The generalized nonlinear Galerkin method applied to hydrodynamics of the open sea

In this paper we present new numerical algorithms based on a generalized no nlinear Galerkin method in order to solve coastal and oceanic circulation p roblems. The equations system is based on the primitive equations of the oc ean under Boussinesq and hydrostatic approximations. These equations are tr ansformed using, at the same time, the classical sigma transformation and a n original homogenization of the boundary conditions. We use a well adapted special basis to apply the usual Galerkin method and the nonlinear Galerki n method. This basis is built on a modelization of the energetic transfers through the different scales of flow. Two approaches are proposed to solve the continuity equation: the (nonlinear) Galerkin method and the method of the characteristics. We present the advantages and drawbacks of both method s.