Dynamics of large-amplitude geostrophic flows: the case of ‘strong’ beta-effect

Abstract

This paper examines the dynamics of geostrophic flows with large displacement of isopycnal surfaces. The β-effect is assumed strong i.e. the parameter (Rd cot θ)/Re (where θ is the latitude, Rd is the deformation radius, Re is the Earth's radius) is of the order of, or greater than, the Rossby number. A system of asymptotic equations is derived, with the help of which the stability of an arbitrary zonal flow with both vertical and horizontal shear is proven. It is demonstrated that the horizontal and vertical spatial variables in the asymptotic system are separable, which yields a ‘horizontal’ set of evolutionary equations for the amplitudes of the barotropic and baroclinic modes (the vertical profile of the latter is arbitrary).