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Chaotic mode competition in parametrically forced surface waves

Published online by Cambridge University Press:  20 April 2006

S. Ciliberto  and
J. P. Gollub
S. Ciliberto
Affiliation:
Department of Physics, Haverford College, Haverford, PA 19041 U.S.A., and Department of Physics, University of Pennsylvania, Philadelphia, PA 19104 U.S.A. Permanent address: Istituto Nazionale di Ottica, 50125 Arcetri-Firenze, Largo Enrico Fermi 6, Italy.
J. P. Gollub
Affiliation:
Department of Physics, Haverford College, Haverford, PA 19041 U.S.A., and Department of Physics, University of Pennsylvania, Philadelphia, PA 19104 U.S.A.
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Abstract

Vertical forcing of a fluid layer leads to standing waves by means of a subharmonic instability. When the driving amplitude and frequency are chosen to be near the intersection of the stability boundaries of two nearly degenerate modes, we find that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. We utilize digital image-processing methods to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques to study the onset of chaos in some detail. Reconstruction of the attractors in phase space shows that in the chaotic regime the dimension of the attractor is fractional and at least one Lyapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 158 , September 1985 , pp. 381 - 398
Copyright
© 1985 Cambridge University Press

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