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Resonant surface waves and chaotic phenomena

Published online by Cambridge University Press:  21 April 2006

X. M. Gu  and
P. R. Sethna
X. M. Gu
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
P. R. Sethna
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

Surface waves in a rectangular container subjected to vertical oscillations are studied. Effects of energy dissipation along the lines of Miles (1967) and the effect of surface tension are included. Sufficient conditions, for two modes to dominate the motion, are given. The analysis is along the lines of Miles (1984a) and Holmes (1986). A complete bifurcation analysis is performed, and the modal amplitudes and phases are shown to have chaotic behaviour. This result is obtained under assumptions different from those of Holmes (1986). The conclusions regarding chaotic motions are based on a theorem of šilnikov (1970).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 183 , October 1987 , pp. 543 - 565
Copyright
© 1987 Cambridge University Press

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