Abstract
A spectral method employing eddy-viscosity eigenfunctions is used to solve the full three-dimensional nonlinear hydrodynamic equations for the numerical computation of flows caused by tides or meteorological forcing. An explicit finite element method is developed to compute the nonlinear advective terms and an explicit treatment of bottom friction is used. This leads to a rapidly convergent expansion and relatively few eigenfunctions are required to obtain accurate solutions. An Arakawa B-grid is used in the horizontal directions and leapfrog time-stepping. The eigenfunctions are computed at the beginning of the program, for an arbitrary spatial dependence of eddy viscosity, using the SLEIGN subroutine. Several model problems have been used to test the accuracy, stability, and computational efficiency of the method.
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