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Whispering gallery like modes along pinned vortices

Employing Unruh's analogy to gravity, we study sound propagation in stationary and locally irrotational vortex flows where the circulation is wound around a long (rotating) cylinder. 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. For supersonic flow velocities (corresponding to an effective ergoregion), these modes can even have zero frequency. Thus they should be relevant for the question of stability or instability of this set-up.