# Modelling of vorticity, sound and their interaction in two-dimensional superfluids

## TL;DR

This paper develops computational methods to model and analyze the interaction between vorticity and sound in two-dimensional superfluids, with applications to detecting quantum vortices in helium films.

## Contribution

It introduces a novel approach to compute vortex and sound flow fields in arbitrary 2D domains and models their dispersive interactions, extending understanding of superfluid dynamics.

## Key findings

- New computational framework for vortex and sound interactions in 2D superfluids.
- Quantitative model for vortex-sound interaction applicable to complex geometries.
- Proposed experiment to detect single quantum vortices in helium films.

## Abstract

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.