A quasi-linear theory for rotating flow over topography. Part 2. Beta-plane annulus

Abstract

An obstacle in westerly flow on a periodic β-plane can generate resonant Rossby waves and cause large perturbations to the flow field. The pattern and strength of the flow can vary markedly in response to relatively small changes in the forces driving the system. The aim of this paper is to develop a simple theory valid in these circumstances. Such a theory has application to the dynamics of planetary scale quasi-steady perturbations in the atmosphere.A series of models for barotropic quasi-geostrophic flow in an annulus is presented. An implicit quasi-linear model, with zonally averaged flow parametrized in terms of topography shape and net zonal mass transport, gives good agreement with nonlinear calculations. In one case stable multiple equilibria are predicted and confirmed, but the multiplicity regime is small.