A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL

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1 Global NEST Journal, Vol 9, No, pp , 7 Copyright 7 Global NEST Printed in Greee. All rights reserved A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL IOANNIS K. TSANIS* USAMA SAIED Department of Civil Engineering MMaster University, Hamilton, Ontario, L8S 4L7, Canada Reeived: 4/3/5 Aepted: 14/7/5 *to whom all orrespondene should be addressed: tsanis@mmaster.a ABSTRACT A program is developed that inludes two hydrodynami models, a D depth-averaged (DH) and a Quasi-3D (Q3D), and a pollutant transport model that uses a 1 st order upwinding and a 3 rd order QUICKEST numerial shemes. Several tests were performed in two test basins in order to examine the performane of the above models. The Q3D model is suessfully applied to Lake Ontario, using a 4-km-square grid, to simulate the wind-indued irulation. Simulations of pollutant transport show that the 1 st order upwinding sheme an be used for estimating pollutant onentrations near the pollutant soure in the ase of ontinuous point soure. However, numerial diffusion affets the estimates further downstream the pollutant soure. Therefore, higher order shemes suh as the third order QUICKEST sheme are required for estimating pollutant onentration at these loations. KEYWORDS: Lake irulation model, pollutant transport model, wind-driven urrents, Lake Ontario INTRODUCTION Hydrodynami and pollutant transport modeling in losed water bodies require a detailed knowledge of the transport proesses that exist within the body. Essential elements for life and produtivity suh as oxygen, heat and nutrients are transported and dispersed through these proesses. These proesses ause the dilution of pollutants though mixing with the ambient water resulting in their redued impat on nearshore areas. The geometry of the losed water bodies suh as lakes reveal that the horizontal length sale is several order of magnitude greater than the vertial length sale. The indued irulation an be hydraulially or wind-driven. For the ase of hydraulially-driven irulation, the urrent vertial distribution is almost uniform over the depth with sharp gradients existing only at the bottom (Blaisdell et al., 1991). The urrent driven vertial veloity profile an be treated as if the whole water olumn is a boundary layer and therefore the Prandtl-von Karman logarithmi veloity profile applies. In this ase, the two-dimensional horizontal depth-averaged model an suessfully simulate the depth-averaged urrent distribution. In the ase of winddriven flows the vertial urrent distribution is ounterurrent with the urrent in lower layers moving in opposite diretion to wind. In order to inorporate the effets of the non-uniform veloity in the vertial plane, Koutitas (1988) developed the so-alled quasi-three-dimensional (Q3D) wind driven irulation model (Wu, 1993). This model, basially, solves the depthaveraged Navier-Stokes equations assuming a paraboli veloity profile in the vertial, to be onsistent with the wind driven veloity profiles. The quasi-three-dimensional model has the advantage of simpliity, requires short omputational time and impliitly implements the vertial urrent distribution. Following the introdution, the analytial bakground of irulation and pollutant transport models are presented. The funtionality of the model and the orresponding program desription with appliations to two basins under different meteorologial and environmental ondi-

2 118 TSANIS and SAIED tions is also presented followed by the appliation of Q3D model and the pollutant transport models to Lake Ontario with the appropriate onlusions. ANALYTICAL BACKGROUND Cirulation Models Two-dimensional horizontal depth-averaged irulation model (DH) Given the large horizontal dimensions (km) relative to the vertial (m) in losed water bodies, the vertial veloities and aelerations are small relative to the horizontal omponents (Csanady, 198). Therefore the vertial equation of motion may be replaed by the hydrostati pressure approximation. The resulting depth-averaged Navier-Stokes equations beome (Koutitas, 1988): U U U ζ τsx τbx + U + V = g + fv+ (1) t x y x ρh ρh V V V ζ τsy τby + U + V = g fu+ t x y y ρh ρh ζ + (UH) + (VH) = (3) t x y where ζ is the water surfae elevation above the mean water level; h is the water depth; H is the total depth of water (i.e. H=h+ζ); U, V are the depth-averaged veloity omponents in x and y diretions respetively; f is the Coriolis parameter; ρ is the water density; τ sx and τ sy are the shear stresses at the water surfae in the x and y diretions respetively, whih represent the vertial boundary ondition as follows: sx CW s x Wx Wy τ = ρ + (4) sy CW s y Wx Wy τ = ρ + (5) where C s is the surfae frition oeffiient (typially of the order of 1-6 assumed.18); W x and W y are the wind speeds in x and y diretions [m s -1 ], respetively. Similarly, the bed frition terms (τ bx, τ by ) are expressed by quadrati forms as follows: bx b τ = ρ CU U + V (6) τ by = ρ CV b U + V (7) where C b is the bottom frition oeffiient (hosen to be.5). In the previous model, the depth averaged approximation of the onvetive terms should have ontain additional terms for horizontal momentum dispersion for the ase of nonlinear vertial veloity profiles, whih is the ase for wind driven flows (Koutitas, 1988). In addition, Equations (6) and (7) imply that when the depth mean veloity omponents are zero, the frition terms are suppressed. However, for wind generated urrents, even in the ase of zero depthmean veloities, the near bed shear is not negligible. Quasi-three dimensional irulation model (Q3D) The advantage of this model is that it an provide the urrent distribution at any depth as well as the depth-averaged urrent struture. The equations of motion in the x and y diretions and the mass ontinuity are simplified under the assumption that a) the water is inompressible and homogeneous, and b) the flow is quasi-hydrostati. The seond assumption is based on the fat that the horizontal dimension of the flow domain is several order of magnitude larger than the vertial dimension (depth). The assumption of nearly horizontal flow is realisti and simplifies the model by exluding the vertial veloity omponent w from the main unknown funtions and leads to a hydrostati pressure distribution. In order to inorporate the effets of the non-uniform veloities in the vertial, espeially in the wind-indued ases, a ()

3 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 119 paraboli veloity profile in the vertial is assumed and the oeffiients are determined from the boundary onditions at the surfae, and the bottom. The veloity profile is defined as follows: 3τsxh 3U z τsxh z u(z) = ρν h ρν h (8) 3τsyh 3V z τsyh z v(z) = ρν h ρν h where the z-axis has its origin oinides with the water surfae; ν is the eddy visosity at the surfae. A onstant eddy visosity is assumed in order to be onsistent with the paraboli veloity profile (Koutitas, 1988). Based on the veloity omponent distributions given by Equations (8) and (9), the onvetive terms are evaluated. The two-dimensional model, improved with respet to the horizontal momentum dispersion and the bed frition for wind generated irulation, beomes (Koutitas, 1988), U τsxh U τsyh U + (1.U + ) + (1.V + ) t 4ρν x 4ρν y ζ τsx U τsx τsx = g + fv + (3λ.5 ) x ρh h ρ ρh V τsxh V τsyh V + (1.U + ) + (1.V + ) t 4ρν x 4ρν y ζ τsy V τsy τsy = g fu + (3λ.5 ) y ρh h ρ ρh ζ + (UH) + (VH) = t x y where τ sx and τ sy are the shear stresses at the water surfae in the x and y diretions respetively and are given by equations (4) and (5). The λ is a oeffiient used to determine the eddy visosity ν through this equation; τ s ν = λh ; τs = τ sx + τ sy ;O[ λ] = ρ (9) (1) (11) (1) 1. (13) Equations (8) and (9) permit the omputation of the urrent pattern at any depth, i.e., the free surfae veloity omponents (z=) are given by: 3U sxh usurf = τ + (14) 4 ρν 3V τsyh vsurf = + (15) 4 ρν The above model was suessfully verified and applied to Lake St. Clair (Wu and Tsanis, 1991) and the model was applied to all the Canadian Great Lakes (Tsanis and Wu, 1991). The quasi-three-dimensional (Q3D) model an estimate the depth averaged veloities as well as the urrent struture in the vertial diretion. Numerial integration A entered finite differene sheme is used to numerially desribe the spatial derivatives. The flow domain is disretized on a spae-staggered grid, and the solution of the finite differene system is ahieved using an expliit leap-frog algorithm for the time integration. The Courant-Friedrihs-Lewy (CFL) riteria ontrols the applied time step as follows (Blaisdell et al., 1991):

4 1 TSANIS and SAIED x t < (16) ghmax where h max is the maximum depth in the alulation domain. As alulation progresses, the kineti energy per unit density ontained in the basin is alulated at eah time step by summing the square of the grid-point veloities U and V: n 1 imax jmax n n n n E = [(Ui,j U i 1 j 1 i+ 1,j ) (Vi,j V i,j+ 1) ]hi,j x = (17) = where i, j and n indies refer to the x, y and time dimensions, respetively. Steady state is ahieved when the ratio between the differene in kineti energy between time steps falls between a ertain auray (typially ). Beause the shortest wavelength omponent whih an be desribed by the omputational mesh is x, and beause of the nonlinearity of the veloity field, aliasing ours (Roahe, 197). Therefore, in order to simulate the transfer of turbulent kineti energy to sales smaller than x, and to ontrol grid dispersion indued by the leap-frog sheme, an artifiial dissipative mehanism is introdued (Blaisdell et al., 1991). Beause it is the long wavelength phenomenon that is of interest herein (surfae elevations and veloities) and not the subsale phenomenon, in ombination with the fat that some damping of the turbulent motions ours naturally, some degree of horizontal smoothing is aeptable and, in fat, desirable. The damping is inorporated into the solution of the temporal derivatives in the following manner: n 1 n U U + ij U ij (1 t h) x U (1 t h) y U = (18) t t 4 t 4 t x y where t h is the smoothing fator, whih may be related to the horizontal eddy visosity by the following relation: ( 1 th ) x υ h = (19) 4 t Pollutant Transport Model The two-dimensional depth-averaged pollutant transport equation for a non-onservative pollutant is: C (CU) (CV) C C + + = (D x ) + (D y ) λc () t x y x x y y where D x, D y are the dispersion oeffiients; U, V are the depth mean veloities in the x and y diretions, respetively; λ is the deay oeffiient (s -1 ). The boundary onditions ompleting the model are; (a) solid boundaries - zero normal flux, (b) free transmission boundaries - uniform flux, and () pollution soures - pollutant onentration is known. A first order deay oeffiient λ is used to model the deay and prodution of a non-onservative pollutant due to the following: (1) biologial growth or deay of bateria, () hemial reation with environment (oxidation, et.), and (3) settlement of floulated pollutant moleules. Two methods are used for the approximation of the onentration at the faes of the grid ells. The 1st is the first-order upwinding sheme, whih usually suffers from numerial diffusion due to the inlination of the veloity vetors with respet to the grid lines. The seond is the third order QUICKEST sheme, whih redues the numerial diffusion. PROGRAM DESCRIPTION The main program onsists of two models; irulation model and pollutant transport model. The irulation model has two options (a) employs the quasi-three-dimensional model and (b) employs the onventional horizontal depth-averaged model. The pollutant transport model is a depth-averaged model and has two options as well (a) employs the 1 st order upwindingdifferening sheme and (b) employs the QUICKEST sheme. The user an hoose different time steps and different simulation times with the above options. Different parameters have to be set by the user to ontrol the following: (1) hoose to run both models simultaneously or separately, () hoose weather the program stops the irulation

5 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 11 model after reahing the steady state or ontinues till the end of the simulation time, (3) hoose the type of the pollutant (instantaneous / ontinuous), (4) hoose the time of introduing the pollutant. The model allows the user to input variable wind onditions as well as steady wind. A two hours warming up period is set for the wind and for the disharge in/out the lake. Table 1 shows the main parameters of the program. dt1 dt tlast tlast nnd nd(k) modtype modsteady nmodel pointtype tpoint n_model nmodel Table 1. Model Parameters Time step for the irulation model (seond) Time step for the pollutant transport model (seond) Simulation time for the irulation model (hours) Simulation time for the pollutant transport model (hours) Number of soure pollutants. Conentration of point soures. =1 if irulation and pollutant transport models are running simultaneously. = if they are running separately. =1 The irulation model will stop after reahing the steady state = The irulation model will stop at the end of the simulation time. =1 The pollutant transport model employs the First order upwinding method = The pollutant transport model employs the QUICKEST method =1 Continuous point soure = Instantaneous point soure Time of introduing the instantaneous point soure (hours) =1 For D depth averaged irulation model = For Quasi-three-dimensional model =1 First order upwinding sheme = QUICKEST sheme The program is designed to write its output as ASCI files, whih an be read by Teplot. The output files an be lassified as two-dimensional output or one-dimensional output. The first inludes the spatial dependent variables suh as veloity, onentration, and water surfae elevation. The later inludes the vertial veloity profile, the time onentration urves, the kineti energy versus time urve and the ross-setion data (i.e. veloity, onentration, et.). A set of Teplot maros were developed in order to prepare the required figures. These maros run in bath mode so that the program with the maros produes a fully objetive-oriented pakage. TEST CASE In order to test the behavior of the irulation model and to ompare between the different hydrodynami and pollutant transport models, two test basins have been assumed. Figure (1) shows the two basins and the horizontal grid. Table () summarizes the test-ase runs. Run# Basin Table. Test-ase runs Model Used Time Step Simulation Time Hydr. Pol. dt1 (s.) dt (s.) Hydr. Pol. Release Time (hr) 1 A Q3D A DH B Q3D B DH A Q3D A DH A Q3D Upwind 8 A Q3D QUIC KEST (,5) (,5) Fore m 3 s -1 Disharge at (,5)

6 1 TSANIS and SAIED Figure 1. Definition of the test Basins Figures and 3 show the irulation patterns, the total kineti energy of flow, and the wind set-up after running the onventional depth averaged model and the Q3D model for basins A and B. There are two resulting irulation ells in basin A due to retangular ross-setion while in basin B there is one lokwise irulation ell due to ross-setion with the sloping bottom The Q3D model results in higher free surfae gradients balaning both the free surfae shear and the bed shear and the total kineti energy is therefore higher in the ase of the Q3D model. Figure 4 shows the vertial veloity profile for two points within the basin A. The Q3D model an resolve the ounterurrent nature of the flow. The Q3D model results in a surfae veloity diretion in almost the same diretion of wind, beause the Coriolis fore is alulated only for the depth-averaged veloity. However, pratially, due to different Coriolis fores for different levels, the Ekman spiral effet results in a surfae veloities defleted 45 lokwise from the wind diretion in the Northern hemisphere (Ekman, 195). The fully three dimensional model developed by Shen and Tsanis (1995) aounts for this phenomenon. The DH model is a good approximation for the ase of hydrauli urrents, where the wind is absent beause the uniform veloity profile is the best approximation for the logarithmi veloity profile. Figure 5 shows the depth averaged hydrauli urrents for the runs 5 and 6. No signifiant differene an be deteted between the depth-averaged veloities in the two runs. Therefore, the paraboli veloity profile (Q3D model) seems to estimate the depth-averaged veloity quite well. Figure 6 shows the differene between the two shemes used to approximate the value of the onentration at the fae of the grid ell namely: 1 st order upwinding sheme and QUICKEST sheme. After 1 hour of release of a 1ppm onservative pollutant at the inlet, the 1 st order upwinding sheme exhibits higher numerial diffusion than the QUICKEST sheme. Case Study: Lake Ontario Lake Ontario is one of the Canadian Great Lakes and is used to demonstrate the appliability of the models. A uniform Cartesian horizontal grid of 4 Km spaing was onstruted and the depth at the enter of eah grid element was obtained. The ourse grid enables hoosing larger time step aording to CFL riteria. The maximum depth of Lake Ontario for this domain is 7 meters, whih makes the maximum possible time step to be 6 seonds in order to meet the stability requirement. Three disharge points on the grid are presribed. The inflow of Niagara River 688 m 3 s -1 at grid point (14,3) and the outflows to the St. Lawrene river, 4118 m 3 s -1 at grid point (75,3) and 76 m 3 s -1 at grid point (71,6).

7 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 13 Q3D, Depth Averaged Veloity 1m/s DH, Depth Averaged Veloity 1m/s (15,8) (15,8) (1,5) (1,5) a) Cirulation pattern after applying Q3D model b) Cirulation pattern after applying DH model Kineti Energy Wind Set-up 6. Q3D DH 5.1 K.E. (Joule/(kg/m3)) 4 3 Q3D DH Wind Set-up (m) Distane (m) Time(hours) ) Total Kineti Energy in both ases d) Wind Set up in both ases Figure. Depth averaged wind indued urrent distribution and wind set-up in Basin-A for 5 m s -1 West Wind. Q3D, Depth Averaged Veloity m/s DH, Depth Averaged Veloity m/s a) Cirulation pattern after applying Q3D model Kineti Energy b) Cirulation pattern after applying DH model Wind Set-up Q3D DH 3 K.E. (Joule/(kg/m3)) 5 15 Q3D DH Wind Set-up (m) Distane (m) Time(hours) ) Total Kineti Energy in both ases d) Wind Set up in both ases Figure 3. Depth averaged wind indued urrent distribution and wind set-up in Basin- B for 5 m s -1 West Wind

8 14 TSANIS and SAIED Horizontal Veloity Profile at (1,5) Horizontal Veloity Profile at (15,8) Depth (m) Depth (m) U(m/s) 1 3 U(m/s) Figure 4. Vertial profile of the horizontal veloity in the diretion of wind for Basin-A due to 5 m s -1 West Wind Veloity Vetors, After 5 hours - DH 1. m/s Veloity Vetors, After 5 hours - Q3D 1. m/s Figure 5. Depth averaged hydrauli urrent distribution for Basin-A under an inflow of 5 m 3 s -1 Conentration Distribuation, After 5 hours - 1st order upwinding sheme 1. m/s Conentration Distribuation, After 5 hours - QUICKEST 1. m/s Figure 6. Equal onentration ontours after 1 hours of the release of 1ppm onservative pollutant for 1-hour using 1 st order upwinding sheme. A numerial test for the hydrodynami model of Lake Ontario found that the time step does not signifiantly affet neither the total kineti energy of flow nor the time required to reah the steady state as long as the stability riteria is satisfied. To study the effet of the wind speed on the time to steady state, several runs were made to obtain the steady state time. All the runs were made using western winds. Table 3 shows the results of this study. It an be shown that it takes longer to reah steady state at lower wind speeds.

9 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 15 Table 3. The effet of wind speed on the time to steady state for Lake Ontario (Western Winds). Wind Speed (m s -1 ) Time to Steady State (hours) Several runs were made for Lake Ontario in order to ompare the results between the different models presented above. Table 4 summarizes these runs. Table 4. Lake Ontario s runs. Run # Model Used Time Step (s.) Simulation (h.) Hydr. Poll. Hydr. Poll. Hydr. Poll. Release time (h.) Fore 1 Q3D m s -1 west wind Q3D m s -1 west wind 3 DH m s -1 west wind 4 Q3D Upwind m s -1 west wind 5 Q3D Upwind m s -1 west wind 6 Q3D QUIC m s -1 west wind KEST 7 Q3D QUIC m s -1 west wind KEST 8 Q3D Upwind m s -1 west wind 9 Q3D Upwind m s -1 west wind 1 Q3D QUIC m s -1 west wind KEST 11 Q3D QUIC KEST m s -1 west wind Figure 7 shows the steady state irulation pattern in Lake Ontario due to 5m/s and 1m/s west wind respetively after applying the Q3D model. Four points have been seleted to inspet the vertial veloity profile within the lake domain as shown in Figure 7. Figure 8, shows the vertial veloity profiles for the four seleted points. It an be shown that strong return flows ours at deep waters in the middle of the lake, while the shallow shores do not have return flows, whih is onsistent with the urrent struture identified by Simons (1973). Figures 9 and 1 show the equal onentration ontours after and 1 days of the release of 1ppm of a onservative pollutant for hours using the 1 st order upwinding sheme and the QUICKEST sheme, respetively. The differene between the two shemes is lear after 1 days, where the numerial diffusion affets the former. In order to ompare the performane of above shemes, the time-onentration urves at four points are shown in Figure 11. The differene between the two shemes is lear. The results of the two shemes for the ase of instantaneous point soure are given in Table 1. Generally, the spread and the time required for the pollutant to appear at the point T i is less in the ase of upwinding sheme.

10 16 TSANIS and SAIED Q3D, Depth Averaged Veloity - Due to 5. m/s Western Wind 1 m/s Q3D, Depth Averaged Veloity - Due to1. m/s Western Wind 1 m/s (3,17) (43,1) (3,17) (43,1) (39,13) (5,9) (39,13) (5,9) Figure 7. Steady State Cirulation pattern in Lake Ontario due to 5 m s -1 and 1 m s -1 West Wind. Horizontal Veloity Profile at (3,17) Horizontal Veloity Profile at (39,13) Depth (m) Depth (m) U(m/s) - -1 U(m/s) Horizontal Veloity Profile at (43,1) Horizontal Veloity Profile at (5,9) Depth (m) Depth (m) U(m/s) - -1 U(m/s) Figure 8. Vertial profile of the horizontal veloity in the diretion of the wind, due to 5 m s -1 west wind (Run#1) Figures 1 and 13 show the equal onentration ontours after and 1 days of the release of 1ppm of a onservative pollutant ontinuously using the 1 st order upwinding sheme and the QUICKEST sheme, respetively. The differene between the two shemes is lear after 1 days sine the pollutant reahes at a farther distane downstream for the ase of the former sheme. Figure 14 shows the time onentration urves for the four points in the downstream path of the pollutant. The results of the two shemes for the ase of ontinuous point soure are shown in Table 6. The differene between the values of the final onentration (C s ) at a point C using both shemes are within.7%. The differene inreases signifiantly further downstream for points, and C5, where it reahes %. The 1 st order upwinding overestimates the onentration for, and C5 due to the numerial diffusion as the pollutant reahes the point muh faster and aumulates earlier as shown in Figure 14.

11 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 17 Lake Ontario, After 3 hours from Applying a 1ppm of Conseravtive Pollutant at for hours 1st order upwinding sheme C Lake Ontario, After hours from Applying a 1ppm of Conseravtive Pollutant at for hours 1st order upwinding sheme C Figure 9. Equal onentration ontours after 3 and hours of the release of 1ppm onservative pollutant for -hours using 1 st order upwinding sheme. Lake Ontario, After 3 hours from Applying a 1ppm of Conseravtive Pollutant at for hours QUICKEST Sheme C Lake Ontario, After hours from Applying a 1ppm of Conseravtive Pollutant at for hours QUICKEST Sheme C Figure 1. Equal onentration ontours after 3 and hours of the release of 1ppm onservative pollutant for -hours using QUICKEST sheme.

12 18 TSANIS and SAIED 18 Conentration (ppm) C 1st order 1st order 1st order C5 1st order C QUICKEST QUICKEST QUICKEST C5 QUICKEST Time(hours) Figure 11. Time Conentration Curves for Points C,,, and C5 Table 5. Comparison between 1 st order upwinding sheme results and QUICKEST sheme results for the ase of instantaneous point soure. Point 1 st order Upwinding Sheme QUICKEST Sheme T i (hours) C p (ppm) T p (hours) T i (hours) C p (ppm) T p (hours) C C T i : Time required for pollutant to appear at the point (hours). T p : Time at whih the pollutant onentration reahes its maximum value (hours). C p : Peak onentration at the point (ppm). Table 6. Comparison between 1 st order upwinding sheme results and QUICKEST sheme results for the ase of ontinuous point soure. Point 1 st order Upwinding Sheme QUICKEST Sheme T s (hours) C s (ppm) T s (hours) C s (ppm) C C5 > T s : Time required for the pollutant onentration to reah the steady state (hours). C s : Conentration of the pollutant at steady state (ppm).

13 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 19 Lake Ontario, After 3 hours from Applying a 1ppm of Conseravtive Pollutant at Continuously 1st order upwinding sheme C Lake Ontario, After hours from Applying a 1ppm of Conseravtive Pollutant at Continuously 1st order upwinding sheme C Figure 1. Equal onentration ontours after 3 and hours of the release of 1ppm onservative pollutant ontinuously using 1 st order upwinding sheme. Lake Ontario, After 3 hours from Applying a 1ppm of Conseravtive Pollutant at Continuously QUICKEST sheme C Lake Ontario, After hours from Applying a 1ppm of Conseravtive Pollutant at Continuously QUICKEST sheme C Figure 13. Equal onentration ontours after 3 and hours of the release of 1ppm onservative pollutant ontinuously using QUICKEST sheme.

14 13 TSANIS and SAIED 7 Conentration (ppm) C 1st order 1st order 1st order C5 1st order C QUICKEST QUICKEST QUICKEST C5 QUICKEST Time(hours) Figure 14. Time Conentration urves for points C,,, and C5 CONCLUSIONS Modeling the hydrodynamis and pollutant transport in lakes an be aomplished by using two-dimensional models that have the advantage of simpliity and reah good results in ases of hydraulially-indued irulation. Quasi-three-dimensional models an simulate both the hydraulially and wind-indued irulation by providing the depth-averaged irulation and the vertial urrent distribution. The 1 st order upwinding sheme an be used for estimating pollutant onentrations near the pollutant soure in the ase of ontinuous point soure. However, with inreasing the transport time this sheme is greatly influened by numerial diffusion resulting in inaurate results. Higher order shemes suh the QUICKEST sheme minimize the numerial diffusion and an estimate the pollutant onentration at these loations. The smoothing fator and the artifiial horizontal eddy visosity play important role in the hydrodynamis and have to be alibrated arefully for the grid size used in the simulation. REFERENCES Blaisdell, M.A., Tsanis, I.K., and Krestenitis, Y. (1991) Modeling the steady-state irulation in a distorted physial model of the Windermere Basin, Canadian Journal of Civil Engineering, Vol. 18-5, Csanady, G.T. (198) Cirulation in the oastal oean, D. Reidel Publishing Company, Dordreht, Holland. Ekman, V.W. (195) On the influene of the earth s rotation on oean urrents, Ark. Mat. Astro. Fys., (11):1-53 Koutitas, C.G. (1988) Mathematial Models in Coastal Engineering, Penteh Press Limited, London. Roahe, P.J. (197) Computational Fluid Dynamis, Hermosa Publishers, Albuquerque, NM. Shen, H. and Tsanis, I.K. (1995) A three dimensional nested hydrodynami/pollutant transport simulation model for the nearshore areas of Lake Ontario, J. Great Lakes Res., 1(): Simons, T.J., 1971, Development of numerial models of Lake Ontario, in Pro. 14 th Conf. Great Lakes Res., Internat. Asso. Great Lakes Res, pp Tsanis, I. K. and Wu, J. (1994) LMS An Integrated Lake Modeling System, Environmental Software. Tsanis, I.K. and Wu, J. (1991) Study of water urrents in the Canadian Great Lakes, Atmospheri Servie (AES) Report.

15 A WIND-DRIVEN HYDRODYNAMIC AND POLLUTANT TRANSPORT MODEL 131 Wu, J. and Tsanis, I.K., (1991) Quasi-three-dimensional modeling for Lake St. Clair, 11 th CSCE Annual Conferene, May 9-31, Vanouver, B.C. pp Wu J. (1993) An Integrated Hydrodynami and Pollutant Transport Model for the Nearshore Areas of the Great Lakes and Their Tributaries, Ph.D. thesis, MMaster University, Department of Civil Engineering.