Barotropic Instability and Rossby Wave Radiation

Abstract

A detailed study of linear barotropic instability confirms that the concept of critical level overreflection is fundamental to the understanding of the entire family of unstable modes in this problem. This is in agreement with the general argument presented by Lindzen and Tung and applied by Lindzen et al.. However, our approach in the analysis is somewhat novel, and it may be seen as an extension of the exact method of calculation employed by Davis and Peltier in their work on stratified parallel flows. The practical numerical utility of the neutral stability boundaries as a basis for the determination of both the radiating unstable modes and the fundamental unstable modes is demonstrated. The actual neutral boundaries provide a much tighter restriction on the real phase speeds of the linear disturbances than the one provided by the usual semicircle theorem. Our presentation of complete stability curves for the entire family of unstable modes allows us to clarify the issue of mode coalescence that first appeared in the paper by Dickinson and Clare.