Stability Criteria Independent from the Perturbation Wavenumber for Forced Zonal Flows

Abstract

Sufficient conditions for the linear stability of quasi-geostrophic forced zonal flows are derived in the presence of bottom friction and horizontal diffusion of relative vorticity. The criteria are able to take into account perturbations of arbitrary structure in the sense that they do not depend on any perturbation wavenumber. The stability is controlled by the maximum of the shear of the basic flow and by the maximum of its meridional derivative and involves the dissipation?diffusion coefficients. A comparison with the stability properties in the pure inviscid case is made showing the effects of bottom dissipation in damping the longer wavelengths.