Waves on a vortex in a stratified fluid

We investigate the waves of a vertical Rankine vortex in a strongly stratified fluid. These waves are very different from their well-known counterpart in homogeneous fluid (Kelvin waves). They exist only for non-axisymmetric azimuthal wavenumbers, their frequency is always positive and strikingly, they are weakly unstable because of radiation towards infinity. Asymptotic results that hint the instability mechanism will be presented.