Faraday waves in 2:1 internal resonance

Diane Marie Henderson, John W. Miles

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

Experiments are reported on Faraday waves in a circular cylinder, which are internally resonant with either the subharmonic mode (with frequency ¼ that of the forcing) or the superharmonic mode (with frequency equal to that of the forcing). For subharmonic resonance both modes achieved comparable amplitudes that were steady, or were modulated with one or two periods, or exhibited quasi-periodic or chaotic motions. A stability map of these responses is presented. Theoretical predictions of linear stability and growth rates are tested. Measurements of steady amplitudes, limit-cycle frequencies and wave slopes at breaking are presented. Some of the measured phase-plane trajectories are shown to have theoretical counterparts. For superharmonic resonance the amplitude of the superharmonic was never comparable with that of the Faraday wave. For low modes an energy exchange occurred during the initial period of growth, and a precession instability sometimes developed. For high modes for which both frequencies and wavenumbers are in a 2:1 ratio, superharmonic resonance occurred irreproducibly; it appeared to be overwhelmed by 1:1 interactions among the possible Faraday-wave modes.

Original languageEnglish (US)
Pages (from-to)449-470
Number of pages22
JournalJournal of Fluid Mechanics
Volume222
Issue number6
DOIs
StatePublished - Jan 1 1991

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superharmonics
Circular cylinders
Trajectories
circular cylinders
precession
energy transfer
trajectories
slopes
cycles
Experiments
predictions
interactions

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cite this

Henderson, Diane Marie ; Miles, John W. / Faraday waves in 2:1 internal resonance. In: Journal of Fluid Mechanics. 1991 ; Vol. 222, No. 6. pp. 449-470.
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Faraday waves in 2:1 internal resonance. / Henderson, Diane Marie; Miles, John W.

In: Journal of Fluid Mechanics, Vol. 222, No. 6, 01.01.1991, p. 449-470.

Research output: Contribution to journalArticle

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AU - Miles, John W.

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