Chaotic motions in a weakly nonlinear model for surface waves

Abstract

Using the averaging method and a perturbation technique originally due to Melnikov (1963), we show that an N -degree-of-freedom model of weakly nonlinear surface waves due to Miles (1976) has transverse homoclinic orbits. This implies that Smale horseshoes, and hence sets of chaotic orbits, exist in the phase space. In this particular example, an irregular ‘sloshing’ of energy between two modes of oscillation results. We briefly discuss the relevance of our results to recent experimental work on parametrically excited surface waves.