.. , --.-1·· - . ~------ ----

·. i,

•

Mixing and Dilution of the Surry Nuclear Power Plant Cooling Water Discharge into the James River

by

John M. Hamrick Albert Y. Kuo

and Jian Shen

A Report To

Virginia Power Company Richmond, VA

"',',.

Department of Physical Sciences Virginia Institute of Marine Science

School of Marine Science The College of William and Mary

Gloucester Point, VA 23062.

July 1995

9508150299 950809- - - ~~--~ -- ---,_ PDR ADOCK 05000280

·.P PDR

•

• I

I_

- - ---·-------------·- --------------

ABSTRACT

This report describes and documents an analysis of the mixing and dilution of the Surry Nuclear Power Plant's cooling water discharge into the James River, Virginia. The analysis involves the application of the Virginia Institute of Marine Science's three-dimensional environmental fluid dynamics computer code, EFDC, to model the cooling water discharge and the mixing and dilutioa of a conservative tracer under field and hypothetical low and mean river flow conditions. The ability of the model to accurately represent mixing and dilution of the cooling water discharge is verified by the simulation of two dye release experiments conducted in January and October 1993. A comparison of observed and model simulated dye transport is presented. Based on preliminary simulations of low, mean and high river flows, the low flow regime, with salinity intrusion beyond Hog Island, was identified as the critical regime for cooling water flow dilution. To predict and analyze the mixing and dilution of conservative materials entering the river in the cooling water discharge, six model simulations were conducted using lQlO, 7Ql0, 30QS river discharges (20, 25, 41 ems respectively) and discharges of 100, 150, and 300 ems. The results of the three statistical low river discharges indicate that there is considerable recirculation of material through the cooling systems. For the three higher discharges, the recirculation effect is proportionally reduced. Relative concentration contour plots are presented for the ~ix simulated flow rates along with procedures for their application in determining the relative concentrations and dilution factors corresponding to specific contaminant mass loading rates from the station's waste stream discharges into the cooling canal .

2

f-~- ----~---- - - --·----- -- ------ --- -- --- -- --- -----------

•

•

ACKNOWLEDGMENT

The work described in this study was·funded by the Virginia Power Company under contract to the Virginia Institute of Marine Science, College of William and Mary. The cooperation and assistance of Messrs. G. Bishop, B. Belsches, and R. Raper of Virginia Power is acknowledged .

3

Abstract

Acknowledgment

Contents

list of Figures

list of Tables

1. Introduction

CONTENTS

2. Field Dye Release Experiments

3. Model Simulation of the Dye Release Experiments

4. Mixing and Dilution Simulations and Analyses

5. Summacy and Conclusions

References

Figures

Appendix: Description of the EFDC Model

2

3

4

s

8

9

10

15

18

28

29

30

69

4

- --- -- ---- - -- -- --- -- ---------------------------- -·· ---·-- -----·

•

. LIST OF FIGURES

Figure 1. 1993 Del Norte Remote Transponder Locations.

Figure .2. Numerical Model Grid of the James River

Figure 3a-3f. Comparison of Observed and Numerical Model Predicted Surface Dye Concentrations for the High Flow Dye Release Experiment.

Figure 4a-4f. Comparison of Observed and Numerical Model Predicted Surface Dye Concentrations for the Low Flow Dye Release Experiment.

Figure Sa. Instantaneous Surface Layer Relative Concentration for lQlO Flow.

Figure Sb. Instantaneous Bottom Layer Relative Concentration for lQlO Flow.

31

32

33-38

39-44

45

46

Figure 6a. Tidal Cycle Averaged Surface Layer Relative 47 Concentration for lQlO Flow.

Figure 6b. Tidal Cycle Averaged Bottom Layer Relative 48 Concentration for lQlO Flow.

Figure 7a. Instantaneous Surface Layer Relative 49 Concentration for 7Q10 Flow.

Figure 7b. Instantaneous Bottom Layer Relative SO Concentration for 7Q10 Flow.

Figure Sa. Tidal Cycle Averaged Surface Layer Relative 51 Concentration for 7Ql0 Flow.

Figure 8b. Tidal Cycle Averaged Bottom Layer Relative 52 Concentration for 7Q10 Flow.

s

----------- - -- - -

6

Figure 9a. Instantaneous Surface Layer Relative 53 Concentration for 3 OQS Flow.

Figure 9b. Instantaneous Bottom Layer Relative 54 Concentration for 3 OQS Flow.

Figure 10a. Tidal Cycle Averaged Surface Layer Relative 55 Concentration for 30QS Flow.

Figure 10b. Tidal Cycle Averaged Bottom Layer Relative 56 Concentration for 30QS Flow.

Figure 1 la. Instantaneous Surface Layer Relative 57 Concentration for 100 ems Flow.

Figure llb. Instantaneous Bottom Layer Relative 58 Concentration for 100 ems Flow.

Figure 12a. Tidal Cycle Averaged Surface Layer Relative 59 Concentration for 100 ems Flow .

• Figure 12b. Tidal Cycle Averaged Bottom Layer Relative 60 Concentration for 100 ems Flow.

Figure 13a. Instantaneous Surface Layer Relative 61 Concentration for 150 ems Flow.

Figure 13b. Instantaneous Bottom Layer Relative 62 Concentration for 150 ems Flow.

Figure 14a. Tidal Cycle Averaged Surface Layer Relative 63 Concentration for 150 ems Flow.

Figure 14b. Tidal Cycle Averaged Bottom Layer Relative 64 Concentration for 150 ems Flow.

Figure 15a. Instantaneous Surface Layer Relative . 65 Concentration for 300 ems Flow.

Figure 15b. Instantaneous Bottom Layer Relative 66

• Concentration for 300 ems Flow .

- ---~-- - --- -- ---------- - -------- ------ ------- -------------------- -- -- ----------------------

•

•

Figure 16a. Tidal Cycle Averaged Surface Layer Relative Concentration for 300 ems Flow.

67

Figure 16b. Tidal Cycle Averaged Bottom Layer Relative 68 Concentration for 300 ems Flow .

7

------

•

•

---------- --- --- - -- -------- ---- - -- -- ------------ -------- -------- ---- ---- - --------- ----------

UST OF TABLES

Table 1. High Flow Dye Release Experiment: 13 January/February 1993.

Table 2. Low Flow Dye Release Experiment: October 14 1993.

Table 3. Maximum Instantaneous Relative 24 Concentration with Respect to Concentration in the Cooling Canal Discharge.

Table 4. Maximum Tidal Cycle Averaged Maximum 25 Relative Concentrations with Respect to Concentration in the Cooling Canal Discharge.

Table S. Instantaneous Recirculation Factors and Conversion Factors for Relative Concentrations with Respect to Concentration in the Waste Stream Discharge.

26

Table 6. Tidal Cycle Averaged Recirculation Factors and 27 Converson Factors for Relative Concentrations with Respect to Concentration in the Waste Stream Discharge .

8

•

1. INTRODUCTION

This report presents the results of a field and numerical ·model study of the mixing and dilution of material discharged with the cooling water from the Virginia Power Company's Surry Nuclear Power Station into the James River. The study consists of three parts: ( 1) prototype field dye release experiments, (2) verification of the numerical model by its ability to simulate the.field dye releases, and (3) application of the numerical model to simulate the distribution of conservative materials discharged in the cooling water into the James River. The dye release experiments served to quantify the mixing and dilution capability of the river, and to provide data for verification of the numerical model (VIMS Environmental Fluid Dynamics Code, EFDC). After being verified, the model is used to predict the distribution and dilution of discharged material in the river under various assumed hydrographic conditions .

The Surry Nuclear Power Station is located at the transition region between fresh tidal river and estuarine proper of the James River, Virginia. Under river discharge condition characteristic of most of the year the upper limit of salt intrusion in the James River is upriver of the power station, located at Hog Island, with power plant cooling water withdrawn from and discharged into saline ambient water characteristic of the estuarine proper. During periods· of very high river flow the saline water is pushed down river of the power station, with the ambient conditions then being characteristic of a freshwater tidal river. Since the characteristics of net circulation under estuarine proper and fresh water tidal river conditions are very different, two dye release experiments were conducted during periods representative of the two regimes. The numerical model verifications were also made for both of the flow regimes.

J

9 I

I

•

•

- - - --- -- -- -----

2. FIEID DYE RELEASE EXPERIMENTS

Two field dye release experiments were conducted: one at high river flow and the other at low river flow. The dye used for the experiments was Rhodamine WT, which is manufactured by E. I. DuPont de Nemours & Company. The dye is sold in 20 % solution with a density of 1.2 g/cubic cm. The stock dye was diluted by one half with water drawn from the cooling water discharge canal in order to adjust the density to be more nearly that of the receiving water. In each of the experiments, a total of 60 gallons of diluted dye solution was discharged at a constant rate over a period of approximately one tidal cycle. The dye solution was injected at the water surface near the head of the cooling water discharge canal. The negative buoyancy of the dye solution, and the turbulence and large eddies in the discharge canal assured fast spreading and mixing of the dye with the cooling water .

At the end of each dye release and for several days thereafter, the dye distributions in the river were measured with a fluorometer aboard a moving vessel. The fluorometry equipment aboard the vessel consisted of a portable generator supplying AC power, a Turner Design Model 10 Fluorometer, and a small pump powered by a 12 volt battery. The pump drew river water from a depth of approximately 0.5 ft. below the water surface and circulated the water through the fluorometer. A portable computer was used for recording the dye concentration as well as controlling the frequency of data recording. The dye concentration was recorded every 6 seconds while the vessel was moving through the area where measurable concentration existed. Calibration of the fluorometer.was accomplished by placing its field sample intake and exhaust into a known volume of freshwater, then incrementally adding known volumes of a known dye concentration so that a curve of final dye concentration versus 'fluorescence units' was obtained. At the beginning and end of each sampling run, the calibration was checked by a sample of known dye concentration so that any shift in calibration might be taken into account during reduction of raw data.

10

• To determine the location of each dye measurement, the vessel was also equipped with a Del Norte transponder positioning system. The master transponder was stationed on the vessel with the DDMU ( digital distance measuring unit). Five remote transponders were strategically located on either bank of the river so that at least 3 of the transponders could receive the signal from the vessel at any point in the area of interest. Figure 1 shows the locations of the remote transponders. The distances from the vessel to remote transponders were also recorded in the computer for calculation of vessel location.

2.1. High Flow Experiment

The high flow experiment was conducted from January 30 to February 4, 1993. The diluted dye solution was continuously released to the cooling water discharge canal at a constant rate from 1725 hours, January 30 to 0655 hours, January 31 (both around slack water before ebb). The dye concentration distributions in the river were measured twice, once in the morning and then in the afternoon, on January 31, the first day after the dye release. Only one measurement.was made on the second day in the afternoon, since the field crew spent the morning replacing some of the batteries for the remote transponders, which became dead because of low temperatures. The night time temperature dropped to 25 deg. F prior to battery failures. No measurements were made on February 2 and 3 because of strong wind, high waves and low temperature. Wind speed on the average of 14 miles per hour and day time high temperatures of 30 deg. F were recorded on those days. The last dye concentration measurements were conducted on February 4 between 0930 and 1230 hours.

Table 1 summarizes the conditions pertinent to the high flow experiment. The field data for dye concentrations are presented in Figures 3(a) through 3(f) for comparison with numerical model

1

11

•

•

~~ -------- - ------

simulation results. Since the model results are instantaneous distributions at selected times, only those field data measured in the two hour interval centered around the model output time are presented. In addition to the measurement of the horizontal dye distribution near the water surface, several vertical distributions were made by stopping the vessel and lowering the intake of sampling pump to the mid-depth and near bottom. It was found that there was little difference in dye concentration at different depths during both measurements on January 31 (Table 1), the first day after dye release. The strong wind and high waves essentially completely mixed the water column vertically.

2.2. Low Flow Experiment

The low flow experiment was conducted from October 22 to October 25, 1993. Salinity in the cooling water was monitored one week prior to the experiment to ensure that this reach of the river was within the estuarine proper. The cooling water salinity was 13 and 12 parts per thousand on October 14 and 21 respectively. The dilutecl dye solution was continuously released to the cooling water discharge canal at a constant rate from 203 2 hours, October 22 to 0800 hours, October 23 (both around slack water before ebb). A total of five surveys were conducted to measure the dye concentration distributions in the river. Two surveys, .one in the morning and the other in the afternoon, were made on each of the next two days following the dye release. The last survey was conducted on the morning of October 25.

12

Table 1. High River Flow Dye Release Experiment January/February, 1993

Study Period Period of Dye Release Total Amount of Dye

Released Cooling Water

Discharge Rate Salinity Intake Temperature Discharge Temp.

Dye Concentration in Discharge Canal during Period of Dye Release

Vertical Distribution of Dye at Selected Locations

January 30 to February 4 1725 hours, 1/30'to Q6SS hours, 1/31 SO pounds in 10% solution

2016 mgd, steady 0 through 2/2, 3 psu on 2/3 and 2/4 5 C-7 C 13 C-16 C S .2 9 parts per billion

surface mid­depth

bottom ( depth)

January 31, a.m. 1.6 1.6 2.6 3.2

1.6 2.4 2.6

January 31, p.m. 3.2 3.4 ( 11 ft.) (about 200 ft. from jetty)

13

Table 2. Low River Flow Dye Release Experiment October, 1993

Study Period Period of Dye Release

Total Amount of Dye Released

Cooling Water Discharge Rate Salinity Intake Temperature Discharge Temp.

Dye Concentration in Discharge Canal During Period of Dye Release

Vertical Distribution of Dye at Selected Locations

October 23

October 24 October 25

October 22 to October 25 2032 hours, 10/22 to 0800 hours, 10/23 SO pounds in 10% solution

2016 mgd, steady 12 psu, steady 17 .1 C-18.S C 23 C-26 C 6.21 parts per billion

surface

0.52 1.8 0.24 0.08

mid­depth

0.42 1.75 0.15 0.07

bottom ( depth)

0.50 ( 8 ft.) 2.00 ( 12 ft.) 0.14 (25 ft.) 0.08

14

•

Table 2 summarizes the conditions pertinent to the low flow experiment. The field data of dye concentrations are presented in Figures 4(a) through 4(f) for comparison with model simulation results. Since the model results are instantaneous distributions at selected times, only those field data measured in the two hour interval centered around the model output time are presented. In addition to the measurements of the horizontal dye distribution near the water surface, several vertical distributions of dye were measured on October 23 and 24. The results are inducted in Table 2. It shows that the vertical mixing was not as complete as that during the high flow experiment.

3. MODEL SIMUIATION OF THE DYE RELEASE EXPERIMENTS

The VIMS three-dimensional estuary and coastal ocean circulation and transport model, EFDC (Environmental Fluid Dynamics Code) (Hamrick, 1991, 1992) was used in this study to simulate the mixing and dilution of the cooling water discharge. The model has been applied to the James River and calibrated with respect to surface elevation, velocity and salinity using field data sets existing at VIMS (Hamrick, et al. 1995). A summary of the model's capabilities and its · previous applications is found in Appendix A. The James River configuration of the EFDC model uses a 370 m square grid in the horizontal and six stretched layers in the vertical. The model domain extends from the entrance to Hampton Roads to Richmond. Figure 2 shows the model grid of the James River. The model's ability to simulate mixing and dilution of the cooling water was verified by simulating the two previously described field dye experiments. The model was then used to predict the mixing and dilution of conservative or non decaying material in the cooling water under various hydrologic conditions.

•

3 .1 Simulation of the High Flow Dye Release

For the January-February 1993 high flow dye release, the model was forced with predicted astronomical tides at the entrance to Hampton Roads, observed winds recorded at the Norfolk, Virginia Airport, and gauged flows in the James, Appomatox and Chickahominy Rivers provided by the U.S. Geological Survey. The gauged river flows were slightly adjusted to account for ungauged drainage areas. Thermal effects due to the increase in temperature ( approximately 8 deg C) of the cooling flow between the cooling canal intake and outlet were accounted for using an equilibrium surface heat exchange formulation with an estimated January equilibrium temperature of 1.2 deg. C and an exchange coefficient of 5. 7E-6 square meters per second (Cereo and Cole, 1993). The model was initialized for the dye release simulation by a preliminary 3 3 day simulation beginning on December 28, 1992. Following the preliminary simulation, the model was restarted and executed for an approximately six day simulation of the dye release. One hour averaged surface and bottom layer dye concentration distributions were output and saved during the simulation. The average total river discharge during the six day simulation was approximately 218 ems (7700 cfs).

Figures 3 ( a) through 3 ( f) show comparisons of model predictions of dye concentration distributions and field samples near the water surface. Model predictions are shown as dotted contour lines with large font numbers indicating contour values. The field observations are point values in small fonts. The model predictions are two hour averages corresponding to the time intervals of the field ·sampling. Figures 3(a&b) show conditions at approximately 15.5 and 17.6 hours after the beginning of the dye release ( approximately 3 and 5 hours after the release ended). The actual dye distributions tend to attach to the shoreline and not mix as rapidly as the model predicts, although the model predicted 1, 1.5, and 2 ppb (parts per billion) contours do tend to qualitatively agree with the field observations. Figures 3(c&d) show conditions 20.7 and 22.8 hours after the

16

beginning of the dye release. Model predictions ,of the 0.5 and 1.0 ppb contours at the point agree well with observations. In the vicinity of the cooling water. discharge, -the agreement is poor. The high field observed concentrations can likely be attributed to the transport of high dye concentration water, initially trapped against the shoreline, into the edge of the cooling water discharge plume and northwestward across the river. Figures 3 ( e&f) show conditions at approximately 4 7 hours after the beginning of the dye release.­Model predicted contours of 0.1, 0.2, and 0.3 ppb eastward of the point generally agree with about one half of the observations, with the remaining observations having higher concentrations. Inspection of the field observations in all six figures (a-f) indicates considerable variability and patchiness, typical of dye distributions under significant wind variability. Since the model was forced with three hour average wind conditions at Norfolk, the degree of agreement between the model predictions and field observations is reasonable.

3.2 Simulation of the Low Flow Dye Release

For the October 1993 low flow dye release, the model was forced with predicted astronomical tides at the entrance to Hampton Roads, observed winds recorded at the Norfolk, Virginia Airport, and gauged flows in the James, Appomatox and Chickahominy Rivers provided by the U.S. Geological Survey. The gauged river flows were sligh_tly adjusted to account for ungauged drainage areas. Thermal effects due to the increase in temperature (approximately 7 deg C) of the cooling flow between the cooling canal intake and outlet were accounted for using an equilibrium surface heat exchange formulation with an estimated October equilibrium temperature of 15 deg. C and an exchange coefficient of 7 .6E-6 square meters per second (Cereo and Cole, 1993). The model was initialized for the dye release simulation by a preliminary 21 day simulation beginning on September 29, 1993. Following the preliminary simulation, the model was restarted and executed for an approximately six day · simulation of the dye release. One hour averaged surface and bottom

17

•

•

layer dye concentration distributions were output and saved during the simulation. The average total river discharge during the six day simulation \'Va.S approximately 49 ems (1730 cfs).

Figures 4(a) through 4(f) show comparis~ns of model predictions of dye concentration distributions and field samples near the water surface. Model predictions are shown as dotted contour lines with large fonts. indicating the contour intervals, \-Vhile point field observations are shown in small font. Figures 4(a&b) show conditions approximately 13 hours after the beginning of the dye release (approximately at the end of the release). Agreement in the vicinity of the 0.1 and 0.3 contours in Figure 4(a) is generally good. In Figure 4(b), the observed concentration southwest of the discharge canal are ll;nderpredicted with agreement being better along the shoreline north of the discharge canal. Figures 4( c&d) show conditions approximately 18 hours after the beginning of the dye release. Approximately one half of the field observations agree well with nearby model predicted contours. Figure 4( e) shows conditions approximately 36 hours after the beginning of the dye release. Agreement is reasonably good in the 0.1 to 0.3 contour interval. Figure 4(f) shows conditions approximately 45 hours after the beginning of the dye release. Agreement is particularly good along the 0.1, 0.15, and 0.2 contours both west and east of the point. The good agreement of far field dye observations and model predictions after a number of days tend to give credence to the numerical model's ability to predict the mixing and dilution of continuous contaminant discharges from the cooling water canal.

4. MIXING AND DILUTION SIMUIATIONS AND ANALYSES

Following the preceding described verification, the EFDC · model was used to simulate the mixing and dilution of a conservative material discharged in the cooling water into the river. These simulations were conducted using three accepted definitions of low flow, a lQlO (one day low flow with a 10 year recurrence) of 20 ems, ·

18

a 7Ql0 (seven day low flow with a 10 year recurrence) of 25 ems and a 30QS (30 day low flow with a five year recurrence) of 41 ems. For comparison, three additional simulations using river flows of 100,

· 150, and 300 ans were conducted. The 150 ems flow corresponds to the long term mean flow for the months of September and October. Tables 3 and 4 lists the simulation flow rates and maximum relative concentrations on the north shoreline of the river. For the six dilution simulations, the model was forced ·with a mean tide amplitude at the M2 period of 12.42 hours at the entrance to Hampton Roads. No wind forcing was applied. The temperature rise through the cooling canal was 8 deg C and the cooling water flow of 88.3 ems. The equilibrium temperature was assumed to be 15 deg. C with a surface exchange coefficient of 7 .6E-6 square meters per second, corresponding to conditions typical of late summer or early fall.

• 4.1 Mixing and Dilution Analysis Procedure

•

The mixing and dilution analysis to be presented is based on the following formulation. For a waste stream discharge of concentration Cw at a volumetric flow rate Qw, into the cooling canal having an intake flow rate of Qi and intake concentration of Ci, the concentration of material in the cooling water discharge, Cd is given by:

Cd= (Q.C; +Q..,C,.,) Qi . ( 1)

Qd = (Q,., + QJ

Since the waste stream volume flow is likely orders of magnitude smaller than the flow rate through the cooling canal, ( 1) is well approximated by:

Cd= (QdC; + Q,.,C,,.) = (QiC; + M,.,) Qd Qd

(2)

19

--------~-----------------~-------~- ----- -----

where Qd now represents the cooling canal discharge and the product, CqCw, can alternately be written in terms of the contaminant mass loading, Mw (with units such as gm/sec or kg/day). The concentration rise between the cooling canal intake and discharge is:

M r, C C C - AC- "' - ~ "' ,- ;-u - Q, -~ (3)

A number of measures of mixing and dilution may be defined. Since the cooling canal is not a regulated public water body, a strict interpretation of regulations leads to the definition of relative · concentration, R based on the ratio of the contaminant concentration at any time and location in the river to the concentration in the cooling canal discharge, defined by

R =.E.._= C = C = C

' c, ( c, + ac) ( c, + i") ( c, + ~-) (4)

where the Rd denotes the relative concentration defined with respect to the cooling water discharge canal concentration. Often the inverse of the above defined relative concentration, which we prefer to call a mixing factor, but is also referred to as a dilution factor, is used. For example, if at some location in the river, the concentration is 1 % of the concentration in the discharge canal, the relative concentration· would be 0.01 indicating a 100 to 1 dilution and a mixing or dilution factor of 100.

If'the cooling canal is considered to be a regulated water body, the relative concentration, Rw with respect to the waste stream concentration is given b_y:

C R=­"' C ...

(5)

20

• and is related to the relative concentration with respect to the discharge canal concentration by:

R. =.£ c" =R"(1+ Q.,ci )Q. C4 c. Q.C. Q,

(6)

Equation ( 4) allows the concentration at the cooling canal intake to be expressed as: ·

c. = RAintake) M. = RAintake) riwc. 1 (t-R4'Intake)) Q, (l-R4(lntake)) Q,

which combines 'With (6) to gives:

R_-( 1 )R f2w - 1-RAinrake) " Q,

(7)

(8)

Equation (8) provides an expression for the relative concentration with respect to the waste stream contaminant concentration, Rw, at any time and location. The relative concentration, Rw, is expressed in terms of the relative concentration with respect to the discharge canal concentration, at the same time and location, the relative concentration at the discharge canal intake with respect to the discharge canal concentration, and the ratio of the waste stream flow rate to the cooling water canal flow rate. The flow rate ratio in ( 8) essentially determines the relative dilution of the waste stream discharge into. the cooling water canal and will be very small considering the high flow rate through the cooling canal. The term in parenthesis, which we call the recirculation factor, accounts for the effect of recirculation of discharged cooling water around Hog Island and back into the cooling canal intake. The recirculation factor has a minimum value of one when Rd(intake) equals zero, i.e. no cooling water is recirculated through the intake. In this case, equation (8) is reduced to: Cd= CwQw/Qd. Equation (8) is useful in providing an alternate measure of mixing and can be used to determine actual

~-- ·-- ---------------

•

contaminant concentrations in the river, given the concentration in the waste stream.

4.2 Analysis of Mixing and Dilution Simulations

A generic set of model mixing and dilution simulation runs at various flow rates were conducted to determine the distribution of relative concentration with respect to the cooling canal discharge concentration and the recirculation factor for use in determining the relative concentration with respect to the waste stream concentration. The generic simulations were performed by specifying a concentration rise between the canal intake and discharge, L\C of 100. For all six river discharge simulations, the model was time integrated until a quasi-steady state (i.e., not changing at any tidal cycle phase from one tidal cycle to the next) concentration distribution was reached. The relative concentration with respect to the cooling canal discharge concentration was then determined by:

R-C- C _ C "- C" - (Ci +~C)- (Ci +100)

(9)

Contour plots at the times of maximum instantaneous across shore or north shore relative concentration and tidal cycle averaged relative concentration with respect to the cooling canal disc.harge concentration for different flow rates are shown in Figures 5 through 16 and summarized in Tables 3 and 4.

Table 3 summarizes the maximum instantaneous across shore surface and bottom relative concentrations with respect to the cooling canal discharge concentration. These values correspond to the highest relative concentrations, or highest absolute concentration on the far shoreline predicted during a tidal cycle. As the river flow rate increases, the far shore location of the maximum relative concentrations moves downstream from Jamestown Island at low

22

• flows toward Mulberry Point at the highest river flow rate. The immediate conclusion which can be drawn from Table 3 is that there is relatively little dilution, indicated by the large relative concentration values, of the cooling water discharge at the three statistical low flow rates and only marginal increases in dilution at the three higher flow rates. The relative concentration of 0.54, for the 150 ems discharge, corresponding to average conditions over the months of September and October indicates that on the far shore, the cooling discharge has only been diluted by a factor of approximately 1.85. The relative concentration of 0.51 for the 300 ems flow indicated only a dilution of approximately 2 to 1, for a flow rate which exceeds the annual mean flow. Table 4 summaries similar results based on tidal cycle average conditions at the same across shore locations.

Tables 5 and 6 summarize the instantaneous and tidal cycle averaged recirculation and conversion factors in Equation ( 8), which can be used to predict maximum relative concentrations on the far shoreline with respect to the waste stream concentration. The recirculation factor remains on the order of 2.25 for the five lower

· flow rates and falls to apprximately 1.9 at the 300 ems flow, indicating a relative insensitivity to river flow rates of less than 150 ems. To illustrate the application of Equation (8) and the results tabulated in Tables S and 6, consider the lQlO and 300cms flow conditions in Table 6. For a waste stream discharge corresponding to 1 per cent of the cooling flow, at the lQlO flow, the maximum relative concentration with respect to the waste stream concentration would be 0.0159 (dilution or mixing factor of 63 to l) , while at the 300 ems flow the value would. be 0.0091 (dilution or mixing factor or 110 to 1). This indicates that the 300 ems river flow results in approximately 80 percent increase in dilution relative to the waste stream concentration.

23

•

•

Table 3. Maximum Instaneous Relative Concentrations with Respect to Concentration in the Cooling Canal Discharge.

Flow Condition Across Shore Relative Across Shore Relative (flow rates in ems) Surface Concentration Bottom Concentration

lQlO 0.71 0.71 20 ems

7Ql0 0.69 0.69 25 ems

30QS 0.67 0.67 41 ems

100 ems 0.57 0.57

150 ems 0.54 0.54

300 ems 0.51 0.51

Note: Minimum dilutions relative to th~ discharge canal concentration are defined as the inverse of Lhe maximum relative concentrations.

24

---------------·--·- ------- -- - -- -----·--·--··-- ----------- -------------

Table 4. Maximum Tidal Cyde Averaged Relative Concentrations with Respect to Concentration in the Cooling

Canal Discharge.

Flow Condition Across Shore Relative Across Shore Relative (flow rates in ems) Surface Concentration Bottom Concentration

lQlO 0.70 0.70 20cms

7Q10 0.69 0.69 25 ems·

30QS 0.66 0.66 41 ems

100 ems 0.57 0.57

150 ems 0.54 0.54

300 ems 0.48 0.48

Note: Minimum dilutions relative to the discharge canal concentration are defined as the inverse of the maximum relative concentrations

/

25

•

Table 5. Instantaneous Recirculation Factors and Conversion Factors for Relative Concentrations with Respect

to Concentration in the Waste Stream Discharge •

. ,

Flow Condition Recirculation Factor Maximum (flow rates in ems) Concentration

1/(1-Rd(intake)) Conversion Factor

Rd/( 1-Rd(intake))

lQlO 2.22 1.58 20cms

7Q10 2.21 1.53 25 ems

30QS 2.30 1.55 41cms

100 ems 2.30 1.31

150 ems 2.24 1.21

300 ems 1.89 0.97

Note: To determine the maximum relative concentration with respect to the waste stream concentration, the conversion factors in column three of the above table should be multiplied by Qw/Qd, the ratio of the waste stream discharge to the cooling canal discharge.

26

Table 6. Tidal Cycle Averaged Recirculation Factors and Conversion Factors for Relative Concentrations with Respect

to Concentration in the Waste Stream Discharge.

<t,

Flow Condition Recirculation Factor Maximum (flow rates in ems) Concentration

1/(1-Rd(intake)) Conversion Factor

Rd/(1-Rd(intake))

lQlO 2.26 1.59 20cms

7Ql0 2.24 1.53 25 ems

30QS 2.33 1.54 41cms

100 ems 2.31 1.32

150 ems 2.24 1.21

300 ems 1.89 0.91

Note: To determine the maximum relative concentration with respect to the waste stream concentration, the conversion factors in column three of the above table should be multiplied by Qw/Qd, the ratio of the waste stream discharge to the cooling canal discharge.

27

--- ------------ - ------------------ ----- ----- --- ------------------------· -- - ----

• S. SUMMARY AND CONCLUSIONS

This report presents the results of a field and numerical modeling study of the mixing and dilution of a generic contaminant in the Surry Nuclear Power Station's cooling water discharge. The two major findings of this study are: the large magnitude of the tidal flow relative to the river discharge and the recirculation of cooling water from the cooling canal discharge to the intake results in little sensitivity of discharge dilution to variations in river flow; and the regulatory definition of dilution plays the primary role in defining mixing efficiency. If the contaminant dilution is defined with respect to its concentration in the cooling water canal discharge, low dilutions ranging from 1.43 to 1 at the lqlO river flow (21 ems) to 2.08 to 1 at a 300 ems river flow result. The marginal increase in dilution with an approximately 15 times higher river discharge clearly indicates the insensitivity to river discharge. If dilution is defined with respect to the concentration in the Power Station's waste stream, which is discharged into the cooling canal, the primary determinant of dilution and mixing is the ratio of the waste stream flow to the cooling canal flow. For a waste stream flow rate corresponding to one per cent of the cooling canal flow, the dilutions at the lQl.0 and 300 ems river flows are 63 to 1 and approximately 100 to 1 respectively. With regard to instre·am standards, the results summarized in this report may be used to determine absolute concentration distributions in the James River, for specified contaminant mass loading in the power station's waste stream.

28

REFERENCES

Cereo, C. F., and T. Cole, 1993: Three-dimensional eutrophication model of Chesapeake Bay. J. Environ. Engnr., 119, 1006-1025.

Hamrick, J.M. 1991. A three-dimensional environmental fluid dynamics computer code: theoretical and computational aspects. SRAMSOE No. 317, Virginia Institute of Marine S~ience, Gloucester Point, VA. 63 pp.

Hamrick, J. M., 1992: Estuarine environmental impact assessment using a three-dimensional circulation and transport model. Estuarine and Coastal 1.'1odeling, Proceedings of the 2nd International Conference, M. L. Spaulding et al, Eds., American Society of Civil Engineers, New York, 292-303.

Hamrick, J.M., et. al., 1995. A three-dimensional environmental fluid dynamics computer code: application to the James River, Virginia. SRAMSOE No. xxx, Virginia Institute of Marine- Science, Gloucester Point, VA. (in preparation). · ·

29

0 rt')

•

~am::tovm ~and

•

Hog Island

Figure 1. 1993 Del Norte Remote Transponder Locations

•

[__ ________________________________________ __,

32

•

I 'I; 1! i 11 q ii I ii 11 i ! I ii'

•

Figure 2. Numerical Model Grid of the James River.

Winter: 15.5 hour after begining of dye release 37.24 r---..:-----r----.....----..-----r-----r----.------,----.-----,

37.23

37.22

37.21

37.2

37.19

37.18 ..... 0:1

37.17 O I IO

· ...... . 37.16

.. ..

37.15 contour level

0.01, 0.1, 0.5, 1.0, 2.0

.·, 5'2 .. ·· .o:sa

. . .1.38~ . .. ··· ,Jp7 ...

· 1·.02 ·

+·0.5 ,·:.11 . . 1

••. i,.41

.....

37· 14L..__ ____ 76....L...-8----76--L.-78----7-6L-. 7-6---7-6....1.... 7-4----76....L. 7-2---7-61--. 7---7-6....1....6_8..c:....:::,, ___ 76--L.6-6 ____ 7__.6.64

UJ (>J

Winter: 17.6 hour after begining of dye release 37.24-~-~---~--~----.-------.----~-----.----.-------.

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.5, 1.0, 1.5

....... 0

·o.oa .. ·········+Q.01·· . , · · ·., 0.66 · ..

. (>:3? .... ) .56 '

.·· 0.24'

: . .1:03 . . . :t

,' t- : . · 1

· :_oia · f0.5 OA4-

o. 1 : o.3a · _._ , , 0,62 T •, 1,;39 '

o·· 0 1

·· ...... ,Q 1.96 0 0 . · .

. ·""'QO .

tx>·.

0

0.39 0.08

. ··. 37.14 i._ __ __i_ ___ ..__ __ --.L. ___ _.___ __ __._ ___ __.__ __ -...L---.J:;..:::.._....._, __ __,

-76.8 -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

I

'i

11 I I

!

• Winter: 20. 7 hour after begining of dye release

37.24 ,--.....,.....--.-----.-----.------...------r-----.------.------r------.

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.5, 1.0

....

. .. .. ~·02'+-0.01

... . .. • 0 . • • ·o.09

o.g?s·. . .·· · · "o.Ra42 ·

.01 :· 1.1a1·-: :t ' : .. ·2.17+.

: : :~

\0.01 ...... r0 ~J-.,. .. + : o:.,if'P · : •0.58 ·

: o.~~3 : 0.09: . 0.3Y· ·.

0.44 1.~1i3

~0.5

37.14 L-__ _.._ ___ ....__ __ __._ ___ _.__ __ __._ ___ _.__ __ ___.____.~ _ _.__ __ __,

-76.8 -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

I

Winter: 22.8 hour after begining of dye release 37.24.--~--.-----,r-----,----.----.----.----r----,-----,

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.5, 1.0

·'-=t:0.01

Q.49

,•"'•, 0 · ..

.. "st-0.5 . . . . . . 0.06 ....

. • 0[37 . . . . . Q.46 ••

1.56· 1·}.~ . . . 0.78 ... ' ..f35 1 '38 •

· .. 2. 1.07 :,:3 ..n,74·. 0.1 ·. -2 8 : 0.8r + ·.

1.3j 0.68 ; 0.96 ,

b.~?9 ... ··· . . . . o:1s .1 48

1.96 1.59

;J.'57 .

37· 14 L-----76..L.-8----76-'.-78 ____ 7_6L... 7-6---7-6..L. 7-4----76--L. 7-2---7-6L... 7---7-6...a...6_8.=..;::,, ___ 76-'.-66 ____ 7__,6.64

• Winter: 46.6 hour after begining of dye release

37.24.....-------.----T---~---~---.-----r-----,,------y------,

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.2, 0.3

~: · ..

•,

'· · ·. 0.36 0:32

. o.2a·· . . ·-· · · ·, 022

·: 0 2

·o:34 · . 0.43 -=t- 0.48

a.st: 0.54-0.6 : 0.69· 0.78 · .

.0 .,.,. 0.57 · . • v ·o.38 . + O:~ ••

0.48 · o.si · 1 . 1.16 1.86 .

1 c1.l2 .= · o;28 01:

... 0.01: .. 0.91 :

2.12 ... . .~·

9i.11

· 0.03 0.35

1.3

.....

37.14 '--------L----L----..L---...1.----.L----'-----'--'=--i-....:..._ _ __,

-76.8 -76.78 -76.76. -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

w ........

• • Winter: 47.6 hour after begining of dye release ·

37.24,--......,---~----.------r----,------,-----,-----,r---~---.

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.2, 0.3

8:h g.1a ...

. . , . . 0.09 • ··b.2 .. · .. 0.18 · .. + ·p.23 ·.

37.14 L..._ __ __._ ___ ..__ __ ___._ ___ _.___ __ __._ ___ __.__ __ __.____,~ _ _._..;.___---.J

-76.8 -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

(JJ

00

• • Summer: 12.4 hour after begining of dye release

37.24r-~---.----,----r------,----~----.-----r-------r----,

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.3, 0.6, 0.9, 1.2

o O o oo O o o I• o • ....

.... ,' .

.o.~o8.'23 q:t : ... . ·1

6, 1 . · ·0~3{::oJP .. . : o'Jii ?.22 ·. 0 33° . ' 1·3 . . 024 ·. ·. , · . .0.68 ': :.0.18, .. :· . : .. 0:30.441 .. ~1

·o· ..... .

.. ·.

37.14 L-----.l-----lL-----L----L---..L-----...L----L---=--'----.1

-76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.8 -76.64

Summer: 13.5 hour after begining of dye release 37.24.---.......,------.-----r-------.----y-----y----.-----,----.-----,

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.3, 0.6, 0.9, 1.2

• o I I

.....

... ~~ +_.0.01 +.0.1 _.· .. 1.J 2 ()

0. 3' ... '+. . +: .

. 008 . .'1.72 1 · · ' : .'O/f · ... (l>'.~i ·. :11.2

'·03 ... . . . 0.17 °:68 Q.27 .0.19 :o.18· · · .. · : 0.2Q).~1 ·.0.14 · ..... .

. 0

0.0~

0

37.14 L----1----lL...-;__ _ _._ __ ----1, ___ ..,L_ __ ---L.. ___ ....._~-----1..----' -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64 -76.8

~ 0

Summer: 18.6 hour after begining of dye release 37.24------------~------~--~------

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.2, 0.3 0.4

......

,,•"'T?:1 . . .

. -1!0:01 .. · . . . · .. T ,' ,,••,,,;' 8:02' ,,

· · · ·o 3 .. ·· f0.2 ..... ~.07

. . olr ,', ... . ,' 0 3 ... . :1 i , ; : ... + : ·0.0. /:'

. . . 0. . '1.·

. . ·. 0. 0.03 .· . ·p.a-0.000.09 · 0·41 0,11 0.1a 6 . ··

Q. 5 ' · O. l 0.2f>:7. 9.16 0 i,

0·2 0 3' 2 · ·0.2~. . · · · 0.27··'Q.41 .

0.35 0.43-0.5aJ.47 '

. 0.55 ; 0.1 0.29 0.3

.... i.1fl ~-~3

·. 0.41 ·. 0.15 ·.p.01

....

37.14L.._ __ ___i_ ___ .L._ __ ____L ___ ....1,__ __ __... ___ -1--__ ____.___.~---L-------I

-76.8 -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

•• Summer: 19. 7 hour after begining of dye release

37.24-------~--~---~--~----.-----.---~-----.

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.2, 0.3, 0.4

. . .. .

····+ ... ', .

.· 0.02 . , · ·.' '''' '• · · • ,' . ·o . : o.04 ··o 06

0 01 ... . . . 0 .. f . . ,' ·.9.181:l . 0.09 0 : o· 2· ..... o .. 28 . . . . 0.26

. . . "... 0 : +.· ........... .. : 0 4 0.44 +. · 0 7 . . . . . . cl, 7.

...... ~0.3 ... '•, · ... ··. • • -i: • • • . .. . . .... ..... ··· ...... .

.... 0.02

0 0

37.14 L,__ __ __i_ ___ .L_ __ --..1.. ___ ..i_ __ --..1. ___ ....L,_ __ ---1__.i::..::::,,,_-1-__ ---1

-76.8 -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

\_

• Summer: 36.23 hour after begining of dye release

37.24r--~-~----r--------r----r------.-----r------,,----~-----.

37.23

37.22

37.21

37.2

37.19

37.18

37.17

37.16

.... n;Q,01

0··1· 0:02' ·+ , . 0:04 • • . 0. f.1

.· · .. -~:01 O.O,f0.03 0.03 0.1 0.13 ', .· .· Q.03 . 0.01

' ', 0.04 .

0 2 ·... . ·.o.os .·· .. ·

• • • ••••

0006 .· .· . · · . 01>1 • . ' . •. • , .+· " . " . ' · · , . ' · · , . . · '. · · 0.01 , . . , · · . . · . 0.08 . o. . : ... 0.1_4· ... <o.n..:: . .-. ·: 0.11-·

· · · · · , · · ·. · · 0·17 ·. ·. : : .· · ... 0 24 · .. ·. :oe~2 0'3 0.12 : 023' · ·. ' ' & ' 0·1· ' ·. ·. '. 0.1 22 0.1 . :

. . ·. 'D, 0170.14 .· ..... . ' · · · 021 · ' · ·. ·. · ... o.r2. . -a 2'3 ...... .

... ·'::: ~:.144·: ....... 0:~2.' .. . . a.1 . . Q 11 . ··.o.o·a · ...... ' .· . o·,,1·.. . . o.1

· ·"' · ·. 0·1 ·.0.08 011 . p.06 •.. 'o i 1 ..

· .. '+.0.01 Q.~ •• 0.11·· . ' 0 1 °· 1 ·. · 0.06

~0.01

37.15 ·. 0.06 •,, .Q.01 contour level

0.01, 0.1, 0.15, 0.2, 0.25, 0.30 37.14 L------L------'---.....__ __ _J.. ___ ....._ __ ..--L.. ___ .,__..=.:::,.._---'-----1

-76.8- -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

Summer: 44.51 hour after begining of dye release 37.24 .-------~---..-.,....-----.-----.------,-----r--------.----.-------.

37.23

37.22

37.21

37.2

37.19

·.p

37.18

37.17

37.16

37.15 contour level

0.01, 0.1, 0.15, 0.20, 0.25

.... o .. ~ 0.12. 0.96

• . . . -0.1 J •• Q.oa .••••.• . • ··0.15·· · .•... P:1 ..

. . . · ....... .a.1g .... · .. · ..... . . 0.22 ... : .' .' .' .' .. .

. ·. 0.17.· .......•. : .....•.• . · 0.15 ·a.· 12' •. · ·

. .·0.13 .. · .· ... ~ .. 12 ... ~·.ur

.:o.1.40 16,. ·o· 25·.p.2 ':},09: . 0.i. . ·.

0.95 · o.15o_;. 0.07 .. 0.04 ...

0.03 . .-··\0.01

. 0.01 0.0'2.

0.02 :

0.02 ·• ..

·· •• 0.02 .. :

0.02

0.03

0.03

0.02 · ..

0.02

0.02

0.03 0.05

. .... ·.. 0.1· · · ····+···

0.04 0.05

.. Q,o.~ o.o~. 0 01 0.06 · 't .

0.04 ·

37.14'------'-----'-------.1..---...,___-----L----..L..------1--c:;..::,,,_--'-__ ____. -76.8 -76.78 -76.76 -76.74 -76.72 -76.7 -76.68 -76.66 -76.64

--- - - . ---~---- -- - - ---- -- - . -- - - ·l

37,241

37.222

37. 193

37 .183

37. 173

37 .1 b4

37. 154

37. 145

37. 135

3 7 . 1 25 .__.__._....._.__.__,_....._....__.__.___.__.__........,___..__._.L......1__._....,__..J._J.__.__._...L.--.L.-L-..1..--'--.1........1---L---'--....__L........1..--..l.-...l...-J:._J

-76.820 -76.770 -76.720 -76.670 -76.620

1~10 NSTANTANEOUS DILUTION timestep= 11 Depth= O.Om Data min= 0.425730 Data max= 0.837745

Figure Sa. Instantaneous Surface Layer Relative Concentration for lQlO Flow.

45

37 . 250 ,......--,--,-.,..-,,........-,---.--,--,--r--.--T-""T--r-....-.,..-,,........-,---,--,.......,.-r--,--,--,-..--,-..,.......,,--,---r--,--,.......,.--,--,-..--,

37.241

37.222

37 .1·93

37 .183

37. 173

37. 164

37. 154

37. 145

37 .135

31. 12s---..__.~~..__. ........ _.__.._,.____.___.__.__..__.~~....._...._.__._...__ ___ ..__.~~--........ ---

- 76. s20 -76.770 --76.720 -76.670 -76.620

1~10 NSTANTANEOUS DILUTION trmestep=· 11 Depth= 99.0m Data min= 0.425966 Data max= 0.951458

Figure Sb. Instantaneous Bottom Layer Relative Concentration for lQlO Flow.

46

----~~~~~-~-~-=-=-=-~-~- -·- - -- -·---- ---·--··---·----··-·-- -----·---- - - --··-- ----- -- ---

37 .241

37.231

37.222

37.212

37.202

37 .193

37 .183

37 .173_.

37 .164

37 .154

37. 145

37 .135

)

\.. 55~

3 7 • 1 2 5 ..__.___.___.__..__.__.__.__...__..__..._,_....__.__.__,___.__.L......L__,__._...__.__.__,_....__..___.___.___.__.L......L__._....._...__...__.___.___.__..___.

-76.820 -76.770 -76.720 -76.670 -76.620

1~10 TIDAL CYCLE AVG OIL timestep= 0 Depth= 0.0m Data min= 0.416439 Data max= 0.766355

Figure 6a. Tidal Cycle Averaged Surface Layer Relative Concentration for lQlO Flow.

47

•

•

37 .241

37. 231

37.222

37 .193

37 .183

37. 173

37. 1 b4

37. 154 \.55

37. 145

37. 135

37 .125

-76.820 -76.770 -76.720 -76.670 -76.620

1Q10 TIDAL CYCLE AVG OIL timestep= 0 Depth= 99.0m Data min= 0.416769 Data max= 0.949256

Figure 6b. Tidal Cycle Averaged Bottom Layer Relative Concentration for lQlO Flow.

48

1------~-=----_ -__ -__ -_ -_-_ -_ -_-__ -_-_-_-__ -_ -_-_-_-_-_ -_ -_-_-_-_-_-__ -_-_ -_-__ -_-_ -_-__ -_ -_-__ -___ -_-_-_ -_-_-__ -_ -_ --- --- --- ------- ---~--- . --1

«;

37.250

37. 241

37.231

37.222

37 .212

37.202

37. 193

37 .183

37 .173

37 .164

37 .154

37 .145

37 .135

37 .125 ,..

-76.820 -76.770 -76.720 -76.670 -76.620

7~10 NSTANTANEOUS DILUTION timestep= 11 Depth= O.Om Data min= 0.394513 Data max= 0.820885

Figure 7a. Instantaneous Surface Layer Relative Concentration for 7Q10 Flow.

49

so

37.241

37. 231

37.222

37.202

37 .193

37 .183

37 .173

37. 1 b4

37 .154

37 .145

37 .135

3 7 • 1 25 ......... _._......_......_.__.__._...__..._.___._......__,___.,__.___.__..r........J__.__._.....___.__._......,_.....___,___.,__._........_......._.__.___.__..r........J_..__._.....___.___,

-76.820 -76. 770 -76.720 -76.670 -76.620

7~10 NSTANTANEOUS DILUTION timestep= 11 Depth= 99.0m Data min= 0.394738 Data max= 0.988327

Figure 7b. Instantaneous Bottom Layer Relative Concentration for 7Q10 Flow. ·

----1

51

37.250

37.241

37. 231

37.222

37.212

37.202

37. 193

• 37 .183

60~ 37. 173

37 .1 b4

37 .154

37 .145

37. 135

37 .125

-76.820 -76.770 -76.720 -76.670 -76.620

7~10 TIDAL CYCLE AVG OIL timestep= 0 Depth= 0.0m Data min= 0.386436 Data max= 0.751637

Figure 8a. Tidal Cycle Averaged Surface Layer Relative Concentration for 7Q10 Flow.

-----------------------------~-~----==-~--- - --- --- ----

37 .241

37.231

37.222

37 .193

37 .183

37 .173

37. 164

37 .154

37. 145

37. 135

37. 125 ~--~_..__....__._.__._.......__..__..._.__.__~_....-......... _.__._....___~_.__.__~_.._-......... _.__._....___~

-76.820 -76.770 .:.76.720 -76.670 -76.620

7~10 TIDAL CYCLE AVG OIL timestep= 0 Depth= 99.0m Data min= 0.386697 Data max= 0.974866

Figure Sb. Tidal Cycle Averaged Bottom Layer Relative Concentration for 7Q10 Flow.

52

37.241

37 .231

37.222

37.202

37. 193

37. 183

37. 173

I .55 37. 1 b4

37. 154

37. 145

37. 135

3 7 . 1 25 ................... ....._...1..-J'--J..-'--'--l-.l.--l.....L-...l-...l-L....L-..l.-l-.l.......L.....l..-.l-...l-L....L-..L.....l~-L...1-L...l-L...L,_L...1-L-1--..I::......l

-76.820 -7b.770 -76.720 -76.670 -7b.620

30~5 NSTANTANEOUS DILUTION timestep= 11 Depth= O.Om Data min= 0.340146 Data max= 0.771065

Figure 9a. Instantaneous Surface Layer Relative Concentration for 30QS Flow.

53

-----------------~---_-_-_-__ -_____ -_-_-_-__ -___ - __ -__ -_-_-_ -_-_-_-_-_ ----~-~~-· - . ---- ---

37. 241

)

37.222

~-65

.65

37 .193

37 .183

37 .173

37 .164

37 .154 .55

37. 145

37. 135 !tr 3 7 . 1 25 ....__.__.__,__.....__.__,___,___.__ .......... __.__._ .......... ........__,__.L-...1---L......L.....1-I......L--'--'--.I-...L........__,__.L-...I---L..--'-~'--l..-J--'--i::.......i

-76.820 -76.770 -76.720 -76.670 -76.620

30G5 NSTANTANEOUS DILUTION timestep= 11 Depth= 99.0m Data min= 0.340333 Data max= 0.991445

Figure 9b. Instantaneous Bottom Layer Relative Concentration for 30QS Flow.

54

------~-----___ -- - - - - -- ----- -- - - - - ------ - - -- ---- -- ---- -- ---- -- -- - - - - -- -- ---- -- - - -- - -- --- - --- -------

37.241

37.231

37.212

37.202

37 .193

37 .183

37 .173

37 .1 b4

37. 145

37 .135

37 . 125 ~--~~_._....__..._.___.__._..__.._..._....._..__. ......... _._....__..._.__.__.._..__.._..._....__.....__. ......... _._........., ........... __.._....,__.___.

-76.820 -76.770 -76.720 -76.670 -76.620

30~5 TIDAL CYCLE AVG OIL Data min= 0.334055 Data max= 0.725533

timestep= 0 Depth= O.Om

Figure 10a. Tidal Cycle Averaged Surface Layer Relative Concentration for 3 OQS Flow.

55

•

•

- ---- ----- -- ---- ----- --- - --- ---- -- --- -- -- -

., 37.250

37 .241

37 .231

37.222 ,,.. .65

37.202

37 .193

37 .183

37 .173

37 .1 b4

37 .15.!

37 .145

37 .135

3 7 • 1 2 5 .__,___,_........_.......__.__.......,__.,__.._..___.__,__,.____,___.__.__ .......... __.......,__...1-..JL...--L.---'--'--"----'---'--'--......... __._....,__...J...-l.._..___.__,__"'--'

-76.820 -76.770 -76.720 -76.670 -76.620

3C~5 TIDAL CYCLE AVG OIL timestep= 0 Depth= 99.0m Data min= 0.334310 Data max= 0.975528

Figure 10b. Tidal Cycle Averaged Bottom Layer Relative Concentration for 30QS Flow.

56

•

-- - --- - ---- -- --- -- ------ ----- - --- -- -- -- ------------- --- -

37 .241

37 .231

37.222

37. 183

37 .173 ~\ .55

37. 164

37 .154

37. 145

37 .135

3 7 . 1 25 ......... _.__.___.__.__.,__.__,._'--'-__._...,__..__.__.__._...I.....J__.,__.__,__.__.__,__...,__..__.__.__._....___.__._-'-...1.....JL......J..-'---'--,.;....,

-7f>.820 -76.770 -76.720 -7f>.670 -7f>.f>20

100cms INSTANTANEOUS DILUTION timestep= 11 Depth= 0.0m Data min= 0. 161610 Data max= 0.689590

Figure lla. Instantaneous Surface Layer Relative Concentration for 100 ems Flow.

•

37 . 250 .--.--,---,--,--,--,--,--,--.......... --,-....,.........--,--,--,-..,...-,......,.-r--r-T"""T--.---.-T"""T--r-"T"'."'.,,-,r,--,-.--r-T-r-.--.-,

37 .241

37. 231

37.222

37.212

37 .193

37 .183

37 .173 f .55

37 .1 b4

37 .154

37 .145

37 .135

37 . 1 25 L..J..-L..J.......L.l-L-L.L_L..J..-L...L_.1.......1._J_..J.......J........l-l.....L...L-l..-l.-1-....L_L....1.-l..-L....1-.J---1..-1--...l..-L-J..--L.....J._J.::,_J

-76.820 -7b.770 -7b.720 -7b.b70 -7b.620

100cms INSTANTANEOUS DILUTION timestep= 11 Depth= 99.0m Data min= 0.161682 Data max= 1 .02279

Figure 11 b. Instantaneous Bottom Layer Relative Concentration for 100 ems Flow.

58

--- -- ·---- ---- - - - -·--- -- ----- - ----- --- - ----

,#.•. 37 . 250 ---.--.-..,........,--,..-......-........ -.-......--"r"-T-..--.-..,......, ........ --.-......--........ -.-...,.......--,,-,--,-.,......,--,--,--r-.----.--.-~..--.

37.241

37.231

37.222

37.212

37.202

37. 193

37. 183

37 .173

37 .1 b4

37 .154

37 .145

37. 135

37 . 1 25 L-.l.-..1....._J_.L-.J..-L....1_..l.-L-..L-1-...L-.L...J.--L_J_.l-.J..-L-1-...L-L-..L--1-...L-.L....L--'--'--.L-J--'--'-...J..-...;._...-'--...._J,;.,..,,i

-76.820 -76.770 -76.720 -7&.670 -7&.620

100cms TIDAL CYCLE AVG OIL timestep= 0 Depth= 0.0m Data min= 0.158986 Data max= 0.622086

Figure 12a. Tidal Cycle Averaged Surface· Layer Relative Concentration for 100 ems Flow.

59

60

37.250

37.241

37.231

37.222

37.212

37.202

• 37 .193

37 .183

37 .173

37 .164

37. 154

37 .145 .55

37. 135 I 37 .125

-76.820 -76.770 -76.720 -u,. 6 70 -76.620

100cms TIDAL CYCLE AVG OIL timestep= 0 Depth= 99.0m Data min= 0.160495 Data max= 1 .00355

• Figure 12b. Tidal Cycle Averaged Bottom Layer Relative Concentration for 100 ems Flow.

-·---- ------­-- --· - - -- - ---- --------·- ---- --· -- -- -- - - - - -···

37.241

37.222

37.212

37.202

37 .193

37 .183

37 .173

37 .164

37 .154

37 .145

37 .135

3 7 • 1 25 ,._.__._....._...__..__.___.__.....__.__...__._.....__...._.__.__.__ ............ __.__._.....__.__.__.__.__ .......... _._....._ ............ __.__._....__,._.__._.....__.._.

-76.820 -76.770 -76.720 -76.670 -7!>.620

150cms INSTANTANEOUS DILUTION timestep= 12 Depth= 0.0m Data min= 0.697638E-01 Data max= 0.755267

Figure 13a. Instantaneous Surface Layer Relative Concentration for 15 0 ems Flow.

---i

61

I ---·-- ---- ---------- --- ---

•

•

•

37.241

37.231

37. 164

37. 154

37 .145

37. 135

3 7 • 1 25 Ll---1.......l-.L...J-1......l-..1_;LJ..._1._..L...L-l.---1......l-.L...J-1..-1-.J.......ILJ...-L-..L....L.-l.-L...l-.L...J--1--1-...l...-L-..L--L-.....__.L:......J

-76.820 -76.770 -76.720 -u,. 670 -76.620

150cms INSTANTANEOUS DILUTION timestep= 12 Depth= 99.0m Data min= 0.700095E-01 Data max= 1 .03949

Figure 13 b. Instantaneous Bottom Layer Relative Concentration for 150 ems Flow.

----i

62

•

•

- -- ---- -- -- -- - - ------------- -

37.241

37 .231

37.222

37.212

37.202

37 .193

37 .183

37 .173

37. 164

37 .154

37.145

37 .135

3 7 . 1 25 ~__.__._...._.._.._.....__._ ............ __.._......_ ......... __._~ .......... .__.__._....._ ......... .......__._ ........... __._...,__-'--'--'---'-....._.__,.,_._...,__.i.:......,

-76.820 -76.770 -76.720 -7b.670 -76.620

150cms TIDAL CYCLE AVG OIL timestep= 0 Depth= 0.0m Data min= 0.658340E-01 Data max= 0.578355

Figure 14a. Tidal Cycle Averaged Surface Layer Relative Concentration for 150 ems Flow.

63

"-37.250

37.241

37.231

37.222

37.212

37.202

37 .193

37 .193

37 .173

37 .1 b4

37 .154

.55

V 37 .145

37 .135

37 .125

-76.820 -76,770 -76.720 -76.670 -76.620

150cms TIDAL CYCLE AVG OIL timestep= 0 Depth= 99,0m Data min= 0.665776(-01 Data max= 1 .01396

Figure 14b. Tidal Cycle Averaged Bottom Layer Relative Concentration for 150 ems Flow.

64

•

---- --- ---- ------ -- ---- -- -- ---- ---- ---- --- ------·- -------- ----- ------ ---- -- -----1

37 .241

37.231

37.222

37.202

37 .193

37 .183

37 .173

37 .1 b4

37 .154

37 .145

37 .135

3 7 . 12 5 .__,,__..._.__........_._,__._..,___....__.____.___._.,__.__,__._...___,_,__._..,___L.....l.__,___,__ .......... __,_....i.:_....__.__,__.__.__1-.1.__,__._...__.

-76.770 -76.720 -76.670 -76.620 -76.570

300cms NSTANTANEOUS DILUTION timestep= 12 Depth= O.Om Data min= 0.509726E-02 Data max= 0.914734

Figure 15a. Instantaneous Surface Layer Relative Concentration for 3 00 ems Flow.

i

65

------------------------------------:--~ -

•

37.241

37. 231

37. 183

37. 173

37. 164

37. 154

37. 145

37 .135

37. 125

-76.770 -76.720 -76.670 -76.620 -76.570

300cms NSTANTANEOUS DILUTION timestep= 12 Depth= 99.0m Data min= 0.511959[-02 Data max= 1 .05552

Figure 15b. Instantaneous Bottom Layer Relative Concentration for 3 00 ems Flow.

66

•

37.250

37 .241

37.231

37.222

37.212

37.202

37 .193

37. 183

37 .164

37 .154

37. 145

37 .135

37 . 1 25 .......... ..-__.__ ........... __.___.._...__ ............ ..-......_ ........... __..___.__...,__.__.__.._......_...._.. _ __.__ ........... __..__.._ ........... __.__.._...__...._.. _ _.._........._.

-76. 770 -76.720 -76.670 -76.620 -76.570

300cms TIDAL CYCLE AVG OIL timestep= 0 Depth= O.Om Data min= 0.438936E-02 Data max= 0.805511

Figure 16a. Tidal Cycle Averaged Surface Layer Relative Concentration for 3 00 ems Flow.

67

-- --- -- - ---- - -­·- - ·--------- -

37.241

37.231

37.222

37.212

37.202

37 .193

37 .183

37 .173

37 .164

37 .154

37 .145

37 .135

37. 125 .._.._.__ .......... __ ~ __ ......... _.__.._........__ .......... _ _.__...._.__._ ......... ...._.._........_....._ .......... _ _.__...._.__.__._....._~

-76.770 -76.720 -76.670 -76.620 -76.570

300cms TIDAL CYCLE AVG OIL timestep= 0 Depth= 99.0m Data min= 0.439369E-02 Data max= 0.870133

Figure 16b. Tidal Cycle Averaged Bottom Layer Relative Concentration for 3 00 ems Flow.

68

---- ----- -------- - ------- --- - - ---- - -----

APPENDIX A: DESCRIPTION OF THE EFDC MODEL

The EFDC (Environmental Fluid Dynamics Code) model was developed at the Virginia Institute of Marine Science (Hamrick, 1992a). The model has been applied to Virginia's James and York River estuaries (Hamrick, 1992b) and the entire Chesapeake Bay estuarine system (Hamrick, 1994a). It is currently being used for a wide range of environmental studies in the Chesapeake Bay system including: simulations of pollutant and pathogenic organism transport and fate from point and nonpoint sources, simulation of power plant cooling water discharges, simulation of oyster and crab larvae transport, and evaluation of dredging and dredge spoil disposal alternatives (Hamrick, 1992b). The EFDC model is also currently being used for a study of high fresh water inflow events in the northern portion of the Indian River Lagoon, Florida, (Moustafa and Hamrick, 1994) and a flow through high vegetation density controled wetland systems in the Florida Everglades (Hamrick, 1994b).

The physics of the EFDC model and many aspects of the computational scheme are equivalent to the widely used Blumberg­Mellor model (Blumberg & Mellor, 1987) and U.S. Army Corps of Engineers' Chesapeake Bay model (Johnson, et al, 1993). The EFDC model solves the three-dimensional, vertically hydrostatic, free surface, turbulent averaged equations of motions for a variable density fluid. Dynamically coupled transport equations for turbulent kinetic energy, turbulent length scale, salinity and temperature are also solved. The two turbulence parameter transport equations implement the Mellor-Yamda level 2.5 turbulence closure scheme (Mellor & Yamada, 1982) as modified by Galperin et al (1988). The EFDC model uses a stretched or sigma vertical coordinate and Cartesian or curvilinear, orthogonal horizontal coordinates. The EFDC model also simultaneously solves an arbitrary number of Eulerian transport-transformation equations for dissolved and suspended

69

•

materials. A complimentary Lagrangian particle transport­transformation scheme is also implemented in the model. The EFDC model also allows for drying and wetting in shallow areas by a mass conservative scheme. A number of alternatives are in place in the model to simulate general discharge control structures such as weirs, spillways and culverts. For the simulation of flow in vegetated environments, the EFDC model incorporates both two and three­dimensional vegetation resistance formulations (Hamrick, 1994b).

The numerical scheme employed in EFDC to solve the equations of motion uses second order accurate spatial finite differencing on a staggered or C grid. The model's time integration employs a second order accurate three time level, finite difference scheme with a internal-external mode splitting procedure to separate the internal shear or baroclinic mode from the external free surface gravity wave or barotropic mode. The external mode solution is semi-implicit, and simultaneously computes the two-dimensional surface elevation field by a preconditioned conjugate gradient procedure. The external solution is completed by the calculation of the depth average barotropic velocities using the new surface elevation field. The model's semi-implicit e..xternal solution allows large time steps which are constrained only by the stability criteria of the explicit central difference or upwind advection scheme used for the nonlinear accelerations. Horizontal boundary conditions for the external mode solution include options for simultaneously specifying the surface elevation only, the characteristic of an incoming wave (Bennett & McIntosh, 1982), free radiation of an outgoing wave (Bennet, 1976; Blumberg & Kantha, 1985) or the normal volumetric flux on arbitrary portions of the boundary. The EFDC model's internal momentum equation solution, at the same time step as the external, is implicit with respect to vertical diffusion. The internal solution of the momentum equations is in terms of the vertical profile of shear stress and velocity shear, which results in the simplest and most accurate form of the baroclinic pressure gradients and eliminates the over determined character of alternate internal mode formulations. Time splitting inherent in the three time level scheme is controlled

70

r-------1

------------- --··---- - -- ---------- ------ -- ----­~- - ~- - - -- - --

by periodic insertion of a second order accurate two time level trapezoidal step. The EFDC model is also readily configured as a two­dimensional model in either the horizontal or vertical planes.

The EFDC model implements a second order accurate in space and time, mass conservation fractional step solution scheme for the Eulerian transport equations at the same time step or twice the time step of the momentum equation solution (Sriiolarkiewicz and Margolin, 1993). The advective step of the transport solution uses either the central difference scheme used in the Blumberg-Mellor model or a hierarchy of positive definite upwind difference schemes. The highest accuracy upwind scheme, second order accurate in space and time, is based on a flux corrected transport version Smolarkiewicz's multidimensional positive definite advection transport algorithm (Smolarkiewicz & Clark, 1986, Smolarkiewicz & Grabowski, 1990) which is monotonic and minimizes numerical diffusion. The horizontal diffusion step, if required, is explicit in time, while the vertical diffusion step is implicit. Horizontal boundary conditions include time variable material inflow · concentrations, upwinded outflow, and a damping relaxation specification of climatological boundazy concentration. For the heat transport equation, the NOAA Geophysical Fluid Dynamics Laboratory's atmospheric heat exchange model (Rosati & Miyakoda, 1988) is implemented. The Lagrangian particle transport­transformation scheme implemented in the model utilizes an implicit trilinear interpolation scheme (Bennett & Clites, 1987). To interface the Eulerian and Lagrangian transport-transformation equation solutions with near field plume dilution models, internal time varying volumetric and mass sources may be arbitrarily distributed over the depth in a specified horizontal grid cell. The EFDC model can be used to drive a number of external water quality models using internal linkage processing porcedures described in Hamrick (1994a).

The EFDC model is implemented in a generic form requiring no internal source code modifications for application to specific study sites. The model includes a preprocessor system which _generates a

71

- --- ---- - - -- -·--- ------ - ---- - - - -- - ------- -- ----- --- - --- --- - ----- ------- ---- --------- -- -- -

•

Cartesian ·or curvilinear-orthogonal grid (Mobley and Stewart, 1980; Ryskin & Leal, 1983), and interpolates bathymetry and initial salinity and temperature input fields from observed data. The model's input system features an interactive users manual with extensive on-line documentation of input variables, files and formats. A menu driven, windows based, implementation of the input system is under development. The model produces a variety of ~eal time messages and outputs for diagnostic and monitoring purposes as well a restart file. For post processing, the model has the capability for inplace harmonic and time series analysis at user specified locations. A number of options exist for saving time series and creating time sequenced files for horizontal and vertical sliced contour, color

· shaded and vector plots. The model also outputs a variety of array file formats for three-dimensional vector and scalar field visualization and animation using a number of public and -inexpensive private domain data visualization packages (Rennie and Hamrick, 1992). The EFDC model is coded in standard FORTRAN 77, and is designed to economize mass storage by storing only active water cell variables in memory. Particular attention has also been given to minimizing logical operations with the code being over 95 per cent vectorizable and benchmark at a sustained performance of 150 MFLOPS on a single Cray Y-MP processor. The EFDC model is currently operational on VAX-VMS systems, Sun, HP-Apollo, Silicon Graphics, Convex, and Cray UNIX systems, IBM PC compatible DOS systems (Lahey EM32 Fortran) and Macintosh 68K and Power PC systems (LSI and Absoft Fortran).

The theoretical and computational basis for the model is documented in Hamrick (1992a). Extensions to the model formulation for the simulation of vegetated- wetlands are documented in Hamrick (1994b) and Hamrick and Moustafa (1994b,c). Model applications to tidal estuaries are documented in Hamrick ( 1992b, 1994a), Moustafa and Hamrick (1994b) and Moustafa, Hamrick and Morton (1994). Model applications to wetland systems are documented in Hamrick (1994b) and Moustafa and Hamrick (1994a).

72

•

Appendix A. References

Ambrose, R. B., T. A. Wool, and J. L. Martin, 1993: The water quality analysis simulation program, WASPS. U.S. Environmental Protection Agency, Environmental Research Laboratory, Athens, GA, 210 pp.

Bennett, A. F., 1976: Open boundary conditions for dispersive waves. J. Atmos. Sci., 32, 176-182.

Bennett, A. F., and P. C. McIntosh, 1982: Open ocean modeling as an inverse problem: tidal theory.]. Phys. Ocean., 12, 1004-1018.

Bennett, J. R., and A. H. Clites, 1987: Accuracy of trajectory calculation in a finite-difference circulation model.]. Comp. Phys., 68, 272-282.

Blumberg, A. F., and L. H. Kantha, 1985: Open boundary condition for circulation models.]. Hydr. Engr., 111, 237-255.

Blumberg, A. F., and G. L. Mellor, 1987: A description of a three­dimensional coastal ocean circulation model. In: Three-Dimensional Coastal Ocean Models, Coastal and Estuarine Sdence, Vol. 4. (Heaps, N. S., ed.) American Geophysical Union, pp. 1-19.

Chikhliwala, E. D., and Y. C. Yortsos, 1985: Application of orthogonal mapping to some two-dimensional domains. ]. Comp. Phys., 5 7, 3 91-402.

Galperin, B., L. H. Kantha, S. Hassid, and A. Rosati, 1988: A quasi­equilibrium turbulent energy model for geophysical flows. ]. Atmos. Sci., 45, 55-62.

Cereo, C. F., and T. Cole, 1993: Three-dimensional eutrophication model of Chesapeake Bay.]. Environ. Engnr., 119, 1006-1025.

Hamrick, J. M., 1991: Analysis of mixing and dilution of process water discharged into the Pamunkey River, a Report to the Chesapeake Corp. The College of William and Mary, Virginia Institute of Marine Science, 5 0 pp.

73

-- ------ --- - --- --- -· ---- --------- -·· ---- --------- ----------- ------------- - -- - ·-- ---- - -- ---- -- --

Hamrick, J.M., 1992a: A Three-Dimensional Environmental Fluid Dynamics Computer Code: Theoretical and Computational Aspects. The College of William and Mary, Virginia Institute of Marine Science. Special Report 31 7, 63 pp.

Hamrick, J. M., 1992b: Estuarine environmental impact assessment using a three-dimensional circulation and transport model. Estuarine and Coastal Modeling, Proceedings of the 2nd International Conference, M. L. Spaulding et al, Eds., American Society of Civil Engineers, New Yrok, 292-303.

Hamrick, J.M., 1992c: Preliminary analysis of mixing and dilution of discharges into the York River, a Report to the Amoco Oil Co. The College of William and ~lary, Virginia Institute of :Marine Science, 40 pp.

Hamrick, J. M., 1994a: Linking hydrodynamic and biogeochemcial transport models for estaurine and coastal waters. Estuarine and Coastal Modeling, Proceedings of the 3nd International Conference, M. L. Spaulding et al, Eds., American Society of Civil Engineers, New York, 591-608.

Hamrick, J. M., 1994b: Evaluation of island_ creation alternatives in the Hampton Flats of the James River. a report to the U. S. Army Corps of Engineers, Norfolk District.

Hamrick, J.M., 1995a: Calibration and verification of the VIMS EFDC model of the James River, Virginia. The College of William and Mary, Virginia Institute of Marine Science, Special Report, in preparation.

Hamrick, J. ~I., 1995b: Evaluation of the environmental impacts of channel deepening and dredge spoil disposal site expansion in the lower James River, Virginia. The College of William and Mary, Virginia Institute of Marine Science, Special Report, in preparation.

Hamrick, J.M., and Z. Yang, 1995: Lagrangian mean descriptions of long-term estuarine mass transport. Proceeding of the 1994 International Conference on the Physics of Estuaries and Bays. D. Aubrey, Ed., American Geophysical Union, in press.

74

•

Hamrick, J. M., and M. Z. Moustafa, 1995a: Development of the Everglades wetlands hydrodynamic model: 1. Model formulation and physical processes representation. submitted to Water Resources Research.

Hamrick, J. M., and M. Z. Moustafa, 1995b: Development of the Everglades wetlands hydrodynamic model: 2. Computational implementation of the model. submitted to Water Resources Research.

Johnson, B. H., K. W. Kim, R. E. Heath, B. B. Hsieh, and H. L. Butler, 1993: Validation of three-dimensional hydrodynamic model of Chesapeake Bay.]. Hyd. Engrg., 119, 2-20.

Knupp, P. M., 1992: A robust elliptic grid generator.]. Comp. Phys., 100, 409-418.

Mellor, G. L., and T. Yamada, 1982: Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. Space Phys., 20, 851-875 .

Mobley, C. D., and R. J. Stewart, 1980: On the numerical generation of boundary-fitted orthogonal Curvilinear coordinate systems.]. Comp. Phys., 34, 124-135.

Moustafa, M. Z., and J.M. Hamrick, 1994: Modeling circulation and salinity transport in the Indian River Lagoon. Estuarine and Coastal Modeling, Proceedings of the 3nd International Conference, M. L. Spaulding et al, Eds., American Society of Civil Engineers, New York, 381-395.

Moustafa, M. Z., and J. M. Hamrick, 1995: Development of the Everglades wetlands hydrodynamic model: 3. Model application to South Florida water conservation area 2a. submitted to Water Resources Research.

Moustafa, M. Z., J.M. Hamrick, and M. R. Morton, 1995: Calibration and verification of a limited area circulation and transport model of the Indian River Lagoon. submitted to Journal of Hydraulic Engineering.

75

- ---- --~ -- --- ------ - ------ --------------

Rennie, S., and J.M. Hamrick, 1992: Techniques for visualization of estuarine and coastal flow fields. Estuarine and Coastal Modeling, Proceedi.ngs of the 2nd International Conference, M. L. Spaulding et al, Eds., American Society of Civil Engineers, New York, 48-55.

Rosati, A. K., and K. Miyakoda, 1988: A general circulation model for upper ocean simulation. J. Phys. Ocean., 18, 1601-1626.

Ryskin, G. and L. G. Leal, 1983: Orthogonal mapping. J. Comp. Phys., 50, 71-100.

Smolarkiewicz, P. K., 1984: A fully multidimensional positive definite advection transport algorithm with small implicit diffusion. J. Comp. Phys., 54, 325-362.

Smolarkiewicz, P. K., and T. L. Clark, 1986: The multidimensional positive definite advection transport algorithm: further development and applications. J. Comp. Phys., 6 7, 3 96-43 8.

Smolarkiewicz, P. K., and W. W. Grabowski, 1990: The multidimensional positive definite advection transport algorithm: nonoscillatory option. J. Comp. Phys., 86, 355-375.

Smolarkiewicz, P. K., and L. G. Margolin, 1993: On forward-in-time differencing for fluids: ex~ension to a curvilinear framework. Mon. Weather Rev., 121, 1847-1859 ..

Zalesak, S. T. , 1979: Fully mulqdimensional flux-corrected transport algorithms for fluids. J. Comp. Phys., 31, 335-362.

_~_ --·-1 76