New Finite Volume Method for rotating channel flows involving boundary layers

Abstract

We investigate in this article the boundary layers appearing for a fluid under moderate rotation when the viscosity is small. The fluid is modeled by rotating type Stokes equations known also as the Barotropric mode equations in the primitive equations theory. First we derive the correctors that describe the sharp variations at large Reynolds number (i.e., small viscosity). Second, thanks to a new finite volume method (NFVM) we give numerical solutions of the rotating Stokes system at small viscosity. The NFVM can be applied to a large class of singular perturbation problems.