Standing capillary-gravity waves of finite amplitude

Abstract

Standing surface waves in an inviscid incompressible fluid of finite depth are considered, taking into account the effect of capillary forces. Perturbation solutions for the surface profile, velocity potential, frequency of oscillation, and pressure are found to third order in the amplitude of the waves. A graph is given showing the regions in which the frequency of oscillation increases with amplitude and those in which it decreases with amplitude. These regions are defined as a function of the depth of the fluid and a parameter called the relative capillarity. A graph is also given showing the surface profile of a wave.