Instability of an axisymmetric vortex in a stably stratified, rotating environment

We investigate the stability of a barotropic vorticity monopole whose stream function is a Gaussian function of the radial coordinate. The model is based on the inviscid Boussinesq equations. The vortex is assumed to exist on an S-plane, in an environment with constant, stable density stratification. In the unstratified, nonrotating case, we find growth rates that increase monotonically with increasing vertical wave number, the so-called "ultraviolet catastrophe" characteristic of symmetric instability. This type of instability leads to rapid turbulent collapse of the vortex, possibly accompanied by wave radiation. In the limit of strong background stratification and rotation, the vortex exhibits a scale-selective instability which leads to the formation of stable lenses. The transition between these two regimes is sharp, and coincides approximately with the centrifugal stability boundary.