Radiative instability in stratified vortices

This paper investigates the stability of a columnar vortex in an inviscid stratified fluid. By means of a WKBJ analysis for large axial wave number, we demonstrate that the normal modes can be stable or unstable owing to the emission of internal waves from the vortex. This phenomenon is shown to be analogous to the radioactive decay of nuclei in quantum mechanics. The destabilized character of the wave emission is shown to be associated with the presence of a critical point in the radial structure of the normal mode. The theoretical predictions for the frequency and growth rate of the normal modes are shown to be in good agreement with numerical results for two examples.