A new ripplon branch in He II

Abstract

We analyse the dispersion relation of ripplons, on the surface of superfluid helium, using the dispersive hydrodynamics approach and find a new ripplon branch. We obtain analytical equation for the dispersion relation and analytic expressions for the limiting cases. We discuss where ripplons can exist in the energy-wavenumber plane. A numerical solution for the ripplon dispersion curve is obtained in the allowed regions. The new ripplon branch is found at energies just below the instability point.Comment: 18 pages, 2 figures; replaced with the published versio