Chaotic mode competition in parametrically forced surface waves

Year: 1985

Authors: Ciliberto S., Gollub J. P.

Autors Affiliation: Department of Physics, Haverford College, Haverford, PA 19041 U.S.A., and Department of Physics, University of Pennsylvania, Philadelphia, PA 19104 U.S.;
Istituto Nazionale di Ottica, 50125 Arcetri-Firenze, Largo Enrico Fermi 6, Italy.

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, it is found that they can compete with each other to produce either periodic or chaotic motion on a slow timescale. Digital image-processing methods are utilized to determine the time-dependent amplitudes of the competing modes, and local-sampling techniques are employed 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 Liapunov exponent is positive. The evidence suggests that a theory incorporating four coupled slow variables will be sufficient to account for the mode competition.

Journal/Review: JOURNAL OF FLUID MECHANICS

Volume: 158      Pages from: 381  to: 398

KeyWords: chaos; flow stability; modes (standing waves)
DOI: 10.1017/S0022112085002701

Citations: 179
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