Barotropic-baroclinic time splitting for the primitive equations of the ocean

Our object in this article is to describe some numerical schemes for the numerical simulations of the primitive equations of the ocean with the rigid lid approximation. The multilevel method used stems from the study of evolution equations from the dynamical point of view and has been successfully applied in other contexts, such as the Navier-Stokes flow. The algorithm is based on a differentiated treatment of the small and the large wave lengths of the flow. Some numerical simulations are presented to illustrate the method.