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Symmetry-breaking bifurcations in resonant surface waves

Published online by Cambridge University Press:  26 April 2006

Z. C. Feng  and
P. R. Sethna
Z. C. Feng
Affiliation:
Deparment of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
P. R. Sethna
Affiliation:
Deparment of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
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Abstract

Surface waves in a nearly square container subjected to vertical oscillations are studied. The theoretical results are based on the analysis of a derived set of normal form equations, which represent perturbations of systems with 1:1 internal resonance and with D4 symmetry. Bifurcation analysis of these equations shows that the system is capable of periodic and quasi-periodic standing as well as travelling waves. The analysis also identifies parameter values at which chaotic behaviour is to be expected. The theoretical results are verified with the aid of some experiments.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 199 , February 1989 , pp. 495 - 518
Copyright
© 1989 Cambridge University Press

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