Capillary waves understood by an elementary method

Abstract

The central physics of capillary waves (or ripples) can be understood by an elementary method which makes use of the balance of static and dynamic pressure differences along the surface streamline between crest and trough, in the steady reference frame, and conservation of mass through vertical cross-section beneath crest and trough. Basically Einstein's (1916) model of surface gravity waves is adapted for the purpose of explaining the existence of capillary waves of infinitesimal amplitude. One product of the physical understanding, the phase speed of capillary waves, is derived as a function of the wave length and surface tension, and the result agrees exactly with that obtained by the classical mathematical procedure. In the elementary method it is not necessary to assume irrotational flow, upon which the classical theory is founded, nor are perturbation expansions of the nonlinear fluid equations employed. The extension to capillary-gravity waves, by including the acceleration of gravity in the physical model, is straightforward, and the calculated phase speed of these waves is identical to what is found in the text books as well.