A Theoretical Study of Three-Dimensional Barotropic Instability with Applications to the Upper Stratosphere

Abstract

Satellite and rocket observations indicate that barotropically unstable waves may exist in the upper stratosphere. To gain some understanding of the effects of vertical mean flow variation on barotropic instability with a view toward stratospheric applications, a numerical method used by other investigators for tropospheric baroclinic instability was employed to establish the structures, phase speeds and growth rates of the normal modes of a number of idealized, barotropically unstable, mean zonal wind fields in a quasi-geostrophic, Boussinesq framework. Both horizontally symmetric and asymmetric flows were considered, but in all cases the flows were vertically symmetric, with depth scales large enough to preclude baroclinic instability. Results showed that the horizontal structure of the waves was affected only slightly by vertical mean flow variation. Growth rates, however, were strongly affected, with reductions of 40% (horizontally symmetric) and 30% (horizontally asymmetric) from the respective two-dimensional values for the largest vertical scales expected in the stratosphere. Vertical structure displayed phase variation in the direction of mean wind shear and amplitude decay with distance from the level of strongest horizontal shear. The scale of variation was on the order of the geometric mean of the vertical mean flow scale and the vertical penetration depth, in analogy with baroclinic waves in latitudinally slowly varying flows. Some deviations from this behavior was found for horizontally symmetric flows, however, where the vertical scale of variation of the amplitude significantly exceeded that of the phase.