On Kelvin-Helmholtz instability in superfluids

The Kelvin-Helmholtz instability in superfluids is discussed, based on the first experimental observation of such instability at the interface between superfluid He-A and superfluid He-B [1]. We discuss why the Kelvin-Helmholtz criterion, the Landau critical velocity for nucleation of ripplons, and the free energy consideration all give different values for the instability treshold. 1 Classical KH instability Kelvin-Helmholtz instability belongs to a broad class of interfacial instabilities in liquids, gases, plasma, etc. [2]. It refers to the dynamic instability of the interface of the discontinuous flow, and may be defined as the instability of the vortex sheet. Many natural phenomena have been attributed to this instability. Most familiar of them are generation by wind of waves in the water, whose Helmholtz instability was first analyzed by Kelvin [6], and flapping of sails and flags analyzed by Rayleigh [4] (see recent experiments in [5]). Many of the leading ideas in the theory of instability were originally inspired by considerations about inviscid flows. The corrugation instability