The bottom stress can be related in a linear or nonlinear way to the bottom velocity, which in this case has to be replaced by the depth-mean averaged velocity. For a formulation of these terms and a discussion of the typical values used in previous modeling efforts see the next section.
We come now to a discussion of the boundary conditions. The main criterion here is whether a boundary is closed (like at a shore) or open (like at a strait where waves and currents can enter and exit the model region). As our first exercise we choose closed boundaries in a rectangular geometry [, ], for which the relevant conditions imposed on U, V, and are as follows:
The vanishing of the tangential velocity implies the existence of frictional boundary layers, because the velocity is brought to zero from the free stream value across a thin boundary layer, and in this layer, friction is important.
Before we discuss the numerical procedure for solving the above equations (2)--(5) we must discuss the formulation and magnitudes of the lateral and bottom friction terms, and the nature and source of the wind stresses used to force or drive the ocean model.