The classical theory of the steady wind-driven circulation in shallow waters described by the linear three-dimensional equations is generalized to include arbitrary variations of the vertical eddy viscosity. The stream function equation is compared to the corresponding equation of a two-dimensional model. The influence, on the solution, of various eddy viscosity profiles and/or bottom boundary conditions is discussed. From the comparison of the equations, a parameterization of the bottom stress in terms of transport and wind stress is derived such that the two-dimensional model can yield results identical to those of the three-dimensional model. © 1987.
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