Counter‐propagating rossby waves in the barotropic rayleigh model of shear instability

Abstract

AbstractWave development, using Rayleigh's 1880 model of barotropic, inviscid and incompressible flow, with a mean zonal wind which is linearly sheared between two edges, is described in terms of the interaction between two counter‐propagating Rossby waves (CRWs). Although the solutions described by this approach could also be described by a sum of the normal modes originally obtained by Rayleigh, we offer a CRW description of Rayleigh's model because it provides a useful pedagogical framework for illustrating, in a precise and quantifiable manner, the interacting Rossby wave view of instability. A CRW interpretation of a modified version of the Rayleigh model, consisting of a jet‐like flow ..