Resolution to a three-dimensional physical oceanographic problem using thenon-linear Galerkin method

This paper presents the numerical results concerning the adaptation of the non-linear Galerkin method to three-dimensional geophysical fluid equations . This method was developed by Marion and Temam to solve the Navier-Stokes two-dimensional equations. It allows a substantial decrease in calculation costs due to the application of an appropriate treatment to each mode based on its position in the spectrum. The large scales involved in the study of geophysical flow require that the earth's rotational effects and the exist ence of a high degree of stratification be taken into account. These phenom ena play an important role in the distribution of the energy spectrum. It i s shown here that the non-linear Galerkin method is very well-suited to the treatment of these phenomena. First, the method for the particular situati on of a rigid-lid with a flat bottom is validated, for which the functional basis used is particularly well-adapted. Then the more general case of a d omain exhibiting variable bathymetry is presented, which necessitates the u se of the transformation sigma, thus providing a study domain with a cylind rical configuration. Copyright (C) 1999 John Wiley & Sons, Ltd.