The Effect of Vorticity-Profile Shape on the Instability of a Two-Dimensional Vortex

Abstract

A simple linear numerical model is used to study the effect of the shape of the vertical vorticity profile on the stability characteristics of a two-dimensional vortex. In all cases, the basic-state vorticity is confined to an annulus. It is found that the most unstable disturbances have azimuthal wavenumber 2 if the vorticity profile is sufficiently narrow relative to its outer radius, and if the profile is sufficiently sharply peaked. The relevance of this result to the multiple-vortex phenomenon in tornado simulators is strongly suggested by the fact that profiles of the type described have been obtained in numerical simulations by Gall and by Rotunno. Thus, some weight is added to the argument that the fundamental reason for the existence of the secondary vortices is the shear of the azimuthal wind.