Resonant frequencies of the hydrodynamic vortex

TL;DR

This paper derives exact resonant frequencies for sound perturbations in a hydrodynamic vortex, revealing their complex nature through solutions involving double confluent Heun functions.

Contribution

It provides an exact analytical expression for the resonant frequencies of the hydrodynamic vortex using special functions, advancing understanding of its perturbation spectrum.

Findings

Resonant frequencies are complex numbers.

Exact solutions involve double confluent Heun functions.

The study enhances theoretical understanding of vortex perturbations.

Abstract

We study the sound perturbation of the hydrodynamic vortex geometry and present an exact expression for the resonant frequencies (quasispectrum) of this geometry. Exact solution for the radial part of the covariant Klein-Gordon equation in this spacetime is obtained, and is given in terms of the double confluent Heun functions. We found that the resonant frequencies are complex number.