Anisotropy effect on the flow-induced instability of the solid-superfluid interface

At the solid-superfluid interface of He-4 a Kelvin-Helmholtz type instability is expected to occur with a tangential flow. Nonlinear effect in the instability is studied with a perturbation expansion. For an isotropic interface the amplitude of the destabilized crystallization wave grows without limit, which suggests a chaotic motion. With a strong crystal anisotropy and for the surface orientation of minimum stiffness, the amplitude has a stable fixed point and a corrugated interface may be stabilized Increasing further the anisotropy changes the type of the bifurcation from subcritical to supercritical.