by Sen-
gupta et al. (1974). The remote sensing effort has been discussed in
detail in previous publications. This volume has been written so as to
enable a user to apply the mathematical model to new sites for predictive
purposes.
The hydrodynamics and thermodynamics of an ecosystem are con-
trolled by geometry, meteorological conditions and physical characteristics
of the water such as density, salinity and turbidity. In this model the
effects of salinity and turbidity have been neglected. Hence, the govern-
ing equations are composed of the three-dimensional Navier-Stokes equa-
tions and the energy equation. Various assumptions can be made for
different situations leading to simplification or elimination of equations.
The main simplifying assumption in this case is the rigid-lid assumption.
This means that surface height fluctuations are not simulated by this
model, and this is a reasonable assumption for most applications (e.g.,
Lakes).
The rigid-lid model has the following capabilities:
1. It predicts the wind-driven circulation.
2. It predicts the circulation caused by inflows and outflows to the
domain.
3. It predicts the thermal effects in the domain.
4. It combines the aforementioned processes.
The calibration procedure consists of comparing ground-truth cor-
rected airborne radiometer data with surface isotherms predicted by the
model.
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SECTION 2
RECOMMENDATIONS
Various numerical models have been developed to study the effects
of heated discharge and meteorological conditions on bodies of water.
Most of these models are one or two dimensional. These models have a
high computational speed but only give horizontally or vertically averaged
values of temperatures.
Three-dimensional models, however, have a much finer resolution
but they consume larger computer time. The three-dimensional rigid-
lid model can be used to obtain detailed temperature and velocity distri-
butions in a domain where surface gravity waves are small compared to
the depth of the domain. This model, as compared to free-surface mo-
dels, runs faster since surface gravity waves are eliminated by the
rigid-1 id assumption.
A proper method of using this model would be to run a one-dimen-
sional model initially to obtain a rough picture of the temperatures and
then using this model to obtain a better resolution, the 1-D results being
used as ambient conditions.
The following improvements have been suggested for the model.
1. Since all natural flows are turbulent, proper turbulent closures are
needed to make the model meaningful. At present, the simplest
possible closures, namely constant eddy viscosities and eddy diffu-
sivities, have been used. However, better results may be obtained
by using a higher order closure.
2. At present, the model uses uniform horizontal grids and stretched
vertical grids. Nonuniform horizontal grids could be introduced for
better resolution near the boundaries.
3. The program has been written to be run as a batch-job on the com-
puter. It could be made interactive so as to enable the user to run
it on a terminal. However, this would require some modifications in
order to reduce the storage space.
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SECTION 3
PROGRAM DESCRIPTION AND FLOW CHART
DESCRIPTION OF PROGRAM ALGORITHM
The governing equations for a body of water which are derived from
the basic laws of conservation of mass, momentum and energy are shown
in Table 1. These equations incorporate a vertically-stretched coordinate
system so as to make the model general enough to handle any kind of
bottom topography. The problem is set up as an initial value problem.
The initial values of the water velocities and temperatures are specified
and the model is run so as to give the values of the above quantities in
subsequent time periods using an explicit scheme. The sequence of the
calculations are as follows:
1. The initial values of the velocities and temperatures are read into
the program, the region of interest within the basin being classified
into interior, corner or boundary points. (Subroutines used are
READ 3K, INITIA, INITIT, HEIGHT.)
2. The data, which includes the boundary conditions such as the
various meteorological parameters like surface wind speed, air
temperature, humidity and solar radiation are read into the program
using subroutine READ 2.
3. Depending on the site chosen, the various discharges (volume flow
rate, velocities and temperatures) in and out of the basin are read
into the model. These are incorporated in the subroutine IN LETT.
4. The momentum, continuity and energy equations are now solved to
determine the velocities and temperatures in the subsequent time
steps. The predictive equation for pressure (viz., the Poisson
equation) is solved iteratively to determine the pressures at various
points of the domain. (Note: Because of the rigid-lid assumption,
the surface or lid pressure is no longer atmospheric.)
THE PROGRAM FLOW CHART IS SHOWN IN FIGURE 1
The various subroutines used are as well as a brief description of
their functions are shown in Tables 2 and 3.
Symbols Used in Governing Equations
(Quantities with bar are dimensional)
-------
p = density
T = temperature
Y
e
a
u
V
w
t
e
P
T
= Z/h(n)y
= y/L
= x/L
= "/Uref
= v/Uref
= w/Uref
= f/tref
= H/L
= P/PrefUref2
= T-Tref
p =
Au
A*
B*
ref
p"p
ref
Aw^Aref
A /A ,
B /B .
nondimensionai horizontal eddy viscosity
nondimensionai vertical eddy viscosity
f nondimensionai horizontal eddy viscosity
nondimensionai vertical eddy viscosity
/Aref RB = Uref/fL- Pr = Aref/Bref
-------
Table 1. Governing Equations
Continuity Equation:
3(hu) , 3(hv)
Momentum Equation:
3(hu) 3(huu) 3('huv) .3. (flu) h ...
3t 3a 38 3T ~ RB
D
if
and 3(hv) 3(huv) 3(hvy) . 3(3v) h
3t 3ct 38 3y RB°
O r **\ *\__ « M H
I*. S
1 i
h 3
Hydrostatic Equation:
Energy Equation:
3(hT) 3 (huT) 3 (hvT) A U3(flT)
3t 3 a 38 " 3Y
Pe 3a3a
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SECTION 4
LIST OF PROGRAM SYMBOLS USED IN MAIN PROGRAM
DESCRIPTION OF MAIN VARIABLES
A. A - constant in equation of state, p = A + BT + CT2
AREF - reference eddy viscosity
AA - value of 'V at plume inlet
ABR - 1 /Rossby number
AH - 1 /Reynolds number
Al - coefficient in front of pressure term
AKT - (Ks)(Href)/(Bz)
AP - coefficient in front of pressure term
ARBP - arbitrary pressure
AV - -yi— where e = ?
e p *•
A3 - normalized vertical eddy coefficient of viscosity
ANGLE - wind direction angle
B. B - constant in equation of state, p = A + BT + CT2
BB - value of 'V at plume inlet (at 1=10)
BZ - PCpBv
BV - normalized vertical eddy diffusivity, normalized with respect
to reference eddy diffusivity
C. C - constant in equation of state, p = A + BT + CT2
CC - value of y (constant)
CW - temperature gradient at vertical boundaries
CB - temperature gradient at the bottom
-------
D. D - U at previous time step
D1TZ -
3T
3Z
DPX -
DRY -
DPSX -
DPSY -
3P
3x
3P
3y
3X
3y
DT - time increment
DX - increment in x-direction
DY - increment in y-direction
DZ - increment in Z-direction
DiHUX - H^
3x
D1HVY -
D1HUUX
D1HUVY
D1HVVY
D1UY -
DWX -
D2UX -
D2VX -
DIVWX -
D1UZ -
3(hv)
3y
3(huu)
3X
3(huv)
3y
3(hvv)
3y
3U
3y
3v
3X
32u
3X2
32V
3XZ
3u
JT
-------
D2UZ -
DtVZ -
D2VZ -
D1A3Z -
(DX)2(DY)2
E. E - V at previous time step
EPS - convergence criterion
EUL - Enler number
EX - residual error in pressure iteration
F. FH - forcing function in pressure equation
FW - factor in wind stress calculation formula
G. G - dummy variable for V (for future time step)
H. H - dummy variable for U (for future time step)
HI - nondimensionai depth = r\
HREF - reference depth
HY - If
I. IN - maximum number of grid points in x-directton
IWN - maximum number of half-grid points in x-direction, IWN
IN - 1
1 - index of x-axis, main grid
1TN - index for number of iterations
IW - index for x-axis, half grid
I RUN - index for number of runs
- 0, first run
= 1, from second time onwards
-------
ISGNX, ISGNY - determine signs of TAUX and TAUX respectively
J. J - index for y-axis, main grid
JW - index for y-axis, half grid
JWN - maximum number of half-grid points in y-direction
JWN - JN - 1
JN - maximum number of main grid points in y-direction
K. K - index for Z-axis
KSTORE - specified usage of tape for storing results
KN - maximum number of main grid points in Z-direction
KISS - surface heat transfer coefficient (nondimensional)
L - maximum length of the domain
LN - number of time steps to be computed
LLN - total number of time steps/LN
M. MAR - number to describe general location of a point in the main
grid
MRH - number of describe general location of a point in the half
grid
MAXIT - maximum number of iterations
O. OMEGA - relaxation factor
P. P - nondimensionai pressure
PN - New pressure, nondimensional
PI NTH - dummy variable for pressure (future time step)
R. R - dimensional density at main grid points
RE - Reynolds number
RB - Rossby number
RINTX - density integrated with respect to x
RINTY - density integrated with respect to y
-------
RO - nondimensional density at main grid points
ROW - nondimensional density at half grid points
RREF - reference density (gm/cc)
RW - dimensional density at half grid points (gm/cc)
RADN - solar radiation (w/m2)
T. T - nondimensional temperature at main grid points
TO - initial temperature (dimensional) (°C)
TAMB - ambient temperature (dimensional) (°C)
TAIR - air temperature (dimensional) (°C)
TAI - coefficient in front of convective terms in the energy equa-
tion, = 1.
TAH - K1- where P = R x P
e e e r
TAV - s-l-y where H
e
TE - equilibrium temperature (dimensional) (°C)
TTOT - total time elapsed
TAUX - 3u/3y (nondimensiona!)
TAUY - 3v/3y (nondimensional)
TEM - dimensional temperature at main grid points
TEMW - dimensional temperature at half-grid points
TREF - reference temperature
TW - nondimensional temperature at half-grid points
TLL - temperature at the discharge point (nondimensional)
TSU - water surface temperature (nondimensional)
TDEW - dewpoint temperature (dimensional)
U. U - velocity in x-direction (nondimensional)
V. V - velocity in y-direction (nondimensional)
10
-------
VVIS - vertical eddy viscosity (nondimensional)
W. W - velocity in Z-direction {nondimensional)
WH - W at half-grid points
WHLDT - time derivative of WH at lid (i.e., ~(WH) /Z = 0)
o t
X. XINT - integral of x terms on the right-hand side of Poisson's
equation
X - horizontal coordinate across discharge
Y. YINT - integral of y terms on the right-hand side of Poisson's
equation
Y - horizontal coordinate across discharge
Z. Z - vertical coordinate
MARKER MATRICES
The following number convention is used for the MAR = matrix sys-
tem, which classifies points (or nodes) on the main grid system =
(Refer to Figure).
MAR = 0, points outside the region of interest.
MAR = 1, point on the far y-boundary.
MAR = 2, point on the near y-boundary.
MAR = 3, point on the near x-boundary.
MAR - 4, point on the far x-boundary.
MAR = 5, outside corner on near x-boundary and far y-boundary.
MAR = 6, inside corner on far x-boundary and far y-boundary.
MAR = 7, outside corner on near x-boundary and near y-boundary.
MAR = 8, inside corner on near x-boundary and near y-boundary.
MAR = 9, outside corner on far x-boundary and near y-boundary.
MAR = 10, outside corner on far x-boundary and far y-boundary.
MAR = 11, points in the interior of the region of interest.
11
-------
The following number convention is used to describe the MRH (ma-
trix for the half-grid system).
MRH = 1, corner at far x-boundary and far y-boundary.
MRH - 2, points on near y-boundary.
MRH = 3, points on near x-boundary.
MRH = H, corner at near x and near y-boundaries.
MRH = 6, far corner on x-axis.
MRH = 7, corner at far x and y-boundaries.
MRH = 9, interior grid points.
12
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SECTION 5
PREPARATION OF RUNS
This section presents the steps to be followed in order to run the
model for a particular location.
1. The boundaries are chosen depending on the particular situation, the
general idea being to include all inflows and outflows. If a heated
discharge enters the body of water the region of interest must be
chosen so as to include this since it is a major factor in determining
the size and spread of the resulting plume.
2. The grid size is chosen depending on the resolution required. The
user should remember that the choice of the grid size directly deter-
mines the maximum allowable time step since this is directly re-
lated by the various stability criteria. (See choice of time step in
Section 6.)
3. Specify number of full-grid points IN, JN, KN and number of half-
grid points IWN, JWN. Since the actual domain may be smaller than
the total rectangular region, INxJNxKN, the marker matrices MAR
and MRH are used to specify the domain so that points outside the
domain of interest skip the subsequent calculations.
4. IRUN is specified (= 0 for the first run, = 1 for subsequent runs).
KSTORE is specified to indicate whether any tape has been assigned
to store results of the run.
KSTORE = 0 if no tape has been assigned.
= 1 if tape has been assigned.
LLN is specified to denote the number of hours of simulation to be
carried out.
5. The depths at various places within the domain are specified using
subroutine HEIGHT. The various inflows and outflows to the domain
are specified using INLET1. (For details please refer to Biscayne
Bay run, Sengupta et al. (1975).)
6. The various data like solar radiation, wind speed, wind direction and
dewpoint temperature are specified in a data file which is made by
the main program.
For further details see the next section.
13
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SECTION 6
INPUT DATA
The data that is required for the execution of the main program is
listed in Table 3 in the order it appears. Note, the data input symbols
have already been defined in Section 4. Moreover, the following remarks
should be observed.
* Free format is used for all data input.
* Distinction must be made for integer and real number.
* The order of the cards must be followed.
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SECTION 7
PLOTTING PROGRAMS
The plotting programs for the 3-D rigid-lid model are distinct from
the main program and subroutines used to run it. The user has an
option of either using a tape (Unit 8) during running the main program
TMAINN to store the results or just run it without storing the results.
For making subsequent continuation runs of TMAINN all that is required
is the result of the last hour in the previous run. For plotting, however,
one needs the results of all the hours for which results are to be plotted.
These results are used as input data to run the various plotting programs.
DESCRIPTION OF PLOT PROGRAMS
The following are the main plotting programs.
PLOT - plots surface isotherms.
PLUV - plots u, v components of the velocities (i.e., 'K' sections).
PLUW - plots u, w components of the velocities (i.e., ']' sections).
PLVW - plots v, w components of the velocities (i.e., '5' sections).
SUBROUTINES
The various plot programs and subroutines are shown in Table 4.
Other subroutines seen in these programs (e.g., ARROHD, FLINE,
etc.) are standard FORTRAN subroutines used for plotting, using a
CALCOMP x,y plotter, and are hence ommitted in the above listing.
15
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REFERENCES
Lee, S., Sengupta, S., Nwadike, E. V. and S. K. Sinha. Verification
of Three-Dimensional Rigid-Lid Model at Lake Keowee. Technical
Report 1980, NASA Contract NAS 10-9410.
Sengupta, S., Lee, S. S. and R. Bland. Numerical Modeling of Circu-
lation in Biscayne Bay. Transaction of the American Geophysical
Union, June 1975.
Sengupta, S. and W. Lick. A Numerical Model for Wind-Driven Circula-
tion and Temperature Fields in Lakes and Ponds. FTAS/TR-74-98,
1974.
Wilson, B. W. Note on Surface Wind Stresses Over Water at Low and
High Wind Speeds. Journal of Geophysical Research, Vol. 65,
No. 10, 1960.
16
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APPENDICES
17
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APPENDIX A
EXAMPLE CASE
INTRODUCTION
The area of interest is Lake Keowee in South Carolina, which was
formed from 1968 through 1971 by damming the Little and Keowee rivers.
The lake is located about 40 km west of Greenville and constitutes Duke
Power Company's Keowee-Toxaway complex.
Lake Keowee has two arms connected by a canal (maximum depth
30.5 m). There are three power plants on the lake, namely, the Oconee
Nuclear Station, Keowee hydro station and Jocassee-pumped storage
station. The Oconee Nuclear Station is a three unit steam-electric sta-
tion with an Installed capacity of generating 2580 MW. The Oconee
Nuclear Station draws in condenser-cooling water from the lower arm
of Lake Keowee and discharges the heated effluent to the upper arm of
the lake. The intake structure for the condenser-cooling water allows
water from 20 to 27 m depth (full pond) to pass through. The discharge
structure has an opening from 9 to 12 meters below the water surface
(full pond) through which the CCW returns directly to the upper branch
of the lake.
Lake Jocassee is located north of Lake Keowee and is used as a reser-
voir for Jocassee-pumped storage station. Lake Keowee also serves as
the lower pond for this station. The Jocassee station has reversible
turbines with a maximum generating flow (into Lake Keowee) of about
820 m3 /sec and a maximum pumping flow (out of Lake Keowee into Lake
Jocassee) of about 775 m3/sec, the net flow into Lake Keowee from Jocas-
see being about 15.5 m3/sec.
Lake Keowee has a full pond elevation of 243.8 £i above MSL. At
full pond it has a volume of approximately 1.18 x 10 m3, an area of
74 km2, a mean depth of 15. 8 m and a shoreline of about 480 km. The
outflow from Lake Keowee is through Keowee hydro station and may vary
from approximately 1.4m3/sec (leakage) to 560 m3/sec. Maximum allow-
able draw-down of the lake Is 7.6 m.
A map of the area of interest is shown in Figure 3.
PROBLEM STATEMENT
The objective of the present work is to find the three-dimensional
temperature and velocity distributions in the region where the effects
of the thermal discharge are noticeable. The effects of Jocassee-pumped
18
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storage station, Keowee hydro station as well as the meteorological condi-
tions have been incorporated.
The region of interest is chosen to include the effects of the Oconee
Nuclear Station discharge, the outflow through Keowee dam and the impact
of the Jocassee-pumped storage station on the velocity and temperature
distributions in Lake Keowee. The depth of the domain is cut off at 16
meters, since this is the level at which the thermocline occurs. Hence,
for running the model, a constant depth region is considered. The plan
view of the domain is shown in Figure 4. (Note: For variable depth
refer to Biscayne Bay simulation studies by the University of Miami
thermal pollution group.) In this Figure, AB is an open boundary which
takes care of the flow from or to the Jocassee-pumped storage station.
'C1 shows the position of the flow in the canal connecting the two arms
of the lake. 'D1 is the discharge point for the Oconee Nuclear Station
and 'E1 is the outflow from Keowee hydro station.
The inclusion of the above results in a domain 2895. 6 m x 2438. 4 m
in the horizontal plane. The horizontal grid size (in x and y directions)
is 152.4 m x 152. 4 m, giving a total of 20 x 17 (= 340) nodes in the
horizontal plane, out of which 293 lie in the region of interest. The
16m constant depth region of interest is divided into 4 equal slices of
4 m each, giving at total of 5 nodes in the vertical (Z)/direction.
Hence, there are 293 x 5 nodes (grid points) in the region of interest.
This region is specified using the MAR and MRH marker matrices (Figure
5 and Figure 6).
Boundary Conditions
On the Jocassee effect boundary, the flow .velocity (varying with
time) is specified. Open-boundary condition (-^— = 0) is specified for
the temperature. v
The same is done for the Keowee hydro boundary. The only differ-
ence is that the values specified are at three points in the vertical plane
(i.e., at K = 1, 2 and 3) since this region covers the discharge area.
For the Oconee Nuclear Station, the discharge velocity as well as
the discharge temperature is specified at the discharge point.
Open-boundary conditions are specified for the temperature and
velocity at the canal. This, however, leads to a possible violation of
mass balance in the region of interest. This mass unbalance will
actually show up as a variation in the water level in the lake which is
beyond the capability of the rigid-lid model.
At all solid boundaries as well as the artificial bottom (since the
bottom is cut off at 16m) perfect insulation (temperature gradient = 0)
and zero velocity conditions are assumed.
At the surface, the vertical component of the velocity is specified
19
-------
as zero (rigid-lid constraint). Surface wind shear stress and heat
transfer coefficient are specified.
Initial Conditions
The initial values of the water velocities are assumed to be zero.
The initial temperature of the lake is assumed to be equal to the am-
bient water temperature (determined by running a one-dimensional
model) and is taken to be uniform throughout the domain.
CALCULATION OF PARAMETERS AND INPUT DATA
Reference Q uantities
Reference length = L = maximum length of the domain = 2895.6 m.
Reference horizontal eddy viscosity A - = 0.002 L 4/3
= 38311.48 cm2sec.
For better agreement with data the value chosen is 60,000 cm2/sec.
Reference depth = H = 16 m.
Reference vertical AV = 0.002 x (H) 4/3.
Eddy viscosity = 37.43 cm2/sec.
Reference velocity = V . = 30 cm/sec.
Reference temperature = T f = 10.0°C.
Reference time = L/V f = 9652 sec.
Calculation of Inflows and Outflows into the Domain (Used in INLET!)
Oconee Nuclear Station Discharge Velocity—
The discharge is considered to take place through a point at a
depth of 12 m (k = 3). The discharge velocity is calculated as follows:
12 m
152.4 m
The total discharge into the basin is equal to:
(100 ~ x V x 152.4 x 12) = Q
20
-------
where Q = average discharge in m3/sec
= 7.42207 cm /sec
The average values of Q over 24 hrs is taken since the variation
is negligible.
V V
Nondimensional discharge velocity = ^— = -^ = 0. 24740
ref
Keowee Hydro Discharge Velocity—
The outflow through the Keowee hydro station is through a channel
152.4 m x 12 m.
The volume flowrate Q = (152. 4 x 12 x V) m3/sec
where V = discharge velocity (m/sec)
Q
.*.V = [Q/O52.4 x 12)] m/sec =
) cm/sec
152.4x12x100
Q is specified as a function of time in IN LETT.
The procedure for nondimensionalization is similar.
Jocassee Flow Velocity—
The entire flow to or from the Jocassee-pumped storage station is
assumed to take place through the entire upper boundary (AB in Figure
4). The flow through this area (shown below) is assumed to be uniform
and is assumed to take place simultaneously with the outflow through the
Jocassee station.
*^ +s
^ v
^
\
16 m
f
V = Q/[(16xl3xl52. 4) x 100] cm/sec.
Q = flow through Jocassee (m3/sec).
Q is positive when Jocassee is generating (i.e., the flow is into
the region of interest) and negative when pumping (i.e., flow out of
region of interest).
21
-------
SAMPLE INPUT
The following are the inputs to TMAINN contained in the data file
IPUT (which includes values calculated earlier).
Input
I
1
No. of Data
In Card
Symbol
Value
IRUN
KSTORE
LLN
VVIS
ABR
A!
AH
AV
AP
EPS
MAXIT
OMEGA
ARBP
DX
DY
DZ
TAI
TAH
TAV
A
B
= 0
= 1
«• O
= 37.43/60,000 = 0.00062
= 0.78
= 1.0
60,000 _ Q
30 x 2895 x 100
,2895.62
1 16 J AH 402'08-
= 1.0
= 0.001
= 60
= 1.8
= 1.0
= 152.4/2895.6 = 0.05263
= 0.05263
= 4/16 = 0.25
= 1.0
= AH = 0.01228172
= AV = 402.08304
= 1.000428
= -0.000019
22
-------
Input
#
8
9
10
11
12
13
14
15
16
No. of Data
In Card
1
3
1
1
6
17
Symbol
C
TO
EUL
CW
CB
AA
CC
TLL
TAU
DT
Value
= -0.0000046
= 10.0
980 x (16x100) _ ljr „„„
= 0.0
= 0,0
= 0. 24740
= 16/16 = 1.0
31.7 - 10
10
= 0.0152 cm2 /sec
Criterion (convectjve)
Ax 152. 4 x 100
~ uv " U 30
- 504 sees > 504 sees
CTTOT
1SOTOP
WS
TSU
TDEW
RADN
1SCNX
ISGNY
ANCLE
Hence, convective criterion
dominates; choose AT = 300
DT - AT - 3QO - o (mnai
UT - t f ~ 9652 ~ °-031081
rer
Note: choose best time step
trial and error
= tref/3600 = 2.6811111
= 0
See Table 5
See Table 5
sees
64
by
23
-------
LAKE KEOWEE APPLICATION-EXECUTION DECK
The following execution deck is for use in the UNIVAC 1100 computer
at the University of Miami. These may have to be modified if a different
computer is used.
(ALL PROGRAMS AND SUBPROGRAMS COMPILED AND STORED IN FILE)
First Run
1. 9 ASG, AX FILE.
(THE FILE IS ASSIGNED FOR THE RUN)
2. 9 ASG,T 8, 16N, TAPENAME.
(A TAPE FILE NAMES '8' IS BEING ASSIGNED. THE TAPE IS
9-TRACK, AND THE REEL NUMBER IS TAPENAME')
3. 9 PRT,S FILE. TMAINN
(THE MAIN PROGRAM IS PRINTED)
H. 9 PACK FILE.
(THE FILE IS PACKED)
5. 9 PREP FILE.
(ENTRY POINT TABLE IS PREPARED)
6. 9 MAP,S
7. IN FILE. TMAINN
8. LIB FILE.
9. END
10. 6 XQT
11. 0
(VALUE FOR IRUN,FIRST RUN: IRUN=0)
12. 21
(NUMBER OF HOURS REQUIRED, MINIMUM=1 HOUR, MAX=24)
-------
13. 0
(0 IF MAGNETIC TAPE IS REQUIRED TO STORE RESULT, IF
NOT, ANY NUMBER)
14. 9 ADD FILE. INPUT
(INPUT DATA FILE FOR THE PARTICULAR RUN)
15. 9 FIN
EXECUTION DECK FOR PLOT PROGRAMS
1. 9 ASG,AX FILE.
2. 9 ASG,T 8., 16N, TAPENAME.
3. 9 ASG,T 11., 16N, PLOTTAPE.
(A MAGNETIC TAPE FILE NAMED '1T IS BEING ASSIGNED. THE
TAPE IS 7-TRACK AND THE REEL NUMBER IS 'PLOTTAPE1. THE
PLOTS ARE STORED ON THIS TAPE)
4. 9 PRT,S FILE.PLOTTER
(THE PLOT PROGRAM IS PRINTED)
5. 9 PACK FILE.
6. 9 PREP FILE.
7. 9 MAP,S
8. IN FILE.PLOTTER
9. LIB FILE.
10. END
11. 9 XQT
12. 9 ADD FILE. INPUT
13. 9 FIN
25
-------
Table 2. Subroutines Required in Main Program TMAINN
No.
Name
Description
Remarks
9
10
11
DVISV
DVISU
DVVY
DUVY
DINERU
TPRINK
PRUV
PRITEX
TPRIN1
STORE2
RWR
Computes D1VY, D2VY, D1VX
and D2VX.
Computes D1UX, D2UX, and
D1UY.
Computes D1HVVY,
Computes D1HUVY.
Computes D1HUUX and
D1HUVX.
Prints temperatures at a grid
point.
Prints the values of U and V
at all main grid points.
Prints the No. of iterations
(1TN) and final residual error
in solving the Poisson equation
Prints the input parameters.
Stores values of input para-
meters and physical quantities
on tape #8
Computes real vertical veloci-
ties from modified vertical
velocities used in equations at
integral grid points.
Called by subroutine INTE.
Schemes used similar to
DVISU.
Called by INTE.
3 y 3u
V*ailBU Wjr •«"» « ^-« r, I n. o
are computed at interior,
boundary or corner pts
by scheme similar to the
one used in DINERU.
Called by INTE. ~ (hvv)
is computed for inferior,
boundary or corner by a
scheme similar to the one
used in DINERU.
Called by INTE. j- (huv)
is computed for interior,
boundary and corner pts
by a scheme similar to the
one used in DINERU.
Called by INTE. The re-
suits are used in Poisson
equation for pressure.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
26
-------
Table 2. Subroutines Required in Main Program TMAINN (Continued)
No.
Name
Description
Remarks
12
13
14
RWRH
DENSTY
TEQB
15
OLDT
16
17
18
19
TEMB2
TEMU
RWH
OLDUV
20
UVTOP
21
UVT
Computes real vertical veloci-
ties at half-grid points.
Uses the equation of state and
computes density field from the
temperature field.
Allows for vertical mixing at a
particular grid point. Program
is called by TMAINN.
Sets the values of temperature
field at time step 'n' equal to
the temperature field at (n+1)
after ail computations for time
step 'n1 are completed.
Computes temperatures at the
boundary points in the domain
of interest.
Computes temperatures at the
interior points of the domain of
interest.
Computes vertical velocities at
half-grid points.
Sets the values of D and E
equal to U and V respectively
in order to retain values of U
and V at one time step lag.
Computes U and V at the top
using wind stress boundary
conditions.
Computes U and V for variable
density at successive time
steps.
Called by TMAINN,
Called by TMAINN.
If the temp at the grid
pt just above it is less
and the difference is more
than a specified maximum,
the two temperatures are
averaged.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN,
Called by TMAINN.
Called by TMAINN. Com-
Dutations are made for
WAR = 11 only (internal
grid points).
Called by TMAINN.
27
-------
Table 2. Subroutines Required in Main Program TMAINN (Continued)
No.
Name
Description
Remarks
22
23
24
25
26
27
28
29
30
31
32
33
34
PRE1L
FORCE
DPSXY
ROINTY
ROINTX
CORINT
INTE
WHATU
WHTOP
ERROR
READ 2
INLET 1
HEIGHT
Computes pressure for far
field from Poisson's; Equation
at half-grid points.
Computes R.H.S. of Poisson's
Equation at half-grid points.
Computes DPSX and DPSY.
Computes Y in the Poisson's
Equation. p
Computes X in the Poisson's
Equation. p
Adds integral of Coriolis1
component XI NT and YINT.
Computes XINT, YINT, DPSX,
and DPSY.
Computes the values of W at
I, J from the values of WH at
IW, JW.
Sets the value of WH equal to
zero at the surface.
Calculates "Hirt and Harlow"
correction term at half-grid
points and at the surface
(WHLDT).
Reads in input parameters and
physical quantities stored on
tape #7.
Puts in velocities u and v
pheme discharge, etc. into
the model.
Inputs depths of the basin
into the model.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Called by INTE.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
Corresponds to store 2.
Called in by TMAINN.
Called by TMAINN.
This subroutine is for a
constant depths model.
Called by TMAINN.
28
-------
Table 2. Subroutines Required in Main Program TMAINN (Continued)
No.
Name
Description
Remarks
35
INITIT
36
37
INITIA
READ 3K
38
I PUT
Sets initial temperature field.
Initializes values of U, V, WH,
W, D, E and PINTH.
Classifies region of interest
into interior, corner and
boundary points using matrix
MAR.
Data files containing values of
input data for the respective
days.
Sets the temperature field
equal to ref temp at all
grid points.
Called by TMAINN.
Called by TMAINN.
Called by TMAINN.
29
-------
j Read data cards
First run? (1RUN = 0)|.
1
READ 2 - Reads tape for
data of previous run
1NLET1 - Inputs V, U,
TD to start run
READ3K - Classifies the re-
gion into interior, corner or
boundary points.
INITIA - Initializes U, V, W,
WH, D, E and P.
I NIT IT - Initializes T and p.
HEIGHT - Inputs depth.
INLET1 - Inputs V, U, TD
TD to start run.
ERROR
WHTOP
WHATIJ -
INTE
ROINTX -
ROINTY -
DPSXY
FORCE
PREtL
UVTOP -
OLDUV
RWH
WHATIJ -
TEM14
TEMB2
OLDT
TEQB
DENSTY -
INLET1 -
Computes WHLDT
Sets WH equal to zero
Computes W
Computes XI NT, YINT, DPSX and DPSY
Computes Xp
Computes Yp
Computes DPSX, DPSY
Computes FH
Computes PN
Computes U and V at the top
Sets D = U and E = V
Computes vertical velocities at half-grid points
Computes W at grid points
Computes temperatures at interior points
Computes temperatures at boundary points
Updates temperatures
Allows for vertical mixing
Computes density field
Inputs V, U and TD every time step
* M«
Yes
RWRH - Computes real vertical velocities
RWR - Computes real vertical velocities
STORE2 - Stores computed results on magnetic tape (unit 8)
TPRIN1 - Prints input parameters
PRITEX - Prints number of iterations and error
Figure 1. Flow chart (main program)
30
-------
PRUV - Prints U and V
TPRINK - Prints temperatures
Time Up?
No
Yes
Put another EOF on tape (unit 8)
i
Stop
Figure 1 (Continued). Flow chart (main program)
-------
J=l J=2
J=Jn
THERMAL
DISCHARGE
I=IN
Figure 2. Coordinate and grid system
32
-------
Table 3. Input Data to TMAINN
Input
f
1
2
3
4
5
6
No. of Data
In Card
3
2
4
4
»
4
3
3
Symbol
IRUN
LLN
KSTORE
VVIS
ABR
Ai
AH
AV
AP
EPS
MAXIT
OMEGA
ARBP
DX
DY
DZ
TAI
TAH
Definition /Value
= 0 for first run
= No of hours of simulation
= 0 if no tape is assigned
= 1 if tape is assigned
= Nondimensional vertical eddy
viscosity
= 1 /Rossby No. = rp=-
ref
= Coefficient in front of inertia
term =1.0
= 1 /Reynolds No. =
Ref eddy hoz viscosity
Uref ' L
= (1/s2Re)(e = H/L)
= Coefficient in fron of pressure
term = 1.0
= Convergence factor = 0.001
= Maximum number of iterations
for Poisson Equation
= Relaxation factor = 1.8
= Arbitrary pressure = 1.0
= Horizontal grid spacing (x dir.)
= Horizontal grid spacing (y dir.)
= Ay/L
= Vertical grid spacing (z dir.)
= AZ/H
= Coefficient of Convective terms
in energy equation = 1.0
= Horizontal eddy diffusivity
= AH (usually)
33
-------
Table 3. Input Data to TMAINN (Continued)
Input
ft
7
8
9
10
11
12
13
U
15
16
No. of Data
In Card
3
1
3
2
1
1
1
1
1
6
Symbol
TAV
A
TO
EUL
CW
CB
AA
CC
TLL
TAU
DT
CTTOT
ISTOP
WS
TSU
TDEW
RADN
Definition /Value
= Vertical eddy dfffusivity
= AV (usually)
= 1.000428 These are coefficients
= -0.000019 in the equation of
= -0.0000046 state for water where
p = A + BT + CT2(gm/cc)
= Reference temperature (°C)
_ prlior Mn _ 9"
— CUICI INO. — ("f I •» J
ref
= Temperature gradient at vertical
boundary
= Temperature gradient at the
bottom
- Nondimensional discharge velocity
= (discharge velocity) /U f
= No dimensional depth = h/H f
= Nondimensional discharge tem-
perature = (TD - TQ) /TQ
= Surface shear stress (from Wilson
Curve) (Refer to Figure 7)
= Nondimensional time step
= AT(L/Uref)
= Converts nondimensional time to
hours
= Number of hours of previous run
= Wind speed (m/sec)
= Air temperature (°C)
= Dewpoint temperature (°C)
= Incident solar radiation (w/m2)
-------
Table 3. Input Data to TMAINN (Continued)
Input
#
No. of Data
In Card
Symbol
Definition /Value
ISGNX
17
ANGLE
= +1 if x component of W is
negative s
= -1 if x component of W is
positive s
= +1 if y component of W is
negative s
= -1 if y component of W is
positive s
= Direction of W (degrees) with
respect to the x axis
35
-------
Table 4. Plotting Programs
No.
1
2
3
4
5
6
7
Name
PLOT
PLUV
PLUW
PLVW
ECHKON
CONLIN
ENDER
Program Description
Plots surface isotherms
Plots velocities, K section
Plots velocities/ j section
Plots velocities, i section
Calculates equal temperature points
Draws the isotherms
Writes the values of the tempera-
ture on the isotherms
Remarks
Called by PLOT
Called by ECHKON
Called by ECHKON
36
-------
u>
Little
River
Dam
N
Lake
Jocassee
OCONEE COUNTY
Oconee
>coneef?r ' Nuclear Stn.
Nuclear ^Keowee Discharge
Station « Dam
Figure 3. Lake Keowee
-------
OJ
00
Discharge
B
20
Outflow
Fiqure 1. Lake Keowee (region of interest) showing inputs and outputs (for 3-D model)
-------
1000000/3
2 _0 0 0 0 0 0 2 11
30000 73611
4 Q 0 0 0 2 11 11 11
50000 93 11 11
6000002 11 11
7007338 11 1!
8 0 0 2 11 I'l 11 11 11
9 0 0 2 11 11 11 11 11
10 7 3 S 11 11 11 11 11
11 2 11 II 11 11 11 11 11
12 9 4 4 4 4 S 11 11
1 30000 094 3
1 4000 0000 2
15 00000002
16 00000002
17 00000009
3 3
11 11
11 11
11 11
11 11
11 11
11 11
11 11
11 11
11 11
11 11
11 11
11 11
11 [~6
11 1
n i
4 10
333
11 11 11-
11 11 11
11 11 11
11 11 11
11 11 11
11 11 11
11 11 11
11 11 11
11 11 11
11 11 11
643
1 0 2
10 0 9
000
000
000
3
11
11
11
11
11
11
11
11
11
11
11
11
8
2
Q
0
3
11
11
11
11
11
11
11
6
1
6
11
11
11
11
u
0
3
11
11
11
11
a
11
6
10
0
3
11
11
n
n
~5
0
T
11
6
I
1
6
1
8
2
9
5
1
1
6
11
4
0
3 3
11 11
4 4
0 0
0 0
3 3
11 11
11 6
11 1
4 10
0 0
0 0
0 0
5 0
1 0
10 0
0 0
5
1
10
0
0
5
1
10
0
0
0
0
0
0
0
0
0
Figure 5. MAR marker matrix
39
-------
1 0000004, 10 tQ
20000002 9 9
300004 10 9 9 9
40000699 9 9
sQOO.0029 9 9
50000029 9 9
7 Q Q 4 10 10 9 9 9 9
3002999-9 9 9
90029999 9 9
in i 10 Q ° 9 9 9 9 9
11 6333399 9 9
12000006S 9 9
'30000000 2 9
14 0 0 0 0 0 0 0 ' ' 2 1
150000000 2-1
16 0 0 0 O.O'O 0 6 1
to to to to to to '
9 9 9 9 9 ' 9
99999 9
9 9 9 9 9*9
999999
999999
99999 9
999997
9 ; 9 9 9 1 0
9 : 9 9 9 1 o
9 |3 8 9 9 10
100299
7.0 0 6 9 9
0, 0 0 0 2 9
0 0 Q 0 6 3
000000
0 !0 10
988
1 0 0
1 0 0
\ 0 0
9 10 '.0
,
T[ 9 9
L
0 2 I
067
000
300
100
1 0 0
9 3 0
370
000
3
7
0
0
0
3
7
0
0
0
0
0
0
0
0
0
Figure 6. MR.H marker matrix
40
-------
Table 5. Meteorological Data for Lake Keowee (February 27, 1979)
Time
(hrs from
midnight)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Wind Speed
tm/s)
1.833
1.073
2.325
1.565
2.056
1.788
2.012
2.280
0.626
1.386
1.609
1.788
3.129
2.593
1.520
1.207
1.565
1.609
2.056
1.162
1.772
2.861
2.995
1.386
Air Temp
(°C)
-0.33
-0.72
-1.61
-2.22
-1.83
-2.17
-2.72
-1.67
0.01
3.06
5.83
8.83
11.06
12.28
13.39
13.89
13.83
13.72
11.72
9.72
8.33
7.78
7.00
5.28
Dewpoint
Temp
(°C)
-2.78
-1.67
-1.61
-2.28
-1.89
-2.22
-2.78
-2.78
-3.33
-2.22
-2.22
-1.39
-2.78
-5.00
-5.56
-5.56
-5.61
-3.33
-4.44
-2.78
5.28
5.56
5.28
3.89
Solar
Radiation
.tw/nv2)
0.0
0.0
0.0
0.0
0.0
0.0
20.94
1 95. 39
369. 85
544. 31
655. 31
725. 75
746. 68
704. 81
579. 20
383. 81
1 46. 55
20.94
0.0
0.0
0,0
0.0
0.0
0.0
Wind
Direction
(Degrees)
15°
75°
60°
15°
50°
85°
85°
60°
5°
75°
15°
40°
80°
70°
80°
75°
55°
15°
30°
25°
55°
55°
50°
60°
41
-------
Table 6. Inflows and Outflows to Lake Keowee
Time
Feb. 27, 1978
12,00 a, in..
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 p.m.
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
9.00
10.00
11.00
12.00 a.m.
Oconee
Discharge
(m2/min)
7505. 3
7498. 1
7492.0
7492. 0
7491.6
7494. 3
7488. 2
7481.8
7485. 6
7488. 2
7497. 7
7504. 1
7503.4
7506.0
7506.4
7503.4
7501.9
7507.5
7511.0
7516.2
751 8. 9
7520. 4
7516.6
7509.4
7507. 2
Oconee
Discharge
Temp (°C)
18.6
18.5
18.4
18.5
18.3
18.3
18.3
18.2
18.3
18.2
18.3
18.3
18.4
18.5
18.5
18.4
18.4
18.4
18.4
18.4
18.3
18.2
18.2
18.2
18.2
Net Jocassee
Flow
(C.F.S.)
-14395
-18754
-18805
-18713
-18698
-18688
-15939
3484
16823
13503
5470
100
100
100
100
100
100
100
100
100
100
100
100
100
-4382
Keowee Hydro
Flow
(C.F.S.)
48
48
48
48
48
48
48
3668
17540
8488
8096
2680
48
48
48
48
48
48
48
48
48
48
48
48
48
42
-------
16"
o
o
o
X
CO
2 8
o
12
TIME (HOURS]
24
Figure 7. Keowee hydro discharge (February 27, 1979)
-------
20 •
o
o
o
w
•
en
*
SM/
Ed
s
S
20
12
TIME (HOURS)
Figure 8. Jocassee-pumped storage station discharae
data (February 27, 1979)
-------
APPENDIX B
FORTRAN SOURCE PROGRAM LISTING
-------
LIST OF MAIN PROGRAM AND SUBROUTINES
46
-------
1 1 ,TMA INN FOR CREATED ON 5 HAY au AT
•> C« THIS IS THL MAIN PROGRAM FOS THF 3-0 RIGID-LID MODEL
3 £ •»»»»*«»»•*•«»*•** »»*»»»»»«*»**»»»»w*»«»»»»»**«»«»»»«»"«*wi* A •»»
<* C
'.?
6 PARAMETER INS17.JN = 20t»N = !»iI«fJ=l
7 DIMENSION UllN,JN,KN),!,£lIN,JN,*NI,
9 CkhLOT ( I UN , JWN) , X INT UN , j;. I , YINf I IN . JN ) ,hl IN, JH , UN I , Gt IN , jN , *N ) ,
10 CHlHX(JN,j>l),HYIlN,jN>,«ARtiN,JM,f"RH(!.iN,J..NI,FH,1UtlN,JN,l6
CO 61 LLS£=l,ISTOP
READ 2f-Sf TSU»TOCu,fliON, Ii&NX,IS(jN»
REAC 2.AN3LE
PRINT 161 .WSiTSU, TOEn.KAOHiANGLt ,HI IOT ,
161 FORMAT I IX ,61 • , • ,f 12.6) ,21 ', ' , 15) )
t 1 CONTINUE
oti, CONTINUE
006LLI1.LLN
, ISu'M , ISGf. f
-------
79 HEAD 2, ANGLE
iC PRINT 1«>1 ,WS ,TSU,TOEu,RAON, ANGLE .ilTTOT , jS&NX ,
ZZZ TSU=T
TSJ = TPEF»( l.«TSUi
:3 TTflTlTTOT'OT
3, TTOTlrTTOt I«OT
s5 TM=t TSU'TuEU 1/2.
si COMMENT : TH£ NEXT fc LINES ARE USED TO CALCULATE THE
37 C : EQUILIBRIUM TEMPER ATuRE .
9« C
s5 Fw:9,2*Q.
11' CALL CORlNTII j,K , IN,JH,KN,A6R ,U,V ,XINT ,YINT .OZ.HI ,MAf? )
111 CALL ROINTXII j,K,IN,JN,KN,Ox,OY,0i,RO,AP,EUL ,H I ,
li: CMAR.HIr, TX.HX.XlNT)
113 CALL BOlNfYlI.J.K.IU.JN.XN.DX.uY.Oi.RU.AFsEULiHl.MAR,
11 - CRlNTY.HY.YlNT)
11? CALL 3PSxr;<,OPSY,P,ox,i)Y,i"fAr()
tlf CALL FORCE (I , J ,lw, JW,XINT,YINT.WHLbT.OX,QY,HI,HX,nY,MfiH,
1 i7 CO?SX,OPSY,FH,AP,lN,JN,luN,JwN,fiINTx,RlNIY,U,V,EUL|AaR,MAr<,nfj|
Ms CALL PREILIEPS.MAXIT,IN,.JN,P,ITN,OPSX.OPSY,FH,OLi,OMEGA,
H? ȣiLt ^Xl'I'Jl^iiW'^tlN.JN.KN.lWN.JWN.U.V.O.E.H.U.Ox.OY.UJ,
Ijl CHINTX,fiUfYt£UL,W,OT,AI,AP,AH,AV,A3,Hl,HX,hY,P,,1A^)
I-' CALL UVTOH IH ,G, TAUX, TAUY,! ,J,K ,0i , I\ , J\,I ( I , J, 1 l -Q.Q
1 30 CONTINUE
: 35 CONTINUE
' CALL TE.iim i ,J,K ,IN.JN ,KN,U,V ,T, ri;,ex ,
5 CC5 ,
» Cat,Oi,«,OT,TAr,TAH,TAtffai,hr,Hx,HY,MAiJ,JKT,TReF,IA(lHl
••J CALL T£MS:(I,JtK,TN,JNfKN,TO,Ox,DY,Or,ilAR,CBIHI,AnT,C-.TA-ilj.
1-1 Chx ,HY,T,TREF,TAV ,T*I ,TAH,a3.0T)
i-- CJLL OLDT (I, J,A ,IN, JA,,XN, T,TP )
1-3 CALL OLOTIi,J,K,IN.JN.KN,to,T i
I" CALL TEQfi I I , J,K, It4, JN, (\N, I ,MAR )
}-j CO 2000 1:9,11
i:* C PRINT 9200, (L,I ,H, (VI I . J,H),j;l,jNj)
Ii3 2QGQ CONTINUE
C9i3U DFORKATi/'iL:«,I3,3x,_ .
DO «0 j:1,JN
h I I , J, 1 }-.0\ I,J,1)
!V^C? l ' i 'J1K ' I", Jf., «"iU , V,»!,(,, f , (UiAA.TLC.Ol , hTTO f i
-------
159 PRTT=1.
Si1) IF(TIME.GE .PRTT) GO TO
leC • GO TO 222
Id 4H«* TTOTlrO.Q
CALL R»RHt I , J,K ,IU, Ju , IN, Jtt.KN, IuN, JUN,U, V.WH.ril ,MX ,HY ,
1S<» CALL Ri^R I I |J|K ,IN, JN.Kh.U, U ,WfUR,HI ,HX ,HY ,UZ,MAR)
165 IF USTORE .GT.QI 60 TO iQQQ
1 ;* CAUL STQR£,2IU,V,WH,P,I,J,K,lW,.jW,Iu.JNfKM,IWN,JwN,U,E,HX,H^,
tc7 CrtI,MAR,«HH,iI,AH,iVlAP,DX,Ul',02,i:n>TAUX,Tiuy,W1«iS)l.Sn,TAI,Till,
lei CTAV,AKT.CB,CU,A,S,C,EUL,T,Tw,RO,RO.,Tt.,RR£F,fi?eF,?0,TA.«iB,I!OT)
li>9 lOGO CONTINUE
173 HTTCT:CTTCT*TTOT
171 PRINT 97.MTTOT
1 7? PRINT 9 J.TAUX.TAUY
173 *3 FORMAT! JX, 'TAUXr'.Fll .6, <*X, 'TAUY:' ,F 1 1.61
IT". 92 FORMAT UX, 'TOTAL TIME THUS FAR : • , F 5 . 1 , • Hl?S • , / I
17S C*UL TpfilNlfTAIiTAM.TA^tCa.Cw.AKT.TRtf.RREF.EUL.A.B.C.TE.Tul
i7c CALL PRITEXI JTN.EX >
177 CAUL PHUV ( I , J,K , IN, Jh,AN,U, V ,UA, V A ,nAK)
17= CALL TPRINK i r.JiK , in, JN.MN, T ,«o, TR£F,M«t< .TACTUL i
175 ISTOPrlSTOPM
i=: o CONTINUE
161 END FILE d
13? END
50
-------
A-SA*NA$AI 1 ) .CORINT FOR CREATED ON 5 MAY 80 AT'lO:H&:36
1 T C*»»«»****•**»•******»***»»«*»*««#*»«»*»*+**«********«*»***•«•*••a
2 C THIS SUBROUTINE ADOS INTEGRAL OF CORIOLIS COMPONENT TO xlNT «
3 C t YINT. «
5 SUBROUTINE CORINT(I,J,K,IN,JN,KN,A6R,U,V,X INT,rINT , OZ,H I , -A^)
6 DIMENSION U(IN,JN,KN),V(lN,JN,KNJ,XlNTClN,JN),TlNTIlN,JSJ,Hl(r. ,
7 CJN ) ,HAR(IN,JN)
9 DO 10 1 = 1,IN
9 DO 10 J=1,JN
10 IF (MARIIiJ) .LT.l 1 I GO TO 9
11 00 8 K:2,*N
1? XlNT»ItJ)=XlNTtl,J)-*BH*HltI|JI*IVJl,j,K-l)«vll,j,h))»0*/2
13 YINTII,J):YlNT(IlJ|«ABR4Hl{I,J)*(UII,J,K-l)*U(I,J,M)«C:/2
It 3 CONTINUE
15 9 CONTINUE
16 10 CONTINUE
17 RETURN
18 END
-------
.»SA«f;*iA< 1) .OENSTY FOR CREATED ON 15 MAY 71 sT H:3b:ia
C ThE FOLLOWING PROGRAM CALCULATES TriE DENSITY FIELD FROM
c THE TEMPERATURE FIELO
* SUBROUTINE DENSTlt I I,J,H, IJ, J*,IN, JN,KN, IWN, JUN, A|(J,Ci
t C«AS,HRH,
7 CT ,T*,RO,ROw,RR£F ,Tft£F
QlMENSlON BOtlNiJN »KN> iT« IM.JN.HM
DIM
9 DIMENSION RO. < I*S, JUK.rtN) , Tw I .N,
1C DIMENSION MAR I IN, JN) ,MRHI IfcN, JUN)
11 00 10 1st ,IN
12 00 10 jsl ,JN
13 IF (MAR( I fJ).£Q.Q) GU TO K
i- CO 1 1 Kll ,KN
15 TEH=Ttl,J,K)*TREF«IREF
1? RO(I ,J,K i:iR-RR£F) /RH£F
1- 11 CONTINUE
19 12 CONTINUE
:: ia CONTINUE
21 CO 20 Iw=l,IWN
2."1 DO 2C jw:i ,JbN
.M IF (MRHl U ,jy ) .EQ. 01 GO TO 22
2f 00 21 K:l ,KN
ZS T£MW = TU(I« ,JW,K)*TREF«T»EF
2f, Rb = A»8»T£MW»C*T£HW«TEM«
27 ROh I IW , Jrf ,K )=iRW-RR£F )
25 21 CONTINUE
2^ 22 CONTINUE
ZZ 2d CONTINUE
Jl RETURN
J2 END
52
-------
FOR CREATED ON 5
80 AT 11:00:12"
1
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7
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C THIS SUBROUTINE COMPUTES UIMUUX,
*****
OIHWV
Y rfHICH
C THE POISSON EQUATION FOR PRESSURE.
C
C
SUBROUTINE OINERUII.J.K,
DIMENSION UJt
2,'j,'
1-2,
)
)
J
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J
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1
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— lffJ))/(
K 1 *V( I *1
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t J ) *U 1 I «
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J,K J 1
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ARE USED IY *
a
*************A
|OY,01HUUX,01HUVX,H«R>
1 ,MAR( IN.jNt
I — 1 f J y K )
I-l. JtK )
I— 1 fJtH )
I -1 , J«K 1
I — lt*J(Kl
I-l»JtK \
3»HI I I, J)*UI I, J(X >
/I2*OX)
1 jr 1^1 T t T tt^lilT 1 ul
J)K ) i/IJiox !"'*"' * """ '
2.J.K
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3«HKI, J)«U( I.J.K)
/( 2»QX 1
3*Hl (I ,JJ*U( I,J,H )
/ I2*OX )
I-l » J»K )
I-l, J,X 1
3«HI( I,J1*U< I, J,K1
3*HI C I . J )«U< I • J.K )
J,K 1 )/ (2«DX)
Jl-Ut
J>-Ut
• HI ( I
1-2^ JiK
-t»Hl 1 I
I-
2, J,K
I-l . J,K)
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•I J)*U(T"1 J K)
) )/( 2*OX )
-1 ,J)*U( I-l , J,x 1
1 l/( 2»OX J
53
-------
11 «C CONTINUE • ' ' ~ - '
i~ • 0 inuyx: (J*Hr«ulI-i,JtK>
T! C»U I 1-1 iJi*) «HI ( 1-2, J) »u( 1 -2t JiK )*Ul l-i, J,K I )/ I 2»UX )
C"vll-l,J,«J*HltI-2,J)*Ull-2,J,M*y(!-2,j,H)l/(2«GX)
SO . CCNT
KET
£NO
-------
». CFSXY FOR CHEATED ON 5 MAY 80 AT 11:05:25
C •>» o *» «i o « » » a «JB»»«# *»»*•» «»»»*« «*»»«.«»**v»»»*
C (Hlb SUBROUTINE CALCULATES -CPSX AND QfSf USED IN C0MP- »
C UUNG Tur l.ti.S OF POISSON'S EQUATION AT HALf GRID PO- •
C IMS ' *
7 SU3ROUTINC OPSXYII.J.IN.JN.IU.JW.TUN.jUN.OPSX.OPSt.P.OX.OY.MAP)
£ DIMENSION P(!wN,JWN),OPSX.(IU,JN),OPSY(:N,JN),MARTTN,jN)
« oo 10 ;=I,IN
1C 00 10 J=ltJN
11 I. -I
I" J*-J
i f t
n»R(I,JI.LT.11) GO TO 9
IS •) CONTINUE
17 10 CONTINUE
1" RETURN
! i END
55
-------
; !•«.< «4 ( 1 1 .Obv Y F0f< C9E4TEO ON 5 i**r 80 AT UrOSjOS
? C HIS SUBROUTINE COMPUTES QIHUVY US£0 BY SUB. INTE
SyBPOUTlNr DUVYfI,J,K,IN,JN.KN.U,V ,Hl,OY,Q1HUVY,MAR)
7
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3: 31*
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57
DIMENSION U(
IFIMAR I,J .
IF IMAR I ,J .
IFIMAR I,J .
IF 1 M4R I , J .
IFIMAS I,J .
IF IMAR I , J .
IFIMAR I,J .
IF IMSR I , J) .
IFIMA9 t'jll
QlHUVf-lUi I
"GO TO so'
OIHUVY: i 3»Hi
c*v 1 1 , J-l ,* ) »
GO TO 50
CONTINUE
QIHUVY: HM-HI
f U 1 I , J , * I * V ( I
GO TO 50
CONTINUE
GlHUVYIIIJtl,
CoY(I,J-l,K|»
GC TC 50
CONTINUE
wilMUVY: (U ( I ,
GO TO Sd'
CONTINUE
DliUVYil 3*HI
r«vi i , j-i ,n ) «
GO TO 50
CONTINUE
EQ
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GO TO 50
CONTINUE
D3HUV Yr maHl
CU(I,J,*)*VII
GO TO 50
CONTINUE
Q1HUVY=IU I I ,
GO TO 50*
CONTINUE
0 LHUVYZ I «*HI
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cc ro so
CONTINUE
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56
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xo*zi/((*'rM-l>n-(>(4rM»iini:xnic
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OS 01 CC
05 01 OD
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ixo*zi/ui«'p'z»iin-(Mtr'i»n»f-iM'p|t»lin*»ii:xmn
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-------
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(H.OVISV FOR CREATED ON 5 MAY 60 AT 11:13:50
~ C I«IS SU3B-OU TINE- COMPUTES D I VY , 02VY ,01 V X
SUSROUTI'lE nvISV 1 I ,J,K ,INfjN,KN, Ui V ,H
CM4H 1
C IMC MS I ON U( IN.JN.KN J , VI IN, JN.KN > ,HI f
IF (MiP | I , Jl ,EQ .Ci GO TO 50
iFlMJRII.Ji.EO.l) GO TO 31
IFIMAqi I ,J) .£0.2) GO TO 52
IF I»*AR l I , j 1 .Ea«3 1 GO TO 33
IF 1 Mil? | I , J 1 ,rS .14 ) GO TC 34
IF (Miff 1 I , J 1 .Eo.5 1 GO TO 35
IF |H«o ( i , j) ,E3.fe 1 GO TO 36
IF (PA* 1 I , Jt.EQ.7) GO TU 37
IF|MiR|[,JI.EQ.8) GO TU 38
IF (MARI I .JI.E0.9 I GO TO 39
IF tnA3 t I , J) .EC.10IGO TO '»Q
01Vxriv(I*l,j,Kl-V(I-l,j,K) )/ 2*0x)
i:iVY:iVII,J«l,K)-V(I,J-l,K))/ 2*DY)
U2VX:t\,II'ltJ.K)-2»V(I,J,K)«V I-1,J,K
0*VYSIV(I,J«l,K»-2'»V4l,J»KJ»V I,J-1,K
GO TO SO
31 CONTINUE
01Vx:ivtl«l,J,iU-ViI-l,j,KM/ 2*OX)
02vx:(V(I»l,J,K)-2»V( I,J,n)«V I-l.J.K
DlVY:tJ*VII,Jf«)-<»»V«vil»J,K
00 TO SO
311 CONTINUE
3lVY:tVtI.J«l,K»-VII,J-lfKI I/(2*OY 1
U2VY:|VIIfJ»l,KI-2*VII,J,K)*VIItJ-l,K
ClvX=l3«V(IiJtK)-H»VlI-l,J.K|*V(l-2,J
C2vx:(V(I,J,K)-2«VlI-!,J.Hi»V(I-2,J,K
GO TO 50
3S CCMTIVUE
LlVYCl3«V(I,J,iM-M*VII,J-l,K)-»V(I,J-2
02vr:iV(l,J,K)«vtI,J-z,H)-29VII,j-l,K
Clvx:t'4*viI»l,j.K}-3«viI,J,x)-vil«2,J
02vx:iv(l«2.j,Hl-?*viI«lfJ,K)*V(I,j,K
GO TO 50
•$<• CONTINUE
01VX:iV(I«llJ,KI-V(I-l,J,KI)/(2*OXI
D1VY:(VII,J»1,K1-VII,J-1,KI1/I2*QYI
D2^x:lviI«l,J,K)-2»V(I,J,K)«viI-i,j,K
22^Y:ivlIiJ*liKi-2«VlI,J,Kj»vil,j-i,K
30 TO 50
37 CCNTINUE
02VY:iV(I,J»2 K)«V(I,J,)tl-2«VII,J«l,K
Oivx:tmvil«l j,Ki-l*vtI|J,K)-v«I«2.J
02vx:iv(I*2iJ K)-2*viI«lfJ,Ki»v(l,j,K
GO TC 50
if CONTINUE
Oivx:|vil«ltj K)-VII-1,J,KI)/I2*OX1
QIVY:IVII,J»I Ki-viI,j-i,x)i/l2*OY)
22vx:iVII»l,J H)-2«VII,J,KI»VII-1,J,K
Q2VY:1V1I,J«1 K)-2«VlI,j,KMVII,J-l,K
GO TO 50
3« CONTINUE
OlVY:m»vir,j«i,K»-l»v(l,j,K»-v(I,j«2
C2vY:
1 I /IOX*OX 1
i i /i DY*OY i
1 )/ (OX*QX )
,K ) )/ 1 2*OY )
I )/ (DY*OY )
) I/ (OX*OX 1
,H I )/ 1 2*OY 1
) )/ (OY«OY )
) ) / IOY*OY )
,K 1 ) / 1 2*OX )
) ) / 1 OX«OX )
1 I/ (OY*OY )
,K ) 1 / 1 2*0X1
1 I/ (DX*OX )
,K ) )/ I2*OY)
1 )/ (OY«OY »
tK ) ) / 1 2»OX)
) )/ / l 2«OX)
1 1/ IDX*OX i
) )/(OX*OX )
) i /i DY*OY >
,K ) )/ (2*DYI
) )/IDY*OY )
,K ) ) / 1 2*0X1
) )/ I OX*Ox )
59
-------
79 DlvY = l3*VIJ,J,A)-t»V(I,J-l,K>*V(I,j-2,«M/(2*Or»
.. C2vxrl v I I ,J,K )-2»V I 1-1 , J,K ) «v I 1-2, J,K I I / (Dx»0x )
50 CONTINUE
RETURN
60
-------
i.Cv\lY FOR CF)t*TEO ON •> MAY 3C AT 11:16:10
C HIS SUBROUTINE COMPUTES DIHVVY *
c. SUBROUTINE nwtl I ,J,K ,IN,JN,XN,U,V ,HI ,OY ,D1HVVY,MAR)
'. CIlENSICN 'J( IN,JN,KN> , V < IN, JN.KN I ,Hl i IN ,JN ) ,MAR( IN, JN)
7 IF IMAP| I ,J| .£3.0) GO TO 50
a IFIMARt ! ,'jl .EO.l I GO TO 31
' IFIMARI I ,j) .£0.2) GO TO 32
It IF MA<*1 1 , J I .£Q. J 1 GO TO 33
I 1 If IMARI I ,JI .EQ.m GO TO 3t
i: IF lf*»( I ,J) .EQ.e ) GO TO 35
IT IF(MAR(I,JI.E0.6) GO TO 36
!•» IF (HAH ( I ,j) .£0.7) GO TO 37
!t IF (KA(?( I ,j) .EQ.8 ) GO TO 38
1' IF IKAfM I ,j) .CO. 9 ) GO TO 39
I7 IF tfA»l I ,JI .f.0.1U)GO To tQ
!•> OlMVVY:iV(I,J»l,K)«VtI,J«l,K)*Hl(I,J»ll-VII,J-l,K)»
i- Cv I I ,J-l ,x ) "Hi i I , j-l ) ) / i2»or I
GO TO so
-1 31 CONTINUE
C»V(I,J-2,K»-t*HIIIfJ-l)*V(I,J-l,H)»VII,J-lfKII/(2«OY)
GO TO so
CONTINUE
ClwvVY:m«Hl(I,J«l)*V(I,J*l,K)*V(I,J«l,K)-3*Hl(I>J>*V(I,J,K)
If GO TO 50
35 3? CONTINUE
I" ClMVVY:tVtI,J«l,K)*VtI,J+l,K)*HI(I,J»l)-'«
!1 CV ! I ,J-1 ,K )*Hl ( 1 , J-l ) J / (2*OY I
3Z GO TO 5U '
i? 31 CONTINUE
i'- 01HVVYI(V(I,J«l,KI*VCI,J»l,K)«HTII,J«ll-VII,J-l,K)»
?5 CV(I,J-l,K»*HI(I,J-in/l2«OY»
-" GO TO 50
.' ? 3S CONTINUE
35 ClHVVY:f3«-HIlI,J)«VtI,J,K)*VlI,J,K)*HHI,J-2)*V
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4T 10
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SUBROUTINE 6i2iii,J,K,iN,JN,KN.U,V
CA3,TAUA,T4UY,niVWZ,01uZ.02UZ,OlvZ,
0 IMENS10N U(IN,JN,KNI,V(IN,JN,KN),
CHX < IN , JN » ,HY i IN , JN )
DIMENSION A3«KNI
IF (X .CQ.1)GO TQ {,1
ClUZ:Tu(I,'j,K«l)-UII,J,M-l))/l2*OZ
ClVZ = lvir,j,H*l)-V«I,JiK-l»/t2*02
0 luwZ: ill i I , J,K « 1 > *u I
01Vwz:iV(f,J,K»l)«ut
GO To 63
b 1 C 0 f 4 T ? N U *"
U IUZ:HI < I , J)*TAUX
D lv2=Hl i I , j )*T4UY
VIA
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RE TURN
END
62
-------
. i i .eSROR FOR CREATED ON 15-M»y-?»» AT 16:07:35
1 £**«•"*«******•«***•*******«**'>•«***»*********'************************<
2 c THIS PROGRAM CALCULATES THE HIRT AND HARLOW CORRECTION TTRM AT n,
? C SURFACE
H c*<***ftei>«««a«»**»**««««*#a*«a»«*««*«4«*«****«*****«*«**4r
5 SUBROUTINE ERROR i lun, JWN,I«(JW, OT,HH,WHLOT ,KN,MRH)
6 OlMtNSlQfJ UHUOT I IWN.JUN) ,WH< IuN,JWN,KNI
1 DIMENSION MRHIIWN.JWN)
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9 00 310U I.rl.IwN
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11 IF (MRH( Iu,JW) .EO.Q) GO ro JOOQ
12 WHLOTl Iw .JU»=-wHt IW.JW, 1 »/OT
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S OlMEHSION HI(IN.JV),HXUN,JM),HVIIN,JN)
7 DO 100 1 = 1,IN
8 DO 100 J=1,JN
9 HI(I,J|=CC
10 HXII,JI:O.O
11 nni ,01:0.3
12 1P3 COf4TlNUE
13 00 ?00 1=1,IN
l"» PRINT 101 ,1, (Hlllt J),j:i.JNI
is :ou CONTINUE
16 101 FOHMATl/' ir'.Ij/,' DEPTH•/5X,9Em.7)
1? RETURN
n ENQ
65
-------
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1 I.IMTIT FOR CREATED ON 15 MAY 74 AT 11:35:25
C "»*'!'«**'****»**<•«*************<*************«********«********'*******
C THIS PROGRAM INITIALISES TEMP ANO DENSITY
« SUBROUTINE INI?IT(ItJ,K,1N,JN,KN,Iw.Jw,IWN,JWN,A,8|C,T,RO,
i CTREF.RREF,
7 CTW.ROW.TO)
8 DIMENSION TlIN,JN,KN),HO oo 11 HH.KN
17 TlI,J,K):TOO
13 ROII,J,Kj:ROC
I1) 11 COMTINUE
20 12 CONTINUE
21 10 CONTINUE
23 00 20 lu:i,IhN
23 00 20 JW:l,JUN
2* IF (MRH(Iw.JWI.EQ.OI GO TO 22
2"5 0021K-1,KN
27 R0«
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tl.lM.CU ELT CREATED ON 5 MAY 30 AT Il:3<*tl2
2 C THIS SUBROUTINE F0« INLET ANQ OUTLETS FOR
3 C DOMAIN
5' .V S-JBROUflNf INLETKI,J,H,IN,JN.XNtU.ViH.G.T,TOtAA.TLLtOT.HTTOTi
% DIMENSION H( 1N,JN,KNI ,GI IN,JN ,KN1 ,UIIN,JH,KN)
7 . DIMENSION V ! IN , JN.KNI,T(IN,JN.KN),TD«:: C«TSOT-U.I)
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ON 19 NQV 79 AT 09:57:00
l.C ,0.0092,301.56,1.0
O.uQl ,10j,1.8,1.0
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1.C.Q.U092,301.56
1.C00428,-0.000019,-0.0000046
1C.Q
1742.22,0.0,0.0
0.227*7,1.0
C.U.0,0,0,0,7,3,3,3,3,3,3,3.3. 3,3.3.3,5
J.U.U.0,11,0.2,11,11,11.11,11,11,11,11,11
U,u, 0,0,7,3, 8,11,11, 11, 11,11, 11. 11, 11.11
a. a, o, Q , 2,11,11,11,11,11, u, 11,11,11,11,
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0,0,0,0,9.3,11.11,11,11,11,11,11,11,1
Q.C.a.n. g,2, u, 11,11, 11, 11,11,il, 11,1
0,0,7,3, 3, 3, it, 11,11,11, 11,11, 11, 11,1
3,U,2,11,11,11,11,11,11,1!,u,n,ll,l
0 .3 . 2, 11,1 1 , 11 , 11 ,11 ,1 1 , fl, U , 1 1 , 11 ,1
7,3,3,11,11,11,11,11,11,11,11,11,11,1 ,i,u,y,4,
2,11.11,11 , lit 11 , 11, 11 , 11,11,11,11, 11 11,6,3,5,
9,4,4,4,4,8,11,11. II,11,6,4,8, 11, 11,1 ,1,0*0.0
0,0,0,0,0,9,4,8,11,11,1,0,2,11,11,11. ,0,0,0
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a,a,o,a,a.0,0,2, u, 1,0.a.a,9,4,4,4,10,a,a
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a,a,a,o.a,0,4,10,10,10,10,10,10,10,10,10,10,10,3
3,0,0,0,0,0,2,9,9,9,3,9,9,9,V,9,8,8, 7
Q,C.Q,0.4,10,9,9.9,9,9,9,9,9, 9, 1,0,0,0
0,3,0,0,6,9,9,9,9,9,9,9,9,9,9, 1,0,0,0
Q,U,Q,0.0,2,9,9,9,9,9,9,9,9,9,1,0,0.0
0,0,0.0.0.2,9,9, 919,9,9,9, 9, 9, 9, 10. I 0,3
J,0,4,10,10,9,9,9,9,9,9,9,9,9,9,3,9,9,7
O.C,2.9,9,9,9,9,9,9,9,9,9,9,7,0,2,1,0
0,J,2,9,9,9,9,9 ,9,9,9,9,9,l,u.0.b, 7.0
4,10,9,9,9,9,9,9,9,9,9,9,9,1,0,0,0,0,0
6,6,8,8,8,9,9,9,9,9,8,8,9,9,10,3,0,0,3
0,0,0,0,0,6,3,9,9,1,0,0,2,9.9,1,0.0,0
0,Q,0,0,0,0,0,2,9,7,0,0,6,9, 9, 1,0,0,0
0,0,0,0,0,0,0,2,1,0,0,0,0.2,9,4,3.0.0
0.0.0.0,0,0,0,2,1,0,0,0,0,6,3,3,7,0,0
0,0,0,0,0,0,0,6,7,0,0,0,0,0,0,3. 0,0,0
1.633,-U.33,-2.78,0.0, -1 , 1
15.0
1.Q7J,-0.72,-I.67,0.0,-1,1
2.325,-1.61,-1.61,0.0,-l.i
6C.O
1.5t5,-2.22,-2.23,Q.U,-J,i
2.J56,-1.33,-1.89,0.0,-l,i
50.0
1.789,-2.17,-2.22,0.0,-1,1
3S.C
2.C12,-2.72 ,-2.78,20.94,1,1
2l283,-1.67,-2.7a,195.39,-l,-l
oT.O
j.026,0.01,-3.33,369.85,1,-1
5.U
I..'86,3.a6,-2.22,544.:fl,-t,-l
1.609,5.83,-2.22,655.96,l.-l
1.763,8.83,-!.39,725.75,1,1
40.Q
3.129,11. 06,-2.78,746.68,1,1
8C.C
2.593,12.28,-5.0,704.SI,1,1
I.b20,13.39,-5.56,579.20,-1,1
iO.O
1.207,13.89,-5.56,383.81, 1,1
1.565,13.83,-5.61,146.55,1,-!
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79 2.Q56,U.72,-1«.1*l».a.Q,-l ,-l
30 3C.O
31 1.162,9.72,-2.78,0.O.-l.-l
S3 2.772,8.33,5.28,0.Q,1,-t
34 55.0
45 2.861,7.78,5.56,0.0,1,-!
36 55.0
37 2.595,7.00,5.28,0.0,1,-!
83 50.0
89 1.386,5.28,3.89,0.0,1,-!
90 60.0
72
-------
1 I .OLDT FOR CRESTED ON 5 *i*Y 30 AT 1 1 : "U : 1 1
? C THIS SUBROUTINE S£TS THE VALUES OF THE TEMPERATURE
3 c«««*»»**»<"««*»* '»****»*"*****"'****»*'>* «***»***#***«***
" C
5 SUdROUTIME OLD1 I I , J ,H , IN , JN ,KN , TO , T )
6 OIMENSIO'V T ( IN, JN.KNI , TD( INt JN.KN)
7 DO 10 Ul.IN
8 DO 10 J=l ,JN
9 DO 10 Krl.KN
1C T (1 ,J,K) = TOt I ,J,K)
11 1C CONTINUE
12
n ENO
73
-------
, • $*«'.«? CREATED ON 1« "AY 74 AT 1S."*9:33
I C »« » a<1»»«»»«»ft««»«««««a«»oo«»»'»a»»*«»*o«»*» ««***«*«*«**«*««*««««*«*« a
C THIS PROGRAM SETS THE VALUES OF D AND E EQUAL TO U AND V RESPC(
3 C IN OROES TO HETAIN VALUES OF U AND V AT ONE TIME STEP LAG
K C»« »***««»*««»»»«o«**«*»«v*««»«««*««*«*«*»««#***«*«**«**«****«*««*«**(
5 SUSROUTI'U OLOUVI I ,J,K ,IN,JN,KN,U,V,Q,£)
^ DIMENSION Ul IN, JN.KN ) , V I IN, JN.KNI ,01 IT4 ,JN,KN) t£ ( IN, JN.KN)
7 00 831 K=l,KN
S 00 831 1:1 , in
9 00 831 jrl.JN
n D 11, J,K »:ui I ,J ,K )
11 t II. J.Kirvll ,J,K )
12 **\ coti~:. ~
l^ RETURN
!•• E'lO
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• -MASAI I).P«UV STM CREATEC ON 5 MIY 80 AT !1:M8:16
1 c««*•***••«•**«*«******«««**«****a****««*
? e- r«rs SUBROUTINE PHINTS THE VALUE OF u AMO v AT ALL MAIN
• 3 C C5IO POINTS.
i) £ u*o•*««•>*«*««*««**«***«*******«o»«flaij»«»ai>»»***»»«»»«»»**»
5 C
i SUBROUTINE PRUVI I ,J,K ,IN,JN(,K^,U, V.UA.VA.MAR;
7 DIMENSION UIIN,JN,HN) , VI IN,JN.KN) ,MAR(IN.JN),
g cui i IN,JN,KNI ,VA:u(I,J,K)»30.
13 VAII,J,Knv(I.J.K1*30.
i« c IFIHARIr,Ji.£o.oiu*:ioaoQoo.oa
15 C IF .EQ.OIVAriOQOQQO.Oa
it ?ino CONTINUE
17 00 150 *:],KN
19 bPUE I 6. 105 IK
1° 00 1«0 1 = 1,IN
?? »«IT£l(>,lOfc)IUAII,J,M,j:l,JNI
21 1<«C CONTINUE
12 153 CONTINUE
23 00 151 K:I.KN
;« .RITElb. 1C7IK
.>s oo mi In,IN
Jb yfiITri6,106l(VA(I,J,KI,j:i,JN)
n 11*1 CONTINUE
1* 151 CONTINUE
29 IQb FORMAT!• I','U-VELOCITY FOS K:«I5I
3^ 107 FORMAT I • 1 ', 'V-VELOCITY FOR K = 'I5)
31 106 FORMAT I//.22F6.2I
3? RETURN
77
-------
\<.t «N»s»M I .READ2 FOR CREATED ON
MAR 79 AT 12:18:36
THIS PROGRAM READS JAPE FOR DATA I FOR THE VARIABLE DENSITY CAS
WVVWVVWVMV
JWN , JwN ,D,E ,
H . WR,yRH,
,TREF,TO,TAMI
JN.KN),
KRH!IWN,JWNI,
ROW( IUN,JWN.K'
I
MUil,J,A),n-i,KM),J-ii-jN) i- i, in i ,
(l£(I.J,K),K:i,KN),J-l,JN) 1 = 1,IN I ,
(IUH(IU,JW,K),K:i.KN).JW=l JWN),I«=lt
(tW(I.J,h),H=ltKN),J=I,JN) 1 = 1, INI t
M W filUJ.K),K;1,KM),j:l,JN ),!::!,IN),
l(Wft(UJ,K),K;l,KN|,j:l,JN),I:l,IN),
i ,JN) ,1 = 1, {N!, i iMARil.ji ,'jit, JNI ,I:I!INI if iMRHTiw.jy) ,jw = i, jyNi"
Iwil, IwN),(iiT11,J ,M) ,K:I ,KN I , j: i, JN ) ,iri, IN),
JltBO(ItJ,KI,K=l,KN),j:I,JN),I=l,INI.
iiipnL'ii..iLi.Ki.K-i.«Mi..i'j:i.jLN).Tw:l.!uNl.
CJItBO(ItJ,K),K:l,KN),j:l,JN),l:i,INI.
C(IITw(lw,JW,K],K;i,KN),jj:itjwN),lu:i,IW
C I ( I ROW I I. , JW ,K ) ,K: 1 ,nN ) , jw: 1 , JWN ) , iw: I , I
CTAI,TAH,TAtf,AKT,CP,C«,A,3,Ct£UL,T,Tw,«0,
CAI,AH,AV,AP,DX,OY,O?,DT,TAUX,TAUY,TTOT
CONTINUE
TR
wN 1 ,
ROWfTE,RREF,TREF,TO,TAM'
78
-------
I >.R£A03h ELT CREATED ON 5 MAY 80 AT 11:50:20
• ? -- C THIS SUBROUTINE R£AQS AND PRINTS THE MAR t MAR MATRICES
3 .*"" c*»*»*»*»*»**-° *************'************"******************
«• C
5 SUBPOUTINf REA03K I I,J,IN, JN , I W , JU , IUN , jWN.MAR.MRH)
5 DIMENSION M»R| IN, JNI ,MRHt IWN, JWN)
T 00 300 1 = 1, IN
? READ 2, (MAR( I.JI ,J=1, JN)
•5 PRINT ill . IMARt I , J) .Jsl.JN)
10 300 CONTINUE
11 co too IU=I,IUN
1C REAO 2, <1RH( IW.JW » ,Jb:l ,JWN)
II PRINT j , IW, IHf?H( IU, JW) , JW = 1 , JWN)
1"* HOO CONTINUE
!5 2 FOHMATI )
If, 3 FORMAT) /ISX
17 RETURN
1" ENO
79
-------
",*-!>NASAt 11 .ROINTx FOB CREATED ON 5 KAY 80 AT 11:52:21
J c THIS SUBROUTINE COMPUTES XP IN THE POLSSONS EQUATION
J C 0» *•"•>*•»» »»»»•««« *•» »»»«»»«»*»»»«*» 4*4 *«««******* *»*••»*»»*
! " SU3ROUTINE ROINTX I I ,J,K,IN,JN,HN,DX,or,OZ,RO,AP,EUL,HI,
t CNAri .RINTX ,HX ,X IN T I
7 DIMENSION RINTXI IN, JN.KNI,RO(IN,JN ,KN),XINTI IN,JN),HII IN,JN!,
a CHAR i IN,JNI,HXiIN.JN)
9 00 100 1=1,IN
1C 00 100 J=l,JN
II IF IMARtl.Jl.EQ.O) GO TO 101
GO TO
13 00 110 K52.KN
IF |«*R(I,J>.EC.1 GO TO U
- - — -.-».. -- - GQ TQ j2
IS IF IMAfltI.JJ.EQ.2
is IF (MAR(I,Jl.EC.3
17 IF IHiRlI,J).Ft.i
IF IM»H( I,JI .EC. 5 GO TO 15
IF IM4RI I ,J) .f.Q.
IF (Miff! I ,J) ,EQ
.6
,7
IF (t»»R 1 I , Jl .EC.8
IF IKASI I ,JI .EQ.9
GO TO 13
Go To
50 TO 16
GO TO 17
GO TO 18
GO TO 19
23 IF (KARII,Jl.EQ.10) GO TO 20
:* RX:OZ»(RO(I + 1,J,K)» BO 11*1,J.K-ll-R Od-1.J,K I-R01I-1 ,J,K-1 ))/(<•»'•
*5 GO TO 102
H II CONTINUE
27 RXIOZ«(RO(IM,J,KI«PO(I«1,J,K-1)-RO(I-1,J,K)-ROII-I,J,K-1I)/IM*(
i"? GO TO 102
23 12 CONTINUE
30 axrQZ'tRQd'UJ.KMROlI'UJ.K-H-RQd-l.J.KJ-ROlI-l.J.R-UWlHof1
31 GO TO 102
32 13 CONTINUE
3? j»xs02«)/li»»OX)
56 GO TO 102
5? 20 CONTINUE
S= (?J:OZ«(3«*(R01I,J,KI«RO(I,J,K-l
7? C/2.0
73 210 CONTINUE
7n 201 CONTINUE
7? :3G CONTINUE
75 DC 300 151, IN
77 ao 303 j:i,JN
7" IF (M»R(I,J|.EO.OI GO TO 301
80
-------
79 S 00 J-10 KI2.KN
:ff) . . RSuHxrtRINTX (I .J,K >*HlNTx.| I r J .« -1 I )*lUZ/2)»AP*EUL"hII I, j
i\ ' XlNT(I,J):xlNT(I,J)+RSUMX
32 310 CONTIHUf:
sj 301 CONTINUE
3t 3QC CONTINUE
35 RETURN
86 ENO
-------
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n ir XJMZ 112 xmir M.Z * i*z
a— — — — — — — -. — — »--*-. «»— ^-*
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— ^ O 0 2T *-• ft 2 * JT *•«
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w VOC lUfUJUJ
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-------
i SA'Na^Al 1 ) .R.H FOR CREATED ON 5 MAY 80 AT 11:56:16
z c THIS SUBROUTINE COMPUTES VERTICAL VELOCITIES AT HALF
J C GRID POINTS.
It C •»****•«* 4-* *«»****4»*«»*a*»»»»»««4*»«»«*»»*«44*«**«»» *«*«****
6 SUBROUTINE RUHi J.,J,K,:U,JW,IN,JN,KN,I«N,JWN,U,V,toH,HItDX,OY,D2«
7 CMRHI
S DIMENSION UtIN,JN.KN),V(IN,JN.KNI,WH«
-------
9 ELT C3EATED ON 5 MAY 80 AT 11:58:57
rms SUBROUTINE COMPUTES REAL- VETICAL VELOCITIES AT
I C INTEGRAL GRID POINTS.
t, ^tanaff 49 «««««*«««•>*«»*«**««***•««<>*'<««**«*******«******«****
5 C
6 SUBROUTINE RWRI I, J,K, I.'J,JN,KN,U,V ,W,WR,HI,HX,HY,OZ,MAR)
7 DIMENSION Ul iNtJN.KN ) ,V < IN,JN,HN ) ,UUN,JN,KNI ,yRI IN, JN.KN) t
3 CHI(IN,JN).HX(IN,JN),HY(IN,JM),MARI1N,JN)
« 00 10 1 = 1, IN
10 00 10 j:i,JN
11 -IF (M4RI I ,J) .LT. 1 1 I GO TO S
12 KNMirnN-1
1 J 00 9 K:! ,KNH1
in wa(I,J.K>=(M-l>*OZ*(UII»JtK) *HX (I,J)+V(I,JtK)*HYlI,J» )«HI(II
15 C*y I I ,J,K I
16 9 CONTINUE
17 S CONTINUE
1" 10 CONTINUE
11
"" END
85
-------
,«SA«NASA 1 1 ) .RbRH ELT CREATED ON 5 MjY 80 AT 12:OIs08
? C THIS SUBROUTINE COMPUTES REAL VERTICAL VELOCITIES AT HA(.F
J C GRID POINTS.
. i» c •*"'»•>*•»»<'•* **0 »*•*»*» ************ ***»»********»»»*»*******
6 SUBROUTINE RURHI If J,X , IW,JK,IN,JN,KN,1WN,JWN,U,V,UH,H! ,HX,HY,
7 COX.OY .QZ.HRH.WRH)
S DIMENSION Ul IN.JN, HN)..V( INTJN,KN) , *H I IWN,JWN,KN» , HI (IN.JN) ,
9 CHX I iNtJN) |HY I IN,JN) tHRHUWN, JWN)
10 DIMENSION yRHl IUN ,
12 oo io
13 00 10 JW=1,JWN
1« IF 1MRH (IW . JW) .EO.Q1GO TO 8
15
IS Hr*V:(HY(I»t,JI«HY(I«l|J«l)«HYlItJI*HY(I.J«l)l/'«»
]7 HlAV=(HllI*ltJ>*HIII«ltJ+l>*Hl(ItJ>*HI(ItJ*l>>/4.
15 00 9 K=l,HNM1
19 I=IU
t° J=J^
22 VAVIIV il«l JjjKi+v II«I Jj* l',K )«V(I J jj« J ««(!,J*liK»>/5.
23 ySH(IW,JH,K)r(K-l)«02*(UAV*HXAV«VAV«HYAV)«HlAV*yH;IU,JW,
2<« 9 CONTINUE
25 8 CONTINUE
2S 10 CONTINUE
27 RETURN
:*
86
-------
.«SA«NASA< I I .STORE2 FOR CREATED ON 5 MAY 80 AT 12:02:30
1
2
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12
13
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16
17
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19
20
22
23
25
23
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31
THIS PROGRAM STORES THE RELEVANT DATA INTO FILE 8
SUBROUTINE. STORT2 (U,V .WH.PINTH, I ,J,K, IU,JW, IN, JN ,KN , I UN , JWN ,0 , E ,
CHX,Hr.Hl,MAR,MRH,AI,AH,AV,AP,nx,DY,DZ.OT,TAUX,TAUY.W,yR,WRH,
CIAI , TAH,TAV,AK TfCB,Cw.A,b,C,EUL,T, T W , RO ,ROW , TE ,RREF , TREF , TO , T AMP
CTTOT)
DIMENSION Ul IN,JN,KNt , V ( IN,JN,KN) ,0»IN, JNiKN) »E( IN, JN , KM) ,
• F"!\iiiri»»J»«ltfnr»( fririirTtjiirtf^NiNJ
DIMENSION Hf ( IN, JN ) ,HY ( Ir<, JN ] ,Hl ( IN.JN ) ,MAR( IN, JN ) ,MRH( IWN, JWN) ,
CV*I IN, JN.KN ,WR(IN,JN,KNI,URH(IuN,J'.N,KN)
DIMENSION (IN,JN,KN) ,ROI IN,JN.KN) ,TjIIUN,JWN,KNI ,ROW! IUN,JUN.KH
WRITE 18) I (U
-------
26
27
31
32
33
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51
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19
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51
a.7
55
Si
57
53
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72
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75
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78
' SA»i«<;A ( i I . HM3? FOR CREATED ON 5 MAY SO AT 12:0t:20
~' C THIS -SUBROUTINE -COMPUTES BOUNDARY T-EJ1-PERA TUBES
1 C«*«« *•**»**«»»««»* "**,«*»»«»*»»**»«*««*•»***«»***>•*»***«**
<4 C
c SUBROUTINE TEMfa2IIfJ,K,IN,jN,KN,TO,CX,OY,OZ,MAR,CB,HI,AKt,Ch.
i CTAMB,MX,HY,T,THEF,TAV,TAI,TAH,B3,OT)
7 DIMENSION TllN,JN,KN),TOIIN,JN,KNI,MARIIN,JNI,HXfIN,JNi,HY(IN,Jr
» CHltlNiJNJ
9
r>
\
2
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7
la
21
iZ
23
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11
12
13
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15
17
do ion KM I^N
00 100 I=liIN
00 100 JS1.JN
01HTVYSQ.
01TWZ=0.0
IF IH4RII
IF (MAR
IF IMAR
IF IMiR
IF IMAR
IF IMArt
IF IMAR
IF IMAR
IF (MAR
IF IMAfl
IF (MAR
IF IMArt
CONTINUE
G ITXKT
D2TX=(T
02T2=(T
I
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300
11
12
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19
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K ) )/(2*OX t
K ) -2»T( I, JtK ) )/IOX*OX )
li-2*Tt I, J,K I )/(DZ*OZ)
02TY=2»lT«I.J-liKJ-Tll,J,K||/lOZ*OZ)
IF IH.EQ.l! GO to 110
IF IK.ea.KN) GO TO 120
&0 TO 200
CONTISUC
DlTX:iTII»l,JtK)-TII-l,J,KI)/l2*OX)
02TXr|T|I.l1J,K)«TI!-l,J,K)-2*T(I,J,K))/IOX*OX)
02TZ = ITIIfJiH-»ll*T(I,J,K-l|-2*TII,J,K))/lD2*OZ>
01 TYZO.O
C2TY:2»ITII,j»l,nl-TlI,j,KI)/IOY«OYl
IF IK. £0.1) GO TO 1!Q
IF IK.EQ.hfJ) GO TO1 120
£0 TO 200
CONTINUE
CITXrQ.O
02TX:2«|T|I«1,J,K)-T(I,J,K))/(OX*OX)
02T?:iT(I.J,K«lI«TlIiJtK-l)-2*T(l,J,K) )/(OZ*OZ)
DirYciTii,j«i,K)-T(iiJ-i,K)»/i2«OYi
02TY:(TII,J»liKl+T(i,j-l,Kl-2«T(I,j,Kl)/(OY*OY)
IF IK.EQ.l) GO TO no
IF IK.EQ.KNI GO TO 120
GO TO 200
CONTINUE
D1TX:O.C
02Txr2«(T(I-l,J.K)-T(I,J,K))/IOX*OX)
02TZ:(T(IiJiK«il«T|I,J.K-n-2»TlI,J,K))/IOZ*OZ)
BlTY:ini,J*l,KJ-TII.J-l, KM/12 *OY>
02TYSIT(I,J«l,K)«TII,j-l,Kl-2*T(I,J,K))/»OY*OYl
IF (K. £0.1 ) GO TO HO
IF (K.EQ.KN) GO TO 120
uO TO 200
CONTINUE
DITXrQ.O
C2TX:2*(T|I«1,J,K]-T(I,J,K))/10X»OX)
02TZsiT
-------
79 IF
55 02TZ = (Tt It JfK»iJ*T (I, J,K-iJ-2*TI J,J,i
at oiTrra.0
37 02TY = 2*ITII,j+ltK»-TlI,J,KM/IDY*OYl
33 IF (K.CQ.l) GO TO 110
39 IF IX.tQ.KNI CO TO 120
9Q GO TO 200
91 20 CONTINUE
9? ClTXlO.O
93 02Tx:2»lTlI-l,J,K)-T(I,J,Kll/(DX«Ox)
95 01TY=0.0
96 D2lY:2«(TlI,j-l,Ki-TtI,j,K))
9T If IK. £0.1) GO TO 110
93 IF IH.EQ.KN) GO TO 120
)9 30 TO 200
ICO IIQ CONTINUE
IQl CT:*KT*llTlI,J,l)*TREF*TflCf J-T
132 CTsCT»HHI,J>
1Q7 D2TZ = 2'»lT(ItJ,2)-CT*OZ-TlI,J,l))yiDZ*OZ)
10<* GO TO 200
135 120 CONTINUE
1C5 02TZ = 2»
-------
3
u
5
7
GO To 100
IF |HAf?t t ,J) .LT.l 1 ) GO TO 9
CONTINUE
UO 8 K;J,KN
DlHTUX:|Ufl*l,J,K)*T(/ I2*0x )
CMJ
(1,J-i):
TIT
OITY:
02TY:
02TZ:
TtI,J+J,K)-T
01TW2 = i T 11 ,J,K«1)*W(
T( I i
»T
ni,j,K*ll«T
I-t,J,K
I,J-1,K
II,J,K»
ItJ-1,K
[F (MAR I I ,J ) ,EO. ID G
6JfS
K-l
)/(2*OX)
)-T(I,J,K-il*«U,JfK-l) >/12»D2)
-2«T(I , J,K))/(OX*oxI
-2*F< I , J,K) )/(OY»OY I
-2«T(1 , JiK))/(OZ«OZ)
200
oIHTVYIO.O
0 ITU2:0.0
CONTINUE
IF IX.£0.11 GO TO 2<*
IF (H.EQ.MN) GO TO 20
SO TO 21
CONTINUE
C1TUZ=0.0
02TZ;2«|T(I,J,K-1)-TII,J,K)*C8*HI(I,J)«02»/(OZ*OZI
00 TO 21
CONTINUE
CT:AKT«ltI(I,J,l)»T(?EF
-------
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-------
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12 11 FOH(*4T|/« KS« .13, Jx,M = l jU/' TTMPE9ATURE V(5X ,8£15.7»
"N*S«M I . IBBINK FOR CREATED ON 19 NOV 79 AT 1 1 : 1 1 2 "•*«*** ****** *********************************************
i SUBROUTINE TfRIHK ( I , J , K j IN , JN ,KN , T , RO , IREF ,MAR,T*CTUL >
f> • .. DIMENSION Ti IN,JN,KNI tRO( IN,JN,KNJ ,MARI IN, JNI , IACTULI IN.JN.KNI
7 IF UN.LE.6 ) GO TO 101
S DO 10 KSl.KN
0 00 10 l-l t IN
1C PRINT 11, K, I, I T ( I ,J,K) ,J=1,JN)
1? 10 PRINT 12, (R0( I , J,K ) ,j:i,JN>
11 FOH(*4T|/« KS« .13, Jx,M = l jU
12 FORMATI' DENSITY1/ |5X,8E15.7) I
Ji 101 CONTINUE
15 00 100 K:I,KN
1A 00 100 J51.JM
i? oc inn isiiiN
1" TiCTUU I I , J,K i:TI I ,J,K >
;o TACTULl!,J,K):(l.«TACTULII,J,K))*TRCF
2'J IF IHiBl I ,JI .EO.OI TACTULU i J,K ) = 1000000.00
21 100 CONTINUE
2? DO 150 K:i,Kf4
23 •RITCI6.105) K
2"« 00 ItO 1 = 1, IN
25 WRITE 16,106 ) I T ACTUL ( I , J , K ) , jr 1 , JN )
2i IMO CONTINUE
27 153 CONTINUE
Z% 10b FORMAT1M'.' TEMPERATURES FOR K = ',I5>
29 10ft FORMAT I// .22F6.2 )
3C RETURN
M ENO
92
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-------
•.S5A-*s<4iii.uvTOP ELT CHEATED ON 19 NOV 79 AT ii:Q9:i9
1 C. THIS PROGRAM CALCULATES U AND V VELOCITIES »T THC SURFACE US
2 C - - BOUNDARY CONDITIONS
S £•**-«**-»»»*•«*»»»»*»*»*»«»****»*««*»«***»»»***«*****»'»******»***»*«*«
t SUBROUTINE UVTOPrH,G,TAUX,TAUY,I,J,H,D2,IN,JN.XN.HI.MARI
5 - DIMENSION -HH IN, JNI ,MARrJH,JM),HUN, JN,KN» ,S( IN, JNfKNI
6 DO 800 1=1,IN
7 DO aao JSI.JN
8 IF (MAR(I,J1.tT.lll GO TO 7QO
1C1 Tx:rtux*HI(l,JI
i: H(I,J,Hi:(i4«H(I,J,H*l)-HII,J,K«2) «2*OZ*TX 1/3.
13 G(I,J,K|:(U*G(l,J,K*l)-GII,J,K«2)-2*OZ»TY)/3.
1» 700 CONTINUE
IS 800 CONTINUE
ji RETURN
1 7 END
-------
t 1 ) .WHATIJ FOB CREATED ON m HAY 71 AT 15:50:10
2 C THIS PROGRAM CALCULATES THE VALUE OF * AT I,J FROM VALUES OF WH AT
t c*"*?********************************* ************** **************«***«*<
* SUBROUTINE WHATIJI I ,J,h ,IW ,JWtIN, JN,KNrIWN, JWN ,H,HH,MAR I
5 DIMENSION HH1-M.N, JUN.KN I ,U I IN.JM.KH) "
4 - DIMENSION *43UN,JN)
f- DO 3550 I=lilN
8 00 3550 J=l,JN
^ IF :(UH(IU,JU,X)*UHIIh,JW-l,K>«WH*UH
-------
1
2
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5
6
7
6
9
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11
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r A •>«*«
FOP CREATED ON 1 M MAY 74 AT 15:50:00
* ««»«**««»
THIS PROGRAM SETS THE VALUE OF HH EQUAL. TO ?ERO AT THE SURFACE
SUBROUTINE
30QQ
J3CQ
DIMENSION UH( IbN , JWN.KN)
DIMENSION MBHIIWN.JWN)
00 I3QO IWIl.IkN
DO 330U JU:i,JWN
IF (M»H|Ih.JW).EQ.QI GO TO JQOQ
UHdW.Ju, I J:0
CONTINUE
CONTINUE
RETURN
END
, iyN,jwN,KN,wH,i<>,MRHi
96
-------
LISTINGS OF PLOT PROGRAMS
97
-------
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TIME. :
CONTINUE
NuMBE3(3.a,7«9,,j,i,P5,Q.o,«
SYM80U(lt5,7.7,3.1,3lHTOTAL
NUMEER(3.a,7.7,a.l,P6,C.3,«2>
SYHeoLU.5,7.E,^.l,2QHl.CndTh SCALElK,ElERS»,O.L,20
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AxISl<«.ll6.7tlH ,»a,l.Q,0.,ii.,12.)
SYMBOLIC.2,6.7,0.21,2H N,<»S.o,2)
PLOT l6.Cf-lS.s,,-3)
LH/^EC.C.H,J
HRS ,0.0,31 I
Q,i2)
TOO
-------
EO«»Sk.- j-i ll 1 .PWV : i- f L.-tATLG ->f. / ,,At t,j -I lo;;v;j_
1 C**»*»'*»«»»»***»****-**»»*»>»*«»». ******»» + •'*••»«••»*. »••*»**»***
2 C ThlS PSCGR.'M PLOTS T*E j - V nELCCITIES FOR THE REGION
3 C CF lNT£r,£ST.
» C THE FOLLOWING VARIABLES ARE R£AO *ITH AN OPEN FORMAT :-
? C PI = CISCHARGE VELOCITY.
6 C P: = CISCHARGE TEMPERATURE.
7 C PICS RUM NUM3E3.
a C P<» = rfINO SPEED (MAXIMUM!.
9 C PS = CURRENT.
13 t CTI31 : USEO TO QlMENSreNALlZE TIME TO HOURS.
11 c NTI*£ - THE NUMBER OF HOURS TO BE PLOTTED.
12 C P6 = TOTAL SIMULATED TIME (HOURS). »« THIS IS NOT READ •*
13 C ALL ThC OTHER VARIASLtS HAVE SEEN OtSCfHBED IN THE
it c jSEa; MANUAL.
15 C
14 C >«»•*» »»»«»»»»*»»»»»»»»»»»**»*»»»*»»»»*»*»*»*»»»***»»»**»»*»
17 C
U C
19 C PLOTS U AND « ON CONSTANT DEPTH SECTIONS (FEBRUARY 1979 MISSION)
:? PAfAMETEP INrl 7, JN = 2U,IUNr 16, J«N = l9,KN:s,KNMi:i»
il DIMENSION III IN ,JN,KN) , V t IN, JN ,KN ) ,0 I IN, JN.KN) ,C < IN ,JN,*N I ,
CHI tlN.jHI ,HX I TN.jN) ,HY UN, jN ) ,MAR (IN. JN ) ,MRh(IUN, J»N)
Olf-ENSION TW(!«N,J.N,KM,SOtIN,JN,KN5fPlNTH t
^5 CKN ) . T( IH, JN.KN )
2*» DIMENSION IBuFllQOO)
27 READ 5l,Pl,P2,Pia,PH,P5,CTTOT,NTIMt:
23 51 FOKMATl)
2? USCALE=1C.O
31 NTI"C:3
32 AfiMIN:n.:!<*
33 AfiMAxra.lS
3* DO 11 INe«:i,U
-- — ---
4, CALL SEAD2IU, V ,JH,PINTH,1 , J.K.IW, J* , I N. JN .*.N ,
3fc CI.J. ,J«N.D,£,HXfHYfHlfMAR.MftHtil,AHfAV,AP,OX,
37 COrf02,Ot,TAUX,TAur,*,dR,;RM,fAl!TAHtTivfAKTl
3* CCr,C.,AtS,C,EaL,T,T-,SO,«0.,TE,fiREF,TREF,TC,
DC 95 1st ,IN
HI II , jjrl ,C
CQMINuC
CALL PLOTS I InUF,1CQQ,11)
Cill HLai «ii.Ot2.Cf-3»
FGA^•r ii
*8 00
<|9 PS;*
SO ?6:CTTiT*TTOT
|1 C»LL FACTOR(Q.2S)
52 IFIK .GT.l ) GO TO 2J
S3 3C 30 1=1, IN
--* CC 2C J = I,j«
IF (HAR( I ,j) .EQ.O) GO TO 3i
Al:(I-l)*I.Q
Ajr|j.j)*i.3
= AI*U(I,J,M»USCALE
J,K >
^i J-=*"A}l(AK.MIN/Q.?S,A»lNl(r^,AR"AX/0.25»)
e3 i- cSliTlNUE ^ ' * ' "* " *
ft? " GO TO 100
t>6 iC cs.'.rrc.jF
t7
6a OQ
Q HC 1:1, IN
0 «»C JSlIjN
IF ihlt I ,J) .GT.CEPTti) GO TO
IF(CCl.EC.O) GO TO 55
101
-------
301
tZ'O'i'CT
(c'C'i 'DM
(Z'O'02'DM
(C'C'OZ'OT
(Z'D'il '0«£
(t* * i I * 3 * ^
!2| 3* 0;| C*~
(2'5*M *"*S
1 ''T'61'0'3!
f?1 ?'il' L" JI
IZjCTII JO'S
< r ' i" o i • 5 • 4
7 « f • , 1 ' 0 M t
±\~'i ' I CMI
Z1?* SI' C* hi
?'C*8T'C'9I
?«3'til« 0*91
?'3*hT' 0' hi
?'0*£I*D**rT
Z'CTI* 3* CI
?'CM I'O'ZI
Z«D« I 1' 0* hi
7*3»QJ* C«fj^
^•n»Ql' 0*ii
(IJO'8*CVI
(Z'O'9'DTT
(t'0*9'D*2I
(£*Q*i*C*2T
********************************************i
*NI?«OQ H3H10 A*)? aOJ 030^7^3 39 iSI* S3NIT
3^1 jo s3tavQNno9 3ui ywi"Vi!Q aoj 3av S3NI
********************************************
icia
i 01 d
1 0 "I d
lOld
lOTel
iCId
ICId
1 01 d
iOld
i 01 d
iOTd
ICTd
1 0"lJ
iOld
iOTd
IDld
101d
iOld
IDTd
iC"ld
1 01 d
ICId
iOTd
iOTd
lOld
iOld
«*»**»
3S3Vi
1 6*1 1
viro
lit:
*n ? 3
11^3
VIVO
T "1 ^ 3
vir;
V1V3
TT f .)
"11 ¥ D
nro
T"U§
TT V D
TT T ^
Vtt3
V! V 3
VlfD
VIV3
11 ^ 3
VIV3
Vl"3
VI T 3
Vt¥3
V1T3
nnr§
VI? 3
VITD
3
********* 3
"NITMOC1 3
*I**3«i*t i
11 v 3
OM*( l-j ); j\r
3fiNllMOD
V*«rrMidlOA
( I4r' I I /\r A3
1 20 0*200*21
3HNI1N03 j"i
D-» Oi 02
f>: A3
A* £-ZA*t) ):A8
10:03
(IOTP* I) ArIA
i A=IA
n:j n
Hi
C-T
til
fci I
it t
-------
l-a
IS9
l&f
Ifc?
!§i
1 ?•»
175
176
1 7T
173
179
Ic3
131
Hi
la»
185
lea
15?
isa
169
IS"
191
145
:»6
197
*. ,. a
2C7
2C9
:n
ft. i C.
213
217
218
219
*
* .. i> r * j «>o > ^ » o 9 ^ *
PLOT IE. c,s. a, 21
CtLU PL3T 1^.0,6.0,21
CALL PLOT<7.g,6.C!,2>
CALL PLOTJ7.5, 3.0,2)
CALL PLOTCIC.0,3.0,2)
CAiL PLOT (1Q.O, 1.0,21
CALL PLOT 11Q. 0,1. 0,31
CALL FACTOSU.O)
CALL PLCTl-l.G,-1.0.-i i
CALL PLOT 1C. C, 1.1 ,31
CALL PLOTU.0,1.1,2
CALL PLOT|6.0,9.0,2
CALL PLOT(C.O,9.0,2
CALL Pc.OT 1C.O, 1.1 ,2
CALL FuOT IO.O,C..C,3
C •» •*» •-»-•*»»»«*«»»»****««•<
C TM£ «CxT 25 L1SES ARf FOR yfilTlNG Th£ CAPTIONS OF THE
c PLCTS. THC SPECIFIC USER MUST SCRUTINIZE THESE LINES
C AND fAKE ACCESSARY CHAH&ES.
^ * ********************************************** **»*»***«**
23
123
in
ll
CALL S»M?3LIO.O,Q.6.J.1'*,2'«HFIG VEUOCITICS AT K = ,1.0,?H)
CSLL NUHSER(999.,999.,Q.m,P8,a.U,Q)
CALL SYH8CL!C.a,i.3,U.I'», 36H LAKE KEOWEE -IRI&ID-LlO MODfD.Q.
CO,36)
IFIP6.&E.25.0)GO TO 22
3C TO 23
CALL SYMSOLIi.Q,a.o,a.i<»,2SHSiHULATloNS FOR FEB. 2a 1979,
CD ,C.26 I
G£ t& 123
CALL SYHSCL 11.0,0.0,0.It,28HSI1ULATIONS FOR FES. 27 197*,
C3.C,2a
CALL SYMSOi(1.5,8.7,C.1,12HRUN NO: LOO »Q.U»12)
CALL .NuMREfii999l ,999.,o.i,PiQ,o.u,u>
CALL SYKBOLI1.5,8.5,0.1,33HOISCHARGE VELOCITY ;
C3)
CALL NuMfEH(3.3,a.5,a.i,Pl,0,0,»2)
CALL SYM60U1.5,3.3,O.I,2$MOISCHARGE TEMPERATURE:
CALL STMfiOL "« .2,3.14 ,L..07. iHO.n.C, 1)
CALL Nu.-BCR 3.a,8.3,Q.l,P2 ,Q.a, *i)
CALL SYMBOL --------
CALL f.oHfecfi
CALL SYMBOL
C3)
1.5,3.1,C.lt32H«INO SPEED (MAX)
3.o,3. 1 rU. 1 ,P"»,C.n, *2)
1.5,7.9 ,3.i,33hCU"RENTlJOCA ,Q . 0, 20 )
CACL AXISU.1.7.2.1H ,+Q,l.C,ri.,1..,6in.) ' '
CALL SY«33L(1.5,6.7,u.l,22HVCLOCITY SCALE < CM/SEC) , C.O ,2T )
ClLL AXIS lt.1 ,6.7, IH ,«D, l.Q.n. ,Q.,12.)
CALL SrnflOL(C.2.6. 7,0.21, 2h N,H5.0,2)
CALL PLOT110.0,1.25 -3)
CC.\T
C,G.0,29)
M/src,o.o,32
CM/SEC,0.0,3
MR 5,0.0, U)
. •> tun
CALL PLOT (o.o, -3.0, -3i
CONTINUE
CALL PLOT(10.Q,-2.a,-3)
E "4d
103
-------
»£ C«»s- •-- • i 1 . .rluW i >.,. i i I i_L u,1-. / , A , t ., - I i •/. Uu ; . -
1 i;<«4*»»»»»»»*»*»»»»*»,*.,»*+.»».»».«*»»»»»*,.-,,»«,,.»•»»«»<»#««•
2 c THIS PRC.CRAH PLOTS THE u • . VELOCITIES FOR THE REGION
3 c OF INTEREST.
* C THE FC.LLO.INC VARIABLE* »rf£ READ *ITn AN OP£N FORMAT :•
e C PI s DISCHARGE VELOCITY.
i C P: : DISCHARGE TEMPERATuHE.
f C Pit: HUN NUMBER.
8 C P"» : .IMO SPEED (MAXIMUM).
t C PS - CUPRENT.
10 C CTTOI = USED TO 0IMENSIONAL121 TIME TO HOURS.
11 C NTIȣ : TOTAL NUMBER OF HOURS SIMULATED
1? C P6 : TOTAL SIMULATED TIME (HOURS). *» THIS IS NOT REAL, »«
13 C «LL TnE OTHER VAHIASLtS HAVE bEEN DESCRIBED IN THE
Js c
li c*******************************************************>'****
17 C
U C
* i, t ,,,«^
C:1 DIMENSION UUN.JN.KNI . V(IN,JN,KN J ,0 UN. JN.l\N) ,E( IN,JN,I\M ,
21 C,H I 1.'. , J.^.HS) ,y ( IN ,JN ,KN) ,.fl (IN, jN.KN ) tta*H( 1,-N, JWN.KN ) ,
22 CHI UNt JM> »HX irtY ( IU, JK) fMAR( IN. JN ) ,HRH(Ii.N,JbNI
rj . DIMENSION TU (TbN.JWN.KN) tROd'^t JNfKN) ,PINTH(lkN«JyN> ,ROw( I.N , J.N,
54 CKNI.TI i'i,jfi,KN),iscu(6)
Ze DIfESSION ISUFilOOQ)
:t> USCALE-IO.C
:« *SCAL£:23.Q
29 HBYLrQ.33
1C NTIME=3
31 DO 11
CALL SEAD2 IU ,\l ,JH,H INTH.I , J,H ,IU . Ju .IN. JN ,KN ,
CI»N.J*N.O,EfHX,HY,Hl>HARlnKH,Al,AHrAv,AP,OX,
COt, 02, OT ,TAUXf TAur,-,«R..Rh,TAI , T Art.T AV , AK T ,C6 , CU ,
35 CA.E.CtEUL.T, T« ,SO,RO^,T£fRREF,TREF,TO,
»6 CTAHB.TTOT)
27 s CONTINUE
13 CALL PLOTStlBUF, lOaOf I U
^ SEAD 51, PI ,P2,PlQtPt,P5tCTTOT,NTIKC
*"3 5 1 FC«MAT( )
"J 1 F2SMAT ()
»•* QC 1C 1=7.13
••5 CALL FACTOPH0.25)
»t CiLL PLOTIC.O, 16.0,-i)
•«T 00 ZZ J-liJN
^4 P»II
i»9 Pt:CTTOT*TTOT
£2 IF IKASII, jj.LT.ll » iO TO
51 A j:( J-l }*l.O
S: 00 15 rtsl.ANMl
i' »n:-IK-l)*hICI,J>
3" AA^ZAJ.V II ,J,K )
ir AlKra«-« { T , J,K )»^SCALC»HaYL
•so Y.:D.2»SQRT ( ( A AJ-A J 1 »»2»( AAh-AK ) »*<; I
i7 Y.rAhAXl(ARMIN/Q.25,AMIf. l(Yi.,ARMAX/C..?i)l
Sa CALL AiOHQ iAj, AK , AA J, AAK , T«,0.3 , 12 )
5? lf CONTINUE
cT 23 CONTINUE
fci c ?.fA:- iOTTQH SURFACE
i J DO~3C J = l , jN
a» IF (,-A" (i , j> .EQ.Q) GU 10 3^
65 HMKN»l
ot. ir iM4.r,r.ii GO To 23
6? AAJ=(J-1 I*1.Q
AAp>:-Ml(T.jl*KNMl
TlAAj,Q.Cf3)
7' CALL FLOT (AAJ, AA«,2 )
?1 GO TC 22
?? il CONTINUE
7? A Aa= (J-l ) *1.U
71* A Af.z -Mi ( I . J(*KNM 1
7S CALL f-LCT I AAJ, AAK.2)
7S JC^J
77 A jcr I JL-1 1*1 .3
104
-------
SOL
~v3 911
3nvil',T3 Tt SM
3r".IJ1«C3 „' »«•!
.*C*tSS313H)31VDS
3ivDS M.Bf,3™oz*i'p*s'i4sMnobwAs no *'|
161'D'D'nviNozlaoHi »;3if3SH6Tjt'ojc-s|s'inoGHAs no £ti
ll£4D'0*S«H : 3WI1 Q3i»inwIS T ViOlHI f 41 • ?* 5- 84S * T ) TO 8^5 TTO jr 1
£'0*D'33S/H3 :C«OTJ 3SSV30T M N3 HMPDUr f 4 T • fl4 ; • R 4 S • t nncul c TTK-I jjj
Zr4OT*3JS/W : (X»H) " --• •- '
1D*D43 " ~ _-:'."_^-y"l_ty'-.' ». «• ".'_'«' o"» ? i'O
I ?»*0'O4trf4t'C'f'64§*f)BSSW^N 1T73 1*1
;40">'33i/H3 : AiI3tn3A 398»H3SigH£ £ JT ' DJ £ ^ 6 J i «T ITOBHAS no"" eil
let 91 I
--- P*03 SIT
*83J UOJ SNOH VTHHISHBZ II* 0 6*D 0* I) TOBMAS TIO £' hit
ret ojnos nt
^C^CJ. CD *" CTl
tl 3HVT 4 f H9£ J ht;D4 Z J T JO'O I109WAS n»3 iOI
HtZ40'0' rl it S3III3013A SI JH»iZ4 «> t • O4 S * I 40 «Onc8H AS TIO SSI
3 1C I
3 101
*»************»«*«»**»*«*»*»******»»»*»****«»«*«***»**«»«i-3 ;; i
3H1 JO SNOIld»3"3Hl SNIlIKr«"" SC J " 3d» " S3NIT "SZ 1X?N 3Hi 3 6*
*»**«»**»*•«*»»***»»***»**»»*»*»••*»»»»»»**»*•«»*********»3 Ei
1 i*
si
I*
Ci
6?
e?
if
99
3E
tiE
IS
c?
I i
-------
£ C ••-••'..I I i .PO/N ..T C.. : iltu «.. 2*' A - -~ ;, l -
C C TrtIS PB3CKA* PLOTS fHt K - * HtLGCITIcS FOR TH£ REGION
3 c CF INTEREST.
4 C THE FGLLO.ING VARIABLES ARE READ rflTH AN OPEN FORM* !-
1 C PI s DISCHARGE VELOCITY.
6 C P2 : CISChA^GE TF MPCP A T USE .
* C PlCt RUN NUMBER.
8 C PH = »XNO SPEED (MAXIMUM).
9 C PS = CURRENT.
IS C CTTOT i USCD TO 0 iMENSIOMAc I ZC TlH£ 10 HOURS.
II C STIHE = TOTAL NUMBE1? OF HOUfiS SlMULAtEO.
12 C ?(t - TOTAL SIMULATED TIttE IHOuRSI. »* ThIS IS NOT REAL »*
II C ALL ThE OTHER VARIABLES HAVE BEEN DESCRIBED IN THE
lH C USCRS MANUAL.
IS C
16 C «»•«*»»»»»«»»«**»•*««*»»»»•*»»»•»•***»«»«»•*»»«»***»**»»»*«*
17 C
ia c
19 PAKAf-tTER lN=17fJN = 2a,I*N = 16tJWN = l'J,KN = 5,KNMl;'»
:g OlHENSION U( IN ,JN,KK) . V(I«N,JUN,KN)
24 OlMt^SION IBUF(lOOQ)
27 USCALE=10.Q
29 ,CCALE:20.0
3t H3tL;C.33
U
00 11 t»JEw =
CALL R£AD2 |U ,V ,»H,PIMTH. I , J,K -Iy , J» ,IN, JN,hN,
CI.(. ,Ji.MTC.E.tJ-U.HY,HlTHA£,,iaHTil,AHTAV,AP,Oxt
COY,DZ,Of,TAUX,fAUT,«fttR,.RH,TAI,TAH,TAV,AKT,CefC«,
CA.b.CffUL.T.TK.ROtROKtTEiRREF.TRCF.fO,
CTA^B.TTOT)
COf.TlNJE
CALL PLOTS (IBUF, IODQ, 1 1 I
51, Pi ,P2,P1Q,PU,P5,CTTOT,NT1ME
•*<* 1 FCS^IAT 0
•»5 DO lr jsl , a
•<£> CALL FACTORia.2SJ
"7 CALL PLDT (C.O,16.C,-J)
Hi DC 2C 1=1 , IN
H9 P3:j
5..T Pb=CTTuT*TTOT
51 IF (I- ASCI ,j) .LT.ll) c.0 TO 20
i: AIllI-1 1*1.0
-3 DC 3C nri,nN«l
i* AM- I * -1 »»nl(l ,J)
I- AAlUI»-j(I J K)*JSCALf
5t « ii , i ,K inlo
ST AAft=AR-H ( I ,J,K )«»SCALE»H&YL
Si r«z0.r»5CRT<(AAI-AI>»*2»lAAi\-AM»»4)
- K.,.W,
'^ ClLL ASOHO (AI , AK ,AAI, AAK, Y.,0.0 ,
tl 3" CO
6! C 3'A.S sOTTGM SURFACE
&5 Do"35 1 = 1,IS
si IF (HAS ( I , J ».t J .3) aO TO
f SMSN*!
e>S IF ^'.N.GT.ll GC TO 33
(AAI,;;.
? CALL PLOT
7T
c^.'.ri..uE
75 AAI:11-1 )*1.0
• i Alr:-hI (I . j)«KNHl
77 CiLL PLOT 1 AAI,AAK,2)
li*---nI(I.J)»KNMl
Cii.L PLOT ( AAI , AAK ,2 )
106
-------
LGl
VM
IT i M
, , . (r-'O-O'D-OTIiClcTl-io •' b*t
,?•><».»< f-inr/uT, •,-,wic''.r?.,I2i?"I,P! '^i*1 's;s* t'Msixv -me »••,•
'-.u OT (31S/W3I 3TY3S Al T 301 3/»"Z Z'T • G4 1 »S 4 S ' mOBHA S Ilr3 £ •• I
iI"i:l'F. IH-Li'lI'r'! ^t.'cp'.T't.tsiirr n*5
' t'C* i*
-------
..EC-
4
5
6
3
9
i?
13
21
H
2*
Jl
t "9
II
3?
• 2
nJ
<»<»
S3
£1
57
£3
£9
fa-
t2
t3
7!^
71
7*
rs
72
C
C
c
c
c
f
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
c
THJS IS ENFSY SUBROUTINt FOR NHC CONIu..hli,o
CCALCOMP OR iILGO TYPE f-LOTlEK}
Tft COMPLETE PACftAoE CONSISTS Of 3 SUfcHOuT I Nt S, ECHKON, CflMLIN, ANJ ENC
ALL 3 A"»F CATALOGUED TOGETHER IN THE UM 3tc/bS UNQI.R MOLULE NAME ECHKO^
AMD DECKS ARE NOT NEEDED.
ANY RECTANGULAR SRIOiJfO SCALAR FIELD CAN EE CCNTOUSEO ON Mil GO
OR CALCOMP TYPE PLOTTER BY SETTING UP PPOPER CALLING ARGUMENTS ANQ
PROCEDURES AS INDICATED BELOW AND THEN CALLING LCHKON.
•CALLING STATEMENT IS AS FOLLO-S-
CAtL ECHKONCHH,lNl,lN2,N£Xl,NFX2,NtYl,NEY2|HI»'iID,l;LTli,C, INI
NEYl >
NEY2 >
fiZ
HI is HEIGHT IN INCHES OF CONTOUH MAP BETWEEN LIMITS
ylL, IS «IDTH IN INCHES OF CONTOUR MAP BCT-EEN LIMITS
i AMJ
l ANO NEX2
IS STRAIGHT LINE PLOT INCREMENT IN INCHES To BE USED
ALONG CONTSUR. GOOD VALUE IS .Q<*. BuT CAN BE tfAhlED UP OR DOWN.
SINCE LARGER VALUES CAUSE PROGRAM TO RUN A LITTLE FASTER, IDEAL VALUE
IS LARGEST THAT wILL STILL GIVE SfOOTH LOOKING CURVES.
--oo soi£ EXPERIMENTING *ITH IT. START yiTH .03 CR .ci AND INCKEASE.
SAMCON IS ANY SAMPLE CONTOUR VALUf. TT TS USED AS A STARTING POINT
FOR COUNTING UP AND OOrfN TO GET OTHEP CONTOUR VALUES.
CONINT is CONTOUR INTERVAL TO BE USED.
RGRID IS Af. INTEGES»2 STORAGE AR«AY USFD INT£R\ALLY IN PROGRAM
AMI HEED NOT BE iNITlALlZtn. II IS INCLUCtD AS ARGUMENT IN O'.'UFR
TO TAKE ADVANTAGE OF VARIABLE DIMENSIONS. OECLAPE AS INTEGn<*2
BEFORE CALLING.
l:.3 ANU IN(« ARE X ANU r DIMENSIONS OF RGRID. DIMENSION R Gfl I DC IN3 , INH 3
IN3 MUST BE AT LEAST AS LAPGf AS NEX2-NEXK1
Ir.4 MUST BE AT LEAST A c. LA"GT AS Nf Y ->-N£. Y 1< 1
CTHUS fiGRID MUST 5E AS LAPGE AS PORTION OF DATA ARWAY HH BLlNC USED
T Af.O ZbIG ARE LC.Eh A'.Q uPPFk CONTOUR CHtCi\ LIrlTS. I, J CONTOUR
.ILL Si£ ORA.N fcLLO. VAIUF OF ^IIT OR ARUVE VALUi OF »'bIC.
CUSEFUL TO PRCrfFNT OSA.INT, TOR ANY COMPLETELY «ILO DATA]
ANCRTH, ASOUTH, AEAST, ANU Ant'ST CAN BE USED TO ELIMINATE ANY
NUMcER OF INCHES FROM ANY SICL OF FINAL ORAuING.
FCK FULL CRA«ING «ITh nt!C' W10,
INITIALIZE ALL H OF AUOVE AKUUMENTS TO ZEKO.
EACH OF THE AbovE hiTn POSITIVE VALUE, THIS MANY .
.iLLJilL ELIMINATED ON SIDE TC. -HICH IT APPLIES.
THIS ALLOWS is TO FIT ANY RECTANGULAR GRID TC ANY M£-»CATGR
0* OTHER MAP LIMITS -ITHOuT ACTUALLY ADJUSTING THE GRID.
.-i£H3 AND huASHU CONTROL IYPC CF CONTOURS CSCLIO OR DACHEO LIf,£SJ
108
-------
7* ; Ir c 1 Tni. K uf- Uuii. A«L 11. ..w 01< LL-_lCL,tw.n(i AWE iOl.I J t f "it i.
aC C
81 C It EGTH ARE PQilTlVt, C-NTOUKS "ILL 6t DASHED AS FOLLOwS----
63 C PEN DOWN SECTION LENGTH ) NOAShG»PLTTNC CPLUnC IS INCREMENT LENGI
E<» C PEN UP SECTION LENGTH > NDASHU*PLTINC
£5 C CTHUS LENGTH OF DAShES ANG SKIPS IS FULLY VARIABLE!
ai C
57 C XLAbEL CONTROLS LABELING OF CONTOURS. LINES ARE LABELED
83 C ONLY IF XLABtL GREATER THAN ZERO. VALUF OF XLABEL
89 C IS HEIGHT IN INCHES CF LABEL NUMBERS. LINES ARE LAPELED
92 C KITH NEAREST .HOLE NUMBER VALUE OF CONTOUR. IF SPECIAL
51 c LABELING TQ INCLUDE ONLY PART OF NUMBER OR 10 INCLUDE
*2 C DECIHALS IS CESIRED. SUBROUTINE ENDER MUST faE CHANGED.
9* C SfOLfri IS A CONTROL FOR VARYING CONTOUR SMOOTHING.
55 C IMTIALI2E SMOOTH TO SOME VALUE BFTȣ.EN 0.25 AND 7.5
«o c CANY VALUE OUTSIDE THIS RANGE, is SET INTERNALLY TO i.nj
97 C LARGER VALUES GIVE SMOOTHER CHART WITH LESS DETAIL, WHiLL
93 c CMALLER VALUES GIVE LESS SMOOTHING AND MORE DETAIL.
59 C Cf.ORMAL VALUE FCR MOST ,.UNS ShUO BE ABOUT 1.53
1C- C ANYTHING LESS THAN ABOUT D.<40 OR LARGER THAN ABOUT 3. IS
1C1 C PROBABLY NO GOOD. BEGIN »ITH 1.5 AND EXPERIMENT UP OR DOtiN
1C2 C TO DETERMINE MOST DESIRABLE VALUE FOP YOUR NEEDS.
1^3 C CINPUT GRID DATA VALUES ARE NOT ALTERED IN THIS SMOOTHING}
ics c . ISECCY is PLOT TAPE RECORD COUNTER. INITIALIZE TO NUMBER
iC6 c OF PLOT RECORDS BRITTEN BEFORE FIRST CALL TO CONTOUR SUBROUTINE.
1:3 c ALL OF THE ABOVE ARGUMENTS EXCEPT ARRAY RGRID MUST BE DEFINED.
1C' C ARGUMENTS ARE NOT ALTERED JlTnlN PROGRAM, AND RETURN INTACT.
in c PLOTTER BUFFER SPACE MUST BE SET UP AND CALL TO PLOTS
112 C MAOE BEFORE FIRST CALL TO THIS SUBROUTINE.
\\* C • PLOT TAPE MUST BE CLOSED OUT AFTER FINAL CALL.
1 ie> (.
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SAMPLE PLOTS
138
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RUN NQs LOB 7.
OISCHRRGE VELOCITY
DISCHflRGE TEMPERRTURE
MIND SPEED CflflX)
CURRENTCJQCRSEE FLOW)
TQTRL SlttULRTED TIME
LENGTH SCRLE(METERS)
6.84CM/SEC
18.49C
4.51M/SEC
4.8 CM/SEC
1.01 MRS
*10l
0.00 61.00
ISQTHERMS RT K= 1.
LRKE KEQWEE-CRIGID-LID MQOEL)
SIMULRTIQNS FQR FEB. 27 1979
139
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RUN N9: LQ9 7.
DISCHRRGE VELQCITY » 6.84CM/SEC
DISCHRRGE TEMPERRTURE* 18.49C
HIND SPEED (MflXJ i 4.51H/SEC
CURRENTCJQCflSEE FLQHJj 4.8 CM/SEC
TQTRL SIMULRTED TIME » 2.01 MRS
*10l
Q.QO
LENGTH SCRLE(METERS)
61.00
ISQTHERMS RT K= 1 -
LRKE KEQWEE-CRIGID-LID MQDEL3
SIMULRTIQNS FQR FEB. 27 1979
-------
RUN NQ: L8Q 6.
DISCHRRGE VELOCITY s 7.42CM/SEC
DISCHRRGE TEtlPERRTURE» 31.7*C
WIND SPEED CtlflX) > 3.09M/SEC
CURRENTCJ8CRSSE FLQHJi 1.1 CM/SEC
TaTRL SIMULRTED TIME » I.01 HRS
LENGTH SCRLECMETERSJ °r°0
61.00
VELOCITY SCRLECCM/SECJ °L£2-
12.00
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VELOCITIES RT K= 1.
LRKE KEQWEE-CRIGID-LIO HQDEL)
SIMULRTIQNS F0R FEB. 27 1979
141
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RUN NQi L88 6.
OISCHRROE VEL8CITY » 7 .42CM/SEC
DISCHflROE TEMPERflTUREi 31.7°C
WIND SPEED (MflXJ i 3.09M/SEC
CURRENTUaCfiSSE FL8M)« 1.1 CM/SEC
T8TRL SIHULflTED TIME i 1-01 MRS
LENGTH SCflLECMETERS)
VEL8CITY SCRLEtCM/SECJ
*IQ1
Q.QO 61.00
0.00
12.00
-. » ^ ^ ^ >. X
VELQCITIES RT K= 2.
LRKE KEQWEE-CRIGID-LID MQDEL)
SIMULRTIQNS FQR FEB. 27 1979
142
-------
RUN NO: LOO 6.
OISCHRRGE VEL8CITY
DISCHRROE TEflPERRTURE
HIND SPEED CMRX)
CURRENTCJ8CRSSE FL0H)
T9TRL SIMULRTED TIttE
LENGTH SCRLEtMETERSJ
VELQCITY SCRLEtCtt/SEC)
7.42CM/SEC
31.78C
3.09M/SEC
1.1 CM/SEC
1.01 HRS
*10l
0.00
61.00
0.00
12.00
VELOCITIES RT K= 3.
LRKE KE8WEE-CRIGID-LID MQDEL3
SIMULRTIQNS FQR FEB. 27 1979
143
-------
RUN NO: L8Q 6.
OISCHflRGE VEL8CITY i 7.42CM/SEC
DISCHRRGE TEMPERRTURE* 31.?8C
MIND SPEEO CMRXJ i 3.09n/SEC
CURRENT(J8CflSSE FL8H)i 1.1 CM/SEC
TQTRL SlflULRTED TIME i 1-01 HRS
LENGTH SCRLECMETERS?
YEL8CITY SCflLE(C«/SEC)
0.00
0.00
61.00
12.00
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VELOCITIES RT K= 4.
LRKE KEQWEE-CRIGID-LID MQDEL3
SIMULRTIQNS FQR FEB. 27 1979
144
-------
RUN NO: LQ9 6.
DISCHRROE VEL8CITY
DISCHHROE TEMPERRTURE
HIND SPEED (ttfiX)
CURRENT(JQCfl33E FL8H)
T8TRL SIMULRTED TIME
LENGTH SCRLEtMETERS)
VELOCITY SCRLECCM/SECJ
7.42CM/SEC
31-7fC
3.09M/SEC
1.1 CM/SEC
1.01 HRS
o.oo
61.00
0.00
12.00
VELOCITIES RT K= 5.
LRKE KEQWEE-CRIGID-LID MQDEL)
SIMULRTIQNS FQR FEB. 27 1979
145
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TECHNICAL REPORT DATA
(Please read Inuructiuns on the reverse before completing)
REPORT NO.
2.
3. RECIPIENT'S ACCESSION* NO.
4 TITLE AND SUBTITLE
Verification and Transfer of
Thermal Pollution Model; Volume IV. User's
Manual for Three-dimensional Rigid-lid Model
5 REPORT DATE
6. PERFORMING ORGANIZATION CODE
7 AUTHORS s.S.Lee, S.Sengupta, E.V.Nwadike, and
S.K.Sinha
8 PERFORMING ORGANIZATION REPORT NO
9 PERFORMING ORGANIZATION NAME AND ADDRESS
The University of Miami
Department of Mechanical Engineering
P.O. Box 248294
Coral Gables, Florida 33124
10. PROGRAM ELEMENT NO.
11. CONTRACT/GRANT NO
EPA IAG-78-DX-0166*
12 SPONSORING AGENCY NAME AND ADDRESS
EPA, Office of Research and Development
Industrial Environmental Research Laboratory
Research Triangle Park, NC 27711
13. TYPE OF REPORT AND PERIOD COVERED
Final? 3/7B-9/80
14. SPONSORING AGENCY CODE
EPA/600/13
15 SUPPLEMENTARY NOTES IERL-RTP project officer is Theodore G.Brna, Mail Drop
61, 919/541-2633. (*) IAG with NASA, Kennedy Space Center, PL 32899,
subcontracted to U. of Miami under NASA Contract NAS 10-9410.
16 ABSTRACT
le six-volume report: describes the theory of a three-dimen-
sional (3-D) mathematical thermal discharge model and a related one-
dimensional (1-D) model, includes model verification at two sites, and
provides a separate user's manual for each model. The 3-D model has two
forms: free surface and rigid lid. The former, verified at Anclote An-
chorage (PL), allows a free air/water interface and is suited for signi
ficant surface wave heights compared to mean water depth; e.g., estu-
aries and coastal regions. The latter, verified at Lake Keowee (SC), is
suited for small surface wave heights compared to depth (e.g., natural
or man-made inland lakes) because surface elevation has been removed as
a parameter. These models allow computation of time-dependent velocity
and temperature fields for given initial conditions and time-varying
boundary conditions. The free-surface model also provides surface
height variations with time. The 1-D model is considerably more econo-
mical to run but does not provide the detailed prediction of thermal
plume behavior of the 3-D models. The 1-D model assumes horizontal
homogeneity, but includes area-change and several surface-mechanism
effects.
7.
KEY WORDS AND DOCUMENT ANALYSIS
DESCRIPTORS
b.IDENTIFIERS/OPEN ENDED TERMS
COSATi field Croup
Pollution
Thermal Diffusivity
Mathematical Models
Estuaries
Lakes
Plumes
Pollution Control
Stationary Sources
13B
20M
12A
08H,08J
21B
3 DISTRIBUTION STATEMENT
Release to Public
19 SECURITY CLASS (This Report I
Unclassified
21 NO Of PAGES
154
20 SECURITY CLASS (Thispagei
Unclassified
22 PRICE
EPA Form 2220-1 1»-7J)
146
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