with the improvement in numerical techniques and computer resources, 

 three-dimensional models have become more advanced. The following discussion 

 centers on the three-dimensional models. 



Time Variation 



If the time scale of the dominant forcing (e.g., wind) is larger than the 

 other characteristic time scales of the water body, a quasi-steady state 

 exists and one may use a steady-state model which essentially removes the 

 effect of time variation from the problem. One may also utilize the 

 steady-state model to study a series of wind-driven events while using 

 different eddy viscosities to simulate the varying randomness effects. The 

 steady-state model has been used extensively for studying currents in enclosed 

 bodies of water such as lakes and reservoirs (e.g., Sheng and Lick, 1972; 

 Sheng, 1975). For instance, if the winter winds over Lake Erie remain 

 relatively steady for more than 1 day, the currents can be predicted with 

 reasonable accuracy by means of a three-dimensional, steady-state, wind-driven 

 circulation model. For coastal studies, however, the steady-state analysis 

 may not always be valid. 



Air-Sea Interface 



Free-surface models allow the vertical movement of air-sea interface and 

 hence the propagation of surface gravity waves. Earlier free-surface models 

 usually solved for the primitive equations with an explicit time-marching 

 scheme (e.g., Leendertse and Liu, 1975; Forristal, et al., 1977; Sheng, 

 1975). Although the numerical algorithm was rather straightforward, the 

 numerical time step was severely restricted by the time for the surface 

 gravity wave to propagate the distance of one spatial grid (on the order of a 

 few seconds). Recently, more efficient free-surface models which do not 

 contain this limit (At - 30 min) have been developed (e.g., Sheng, et al., 

 1978). If the time period of interest is much greater than the dominant 

 seiche periods in the water body, however, one can use a rigid-lid model which 

 treats the air-sea interface as a rigid lid with no vertical motion and hence 

 eliminates the gravity wave propagation altogether. A larger numerical time 

 step is allowed this way. The trade-off is that one now has to solve a 

 Poisson equation for the surface pressure which may offset the gain in the 



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