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Faraday resonance in rectangular geometry

Published online by Cambridge University Press:  26 April 2006

Makoto Umeki
Makoto Umeki
Affiliation:
Department of Physics, University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113, Japan
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Abstract

The motion of subharmonic resonant modes of surface waves in a rectangular container subjected to vertical periodic oscillation is studied based on the weakly nonlinear model equations derived by both the average Lagrangian and the two-timescale method. Explicit estimates of the nonlinearity of some specific modes are given. The bifurcations of stationary states including a Hopf bifurcation are examined. Numerical calculations of the dissipative dynamical equations show periodic and chaotic attractors. Theoretical parameter-space diagrams and numerical results are compared in detail with Simonelli & Gollub's (1989) surface-wave modecompetition experiments. It is shown that the average Hamiltonian system for the present 2:1:1 external-internal resonance with suitable coefficients has homoclinic chaos, which was mathematically proven by Holmes (1986) for the specific case of 2:1:2 external-internal resonance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 227 , June 1991 , pp. 161 - 192
Copyright
© 1991 Cambridge University Press

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