Three-dimensional model for tides and surges with vertical eddy viscosity prescribed in two layers—I. Mathematical formulation

Summary. The mathematical basis of a spectral method for the numerical solution of the three-dimensional hydrodynamic equations for tides and surges is described. Vertical eddy viscosity is prescribed in two layers, upper and lower. In each layer, horizontal components of current are expanded through the vertical in terms of a set of eigenfunctions. Coefficients of these expansions are evaluated in the horizontal and through time using a two-dimensional numerical time-stepping procedure. Thence the three-dimensional current structure is determined.