On the propagation of long waves on the surface of helium - II: linearized theory

Abstract

The propagation of small amplitude long waves on the surface of superfluid helium II is considered. The equations describing the viscous, heat conducting, compressible fluid, with healing and relaxation effects included, are non-dimensionalized and a suitable limiting process is chosen. This limit reflects the physical situation which ignores the effects of healing on the wave (but not on the equilibrium configuration), and incorporates evaporation/condensation at the surface. The compressibility of the fluid is also retained. The leading order perturbation equations are solved exactly giving an equation for the surface wave which describes a two-wave-speed hierarchy coupled by a time constant. It is shown that the wave ultimately travels-not surprisingly-at the speed governed by the evaporation/condensation at the surface. Predicted values of wave speed are presented (calculated from tabulated data) for fluid films of thickness 5-100 Å+ by ignoring healing in the equilibrium state. The results show an improvement over previous work owing to the compressibility effects which become significant for the thinner films. The detailed effects of healing are relegated to a later paper.