Despite the wide application of eddy viscosity models in simulating the 

 large-scale circulation in water bodies, many dynamic processes cannot be 

 accurately simulated by the eddy viscosity models. This is particularly true 

 in highly stratified and/or highly oscillatory flow conditions, such as the 

 mixed layer dynamics and the benthic boundary layer dynamics. Under these 

 circumstances, the turbulence is generally not in equilibrium with the mean 

 flow gradients and one has to use models that resolve the time rate of change, 

 convection, diffusion, production, and dissipation of turbulence. These 

 Reynolds stress models, also called second-order closure models, solve the 

 dynamic equations for the mean flow variables as well as the second-order 

 turbulent correlations. The dynamic nature of this type of model permits one 

 to use a universal set of model constants for a wide variety of flow 

 simulations without having to do site-specific parameter tuning normally 

 required for eddy viscosity models. Although fully three-dimensional 

 application of such a model is still limited by the prohibitive computational 

 cost, one can use simplified versions of this model to derive a physically 

 more meaningful eddy coefficient formulation. A brief discussion on the 

 formulation and applications of a Reynolds stress model is given in 

 Appendix D. 



Forcing 



Models can also be classified according to the type of forcing (in 

 parenthesis) as either a wind-driven circulation model (wind), a 

 density-driven circulation model (density gradient), a storm surge model 

 (storm), or a tidal circulation model (tide). In the most general case, all 

 the forcings should be resolved by the numerical model. 



Model for the Present Study 



For the present study, an efficient three-dimensional, time-dependent, 

 free-surface model has been developed. Forcings including tides, winds, and 

 density gradients are properly resolved. To better resolve the complex 

 geometry and bottom topography in coastal waters, vertical as well as 

 horizontal stretchings are applied to the generally non-uniform coordinates. 

 A special effort has been made to significantly improve the computational 

 efficiency of the model such that long-term simulation can be performed. In 



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