Analog of Kelvin—Helmholtz instability on superfluid liquid free surface

We analyse the analog of the Kelvin—Helmholtz instability on free surface of a superfluid liquid. This instability is induced by the relative motion of superfluid and normal components of the same liquid along the surface. The instabilty threshold is found to be independent of the value of viscosity, but turns out to be lower than in absence of dissipation. The result is similar to that obtained for the interface between two sliding superfluids (with different mechanism of dissipation) and confirmed by the first experimental observation of the Kelvin-Helmholtz instability on the interface between $^3$He-A and $^3$He-B by Blaauwgeers et al. (cond-mat/0111343).