Wave boundary layers near the surface and bottom in a stratified fluid

Abstract

The paper examines so-called wave boundary layers arising in a bounded stratified fluid for large times. Each the layer is a narrow domain in the vicinity of the fluid surface and/or bottom characterized by sharp, growing with increasing time, vertical gradients of the buoyancy and horizontal velocity. The layers arise as a result of free linear wave evolution of the initial fields if the initial buoyancy at the boundaries depends on the horizontal coordinates. An asymptotic solution for the boundary layer for large times is presented, and it is shown that this solution describes exact fields fairly well even for moderate times.