Symmetric stability of steady axisymmetric and geostrophic motion in a compressible stratified medium

Abstract

We studied the stability of symmetric (i.e., independent of one of the coordinates) steady motion, axisymmetric and geostrophic. This motion is of considerable interest because it qualitatively describes the basic structures of atmospheric motion, such as zonal flows, vortices, and states of geostrophic balance. Since the first publication by Fjortoft [1], this problem has been studied (see, for example, [2–4]) with the aim to generalize its formulation and extend the range of possible application. It is worth noting that almost all studies were made in the approximation of incompressibility, which limits the use of the results to smallor moderate-scale atmospheric processes. Our study was undertaken to overcome the shortcomings of this approximation and to formulate the criteria of symmetric stability of compressible media described by an arbitrary equation of state. We consider here the general case of axisymmetric motion, including zonal flows, on the basis of the direct Lyapunov method (a variational approach).