A study of the phase instability of quasi-geostrophic Rossby waves on the infinite β-plane to zonal flow perturbations

Abstract. The problem of the linear instability of quasi-geostrophic Rossby waves to zonal flow perturbations is investigated on an infinite β-plane using a phase dynamics formalism. Equations governing the coupled evolutions of a zonal velocity perturbation and phase and amplitude perturbations of a finite-amplitude wave are obtained. The analysis is valid in the limit of infinitesimal, zonally invariant perturbation components, varying slowly in the meridional direction and with respect to time. In the case of a slow sinusoidal meridional variation of the perturbation components, analytical expressions for the perturbation growth rates are obtained, which are checked against numerical codes based on standard Floquet theory.