Whispering gallery like modes along pinned vortices

We study sound propagation in stationary and locally irrotational vortex flows where the circulation is wound around a long (rotating) cylinder, using Unruh's formalism of acoustic space-times. Apart from the usual scattering solutions, we find anomalous modes which are bound to the vicinity of the cylinder and propagate along its axis – similar to whispering gallery modes. These modes exist for subsonic and supersonic flow velocities. In the supersonic case (corresponding to an effective ergo-region in the acoustic space-time), they can even have zero frequency $\omega=0$ and thus the associated quasi-particles with $E=\hbar\omega=0$ are easy to excite from an energetic point of view. Hence they should be relevant for the question of stability or instability of this setup.