Rayleigh-Taylor instability of crystallization waves at the superfluid-solid 4He interface

TL;DR

This paper investigates the Rayleigh-Taylor instability at the superfluid-solid helium-4 interface, analyzing how acceleration and damping influence the onset and growth of interface disturbances.

Contribution

It introduces the first analysis of Rayleigh-Taylor instability analogues at the superfluid-solid helium-4 interface, considering both uniform and impulsive accelerations.

Findings

Instability occurs only for growing solid phases when acceleration exceeds a critical value.

Impulsive acceleration leads to instability onset independent of acceleration sign.

Crystallization wave damping reduces the growth rate of unstable perturbations.

Abstract

At the superfluid-solid 4He interface there exist crystallization waves having much in common with gravitational-capillary waves at the interface between two normal fluids. The Rayleigh-Taylor instability is an instability of the interface which can be realized when the lighter fluid is propelling the heavier one. We investigate here the analogues of the Rayleigh-Taylor instability for the superfluid-solid 4He interface. In the case of a uniformly accelerated interface the instability occurs only for a growing solid phase when the magnitude of the acceleration exceeds some critical value independent of the surface stiffness. For the Richtmyer-Meshkov limiting case of an impulsively accelerated interface, the onset of instability does not depend on the sign of the interface acceleration. In both cases the effect of crystallization wave damping is to reduce the perturbation growth-rate of the Taylor unstable interface.