Wave Boundary Layers in a Stably Neutrally Stratified Ocean

Abstract

The theory of wave boundary layers developed in [7] is generalized to the case of a stably neutrally stratified ocean consisting of a homogeneous upper layer and a stably stratified lower layer. In such a configuration, a wave boundary layer arises near the interface in the lower stratified fluid, in addition to the boundary layers near the surface and bottom. Each boundary layer is a narrow domain characterized by sharp buoyancy and horizontal velocity gradients that increase with time. As in [7], the boundary layer near the interface can evolve as a result of the free linear wave evolution of an initial perturbation. An exact solution and asymptotic solution valid at large times are determined; the asymptotic solution approximates the exact one fairly well even for moderate times.