The superradiant instability spectrum of the hydrodynamic vortex model

We study analytically the superradiant instability properties of the hydrodynamic vortex model, an asymptotically flat acoustic geometry which, like the spinning Kerr black-hole spacetime, possesses an effective ergoregion. In particular, we derive a compact analytical formula for the complex resonant frequencies that characterize the long-wavelength dynamics of sound modes in this physically interesting acoustic spacetime.