| his paper is devoted to the theoretical and numerical study of a method which computes the variability of current and density in an oceanic domain. The equations are of Navier-Stokes type for the velocity and of transport-diffusion type for the density. They are linearized around a given mean circulation and modified by physical assumptions including hydrostatic approximation. The existence and uniqueness of a solution are proved for two sets of equations: first the three-dimensional problem and then the two-dimensional cyclic problem derived by assuming a sinusoïdal x-dependence for the perturbation of the mean flow. The latter corresponds to a modellization of tropical instability waves which are illustrated by the 'El Nino' phenomenon. These two problems differ from classical ones because of hydrostatic approximation, boundary conditions imposed by the oceanic domain and complex-valued functions for the cyclic case. A numerical model is developed for the two-dimensional cyclic equations. Time discretization is performed by the characteristics method; space discretization uses Q1 finite elements. Numerical results are presented in a realistic case corresponding to the tropical Pacific Ocean. |
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