Kelvin–Helmholtz instability in anisotropic superfluids

Motivated by recent theoretical and experimental interest in the subject, we derive the condition of interfacial Kelvin–Helmholtz instability for a system of two flowing superfluids (one sliding on the other). The tensor structure of superfluid densities in anisotropic superfluids – such as $^3$He-$A$, and also $^3$He-$B$ under external magnetic field – is properly taken into account. The consequences relevant to experiments on the $A{-}B$ phase boundary in superfluid $^3$He are discussed.