Further Results on the Stability of Rapidly Rotating Vortices in the Asymmetric Balance Formulation

Abstract

Two kinds of wave-activity invariants, analogous to the pseudomomentum and pseudoenergy densities in the quasigeostrophic theory, are derived for both three-dimensional baroclinic and two-dimensional barotropic asymmetric balance models, and applied to examine the stability of asymmetric circular basic-state vortices under general disturbances. Stability theorems obtained in this paper extend the results of Montgomery and Shapiro, which are valid only for normal mode disturbances. The general properties of normal mode disturbances in quasigeostrophic dynamics are generalized to the asymmetric balance models, which include an orthogonality principle, bounds on the angular phase speeds of neutrally stable regular normal modes, and a semicircle theorem bounding the angular phase speeds and growth rates of unstable normal modes.