Vortex Formation By Kelvin–Helmholtz Instability

This chapter discusses nucleation of vortices due to instability of the interface between two superfluids moving with different velocities. The classical counterpart of this instability is the Kelvin–Helmholtz instability. In quantum liquids, there are two thresholds. The motion of superfluids with respect to the normal component becomes unstable when the Landau critical velocity for the surface excitations — ripplons — is reached and the ripplon energy becomes negative. In the shallow water limit, when ripplons acquire relativistic spectrum and obey the effective metric discussed in Chapter 32, the region with negative energy becomes analog of ergoregion or event horizon, and nucleation of ripplons at the Landau threshold becomes equivalent to Hawking radiation. However, if this process is sufficiently slow the second threshold can be reached, which is equivalent to Kelvin–Helmholtz criterion and corresponds to singularity in the centre of the black hole in the effective gravity for ripplons. In experiments with the interface between ³He-A and ³He-B, the onset of the Landau instability is marked by the appearance of the vortex lines in ³He-B, which are monitored in NMR measurements. Vortices appear at the non-linear stage of the growth of instability.