maximum allowable time step. The rigid-lid model has been used quite 



extensively to study circulations in the atmosphere (Mason and Sykes, 1978; 



Lewellen and Sheng, 1981), oceans (Bryan, 1969) and lakes (Sheng, 1975; 

 Bennett, 1977). 



Scale of Interest 



Global circulation in an enclosed basin can generally be resolved with a 

 numerical model and a grid encompassing the entire basin. In coastal waters, 

 however, limited-area models with a fine grid resolution in the nearshore 

 region are often desired. In such a case, proper coupling between the 

 nearshore region and the offshore region not resolved by the model is 

 required. Open boundary conditions need to be properly specified to ensure 

 correct forcing and to eliminate computational modes and numerical 

 instability. These aspects shall be addressed later. 



Even if one's interest is only in the large-scale motion in a water body, 

 the ability of a numerical model to simulate realistic events may still depend 

 upon how well the model parameterizes the important small-scale 

 (boundary-layer) processes. Consider relatively deep water under the action 

 of wind and earth rotation. There are generally seven layers in the vertical 

 direction when proper averaging in time and space is performed on the flow 

 variables: 



(1) a very thin laminar sublayer below the free surface, within which 

 the velocity varies linearly with depth, 



(2) a constant flux layer within which the velocity varies 

 logarithmically with depth, 



(3) a surface turbulent Ekman layer within which turbulent mixing is 

 important. 



(4) a generally non-turbulent geostrophic core within which the velocity 

 varies relatively little with depth, 



(5) a bottom turbulent Ekman layer, 



(6) a constant flux layer near the bottom, and 



(7) a very thin laminar sublayer adjacent to the bottom. 



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