  Recent experiments have shown remarkable dynamics of solid $^4$He melting and
growth, driven by the normal incidence of an acoustic pulse on the solid-liquid
interface. The theory of solid growth/melting, driven by the radiation pressure
of the acoustic pulse, accounts well for the temperature dependence of the
measured data. There is however an observed source of extra,
temperature-independent, melting. We here propose that this extra melting is
due to solid-liquid mixing (and consequent melting) at the interface, in a
process similar to the Richtmyer-Meshkov instability: Initial undulations of
the rough interface, grow when accelerated by the acoustic pressure
oscillations. This model predicts a temperature-independent extra melting and
its dependence on the acoustic power, which is in agreement with the measured
data.
