Waves on a columnar vortex in a strongly stratified fluid

This paper investigates the discrete bounded waves sustained by a vertical columnar Rankine vortex in a strongly stratified fluid. We show that these waves are very different from their well-known counterpart in homogeneous fluid (Kelvin vortex waves); they exist only for nonzero azimuthal wavenumber m, their frequency lies in the interval [0, mΩ] (Ω is the angular velocity in the vortex core) and they are unstable because of an outward radiation from the vortex. The instability mechanism is explained in terms of an over-reflection phenomenon by means of a Wentzel-Kramers-Brillouin-Jeffreys analysis for large axial wavenumber.