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. 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.
In order to minimize the possibility of spin flips due to interactions with and on the walls of a sample cell, spin-polarized hydrogen (H\ensuremath{\downarrow}) is studied in a
4He sample cell, i.e., a sample cell which has been coated with a film of superfluid
4He. At low temperatures it is expected that the most dense H\ensuremath{\downarrow} sample will first form in the physisorbed state on the
4He film. In this paper we examine in detail the hydrodynamic consequences of this layered film configuration. We derive the expression for third sound in the general case that the films are compressible and both films have undergone superfluid transitions. In this case two propagating modes will be seen which will provide an uneqivocal demonstration of a superfluid transition in the H\ensuremath{\downarrow} film. We specialize to various limiting cases: incompressible films, saturated and unsaturated films, and the normal fluid H\ensuremath{\downarrow} blanket. In our discussion we stress the point that even if the H\ensuremath{\downarrow} has not gone superfluid it will still shift the
4He third-sound speed, that this shift is a direct measure of the H\ensuremath{\downarrow} film areal density, and that the magnitude of this shift is expected to be well within the precision of present-day third-sound experimental techniques. Thus third sound is expected to be a primary diagnostic tool in the study of H\ensuremath{\downarrow} films.