WAVES AT LIQUID SURFACES - COUPLED OSCILLATORS AND MODE MIXING

The dispersion of surface waves on liquids has been reconsidered in the framework of currently established linear theory. Mixed excitations, which are neither capillary nor dilational in nature, can occur due to the coupling between the lossy oscillators formed by the vertical and horizontal motions of a surface element. The results emphasize that the capillary and dilational waves are only approximately transverse and longitudinal in nature and that it cannot, in general, be correct to neglect the coupling between these degrees of freedom. In the present case mode mixing only occurs when a particular surface viscosity - that affecting shear normal to the surface - exceeds a critical value. Experimentally accessible tests of the predicted mode mixing are proposed, which would further test the physical reality of the surface viscosity involved.