Bounded capillary–gravity waves obliquely incident on a plane beach

Abstract

Surface tension effects upon bounded standing capillary–gravity waves over a flat beach are investigated in a linearised framework of a classical non-hydrostatic model of a perfect fluid. Existing theory for oblique pure gravity waves is extended to capillary–gravity waves. The solutions are presented in a way that is easy to compute using a combination of finite sums and Laplace integrals. Examples are given for oblique incidence. Solutions are determined, subject to boundedness at the contact line. It is found that surface tension lowers the amplitude, generally lengthens the wavelength and reduces the refractive effect of shoaling. However, very near the shore-line it is found that the refractive effect is reversed by the combined action of surface tension and shoaling in very shallow water. The Hocking edge condition is briefly examined.