Viscous boundary layers in rotating fluids driven by periodic flows

Abstract

The paper analyzes the boundary layers formed in a rotating fluid by an oscillating flow over an infinite half plate, with particular attention paid to the effects of unsteadiness, the critical latitude effect and the structure of the solution to the boundary layer equations at resonance. The Navier-Stokes boundary layer equations are obtained through an asymptotic expansion with the incorporation of the Rossby and Ekman numbers and are analyzed as the sum of a nonlinear steady solution and a linearized unsteady solution. The solution is predominantly composed of two inertial wave vector components, one circularly polarized to the left and the other circularly polarized to the right. The problem considered here has relevance in oceanography and meteorology, with special reference to the unsteady atmospheric boundary layer.