  Vorticity in two-dimensional superfluids is subject to intense research
efforts due to its role in quantum turbulence, dissipation and the BKT phase
transition. Interaction of sound and vortices is of broad importance in
Bose-Einstein condensates and superfluid helium [1-4]. However, both the
modelling of the vortex flow field and of its interaction with sound are
complicated hydrodynamic problems, with analytic solutions only available in
special cases. In this work, we develop methods to compute both the vortex and
sound flow fields in an arbitrary two-dimensional domain. Further, we analyse
the dispersive interaction of vortices with sound modes in a two-dimensional
superfluid and develop a model that quantifies this interaction for any vortex
distribution on any two-dimensional bounded domain, possibly non-simply
connected, exploiting analogies with fluid dynamics of an ideal gas and
electrostatics. As an example application we use this technique to propose an
experiment that should be able to unambiguously detect single circulation
quanta in a helium thin film.

Quantum Gases;Fluid Dynamics;Quantum Physics