Nonlinear Stability of the Generalized Eady Model

Abstract

Linear and nonlinear stability theorems for the generalized Eady model are obtained by the normal-mode method and the energy?Casimir method, respectively. The nonlinear stability criterion is optimal in the following sense: if it is destroyed, then there always exists a finite periodic zonal channel in which there is an exponentially growing normal mode. The theorems show that the ?long-wave cutoff? phenomenon exists if and only if the ? effect is considered in the model, and the ?short-wave cutoff? phenomenon always exists both on an f plane and on a ? plane.