Third Sound in Superfluid Helium Films of Arbitrary Thickness

Abstract

The hydrodynamic equations of a superfluid helium film are solved numerically to yield the dispersion equation of third sound over a wide range of thicknesses, including both unsaturated and saturated films. An analytical approximation to the dispersion equation is found that is good for the entire range where the equations are valid, and which becomes particularly simple in the case of either very thin or very thick films. A clear physical picture is formed of the processes determining the properties of third sound in thick helium films.