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Chaotic motions in a weakly nonlinear model for surface waves

Published online by Cambridge University Press:  21 April 2006

Philip Holmes
Philip Holmes
Affiliation:
Departments of Theoretical and Applied Mechanics and Mathematics, and Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, U.S.A.
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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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 162 , January 1986 , pp. 365 - 388
Copyright
© 1986 Cambridge University Press

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