SINGULAR PERTURBATION ANALYSIS ON A HOMOGENEOUS OCEAN CIRCULATION MODEL

Abstract

In this article, we consider the barotropic quasigeostrophic equation of the ocean in the context of the beta-plane approximation and small viscosity (see, e. g., [21, 22]). The aim is to study the behavior of the solutions when the viscosity goes to zero. To avoid the substantial complications due to the corners (see, e. g., [25]) which will be addressed elsewhere, we assume periodicity in one direction (0y). The behavior of the solution in the boundary layers at x = 0, 1 necessitate the introduction of several correctors, solving various analogues of the Prandtl equation. Convergence is obtained at all orders even in the nonlinear case. We also establish as an auxiliary result, the C-infinity regularity of the solutions of the viscous and inviscid quasigeotrophic equations.