The Sinc-Galerkin method for problems in oceanography

Abstract

The model for a wind-driven current with depth-dependent eddy viscosity is developed as a complex velocity formulation and a coupled system formulation. The numerical solutions, calculated by a Sinc-Galerkin method, are compared. A fully Sinc-Galerkin method in both space and time for a partial differential equation with time-dependent boundary conditions is developed. This entirely new technique is applied to the model for a wind-driven current with time-dependent viscosity. Several numerical examples are used to test the performance of the method. This fully Sinc-Galerkin method is then applied to the spin-up and the episodic wind stress oceanography problems.