  We investigate wave-vortex interaction emerging from an expanding compact
vortex cluster in a two-dimensional Bose-Einstein condensate. We adapt
techniques developed for compact gravitational objects to derive the
characteristic modes of the wave-vortex interaction perturbatively around an
effective vortex flow field. We demonstrate the existence of orbits or
sound-rings, in analogy to gravitational light-rings, and compute the
characteristic spectrum for the out-of-equilibrium vortex cluster. The spectrum
obtained from numerical simulations of a stochastic Gross-Pitaevskii equation
exhibiting an expanding vortex cluster is in excellent agreement with
analytical predictions. Our findings are relevant for 2d-quantum turbulence,
the semi-classical limit around fluid flows, and rotating compact objects
exhibiting discrete circulation.
