An intermediate wavelength, weakly nonlinear theory for the evolution of capillary gravity waves

A new nonlinear evolution equation is derived for surface solitary waves propagating on a liquid–air interface where the wave motion is induced by a harmonic forcing. Instead of the traditional approach involving a base state of the long wave limit, a base state of harmonic waves is assumed for the perturbation analysis. This approach is considered to be more appropriate for channels of length just a few multiples of the depth. The dispersion relation found approaches the classical long wave limit. The weakly nonlinear dispersive waves satisfy a KdV-like nonlinear evolution equation with steeper nonlinearity.

Research highlights► Derivation of new evolution equation for capillary gravity waves. ► Perturbation expansion about a harmonic base state. ► Dispersion relation consistent with KdV shallow water theory in long-wave limit.