COASTAL, ESTUARINE, AND LAKE CURRENTS 



Sheng and Butler (15) developed an efficient three-di/nensional , 

 time-dependent nunerical model of coastal, estuarine, and laKe 

 currents. Special computational features included in tne model are: 

 (1) a time-splitting technique which separates the computation of the 

 slowly-varying internal mode (3-D variables) from the computation of 

 the fast-varying external mode (water level and vertically-integrated 

 velocities) , (2) an efficient ADI algorithm for the computation of the 

 external mode, (3) a vertically-stretched coordinate that allows the 

 same order of accuracy in the vertical direction at all horizontal 

 locations, and (U) an algebraically-stretched horizontal grid tnat 

 allows concentration of grid lines in regions of special interest. 

 These features make the model suitable for long-term simulation of the 

 dynamic response of coastal, estuarine, and lake waters to winds, 

 tides, and meteorological forcing. 



It remains a challenge for hydraulic engineers and oceanographers 

 to properly resolve the turbulent transport phenomena in such 

 meso-scale circulation models. In Sheng and Butler (15). turbulence 

 parameterization is based on the assumption that the production of 

 turbulence equals the dissipation of turbulence. Quadratic stress laws 

 are assumed at the air-sea interface and the bottom. To improve the 

 predictability of the three-dimensional hydrodynamic model, the 

 turbulent transport model described early in this paper could be 

 utilized. The basic model, as represented by Equations (1) through (7) 

 and appropriate boundary conditions, could be applied to the general 

 three-dimensional time-dependent flow. In such a case, however, tne 

 numerical computation of all the dynamic equations represents a 

 formidable task. To keep the problem manageable, I believe a condensed 

 version of the turbulent transport model should be used. Assuming a 

 high Reynolds nunber local equilibrium, the Reynolds stress and heat 

 flux equations form a set of algebraic relationships between the 

 turbulent correlations and the mean flow derivatives. The turbulent 

 dynamics is carried by the dynamic equation for q =u^u^: 



^ ^ U. -^ = -ZITT-— -2g, -^^-^ (q/.Sa_ ) (13) 



dt J dXj ^ J axj 



and Equation (7) for the tur bule nt macroscale A. An extra term needs 

 to be added to each of the u^^u^ equations to allow Equation (13) to be 

 added without making the system overdetermined . This approximation 

 allows for much better representation of the turbulent boundary layers 

 in the ocean than do the standard eddy-viscosity models , and should be 

 valid so long as the time scale of turbulence, A/q, is less than the 

 time scale of the mean flow. 



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