Multiple surface wave solutions on linear viscoelastic media

Abstract

We study the generic dispersion relation of surface waves on a semi-infinite viscoelastic medium bounded by a 2D viscoelastic interface, including the effects of gravitation, surface tension and bending rigidity. The classical Rayleigh, capillary-gravity and Lucassen wave solutions result as limiting cases. We identify an additional solution that differs from all previously described waves in that gravitation, surface tension and bulk shear viscosity must simultaneously be nonzero, and which exists on a pure air-water interface. For a surfactant monolayer on water, the number of coexisting wave solutions switches between one and three, depending on interfacial compressibility and frequency.