Faraday resonance in two-dimensional standing gravity waves of finite depth

Yutaka Wada, Makoto Okamura

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3 Citations (Scopus)

Abstract

Faraday waves arise on the surface of a liquid in a container that is undergoing vertical periodic oscillations. The motion of two resonant modes with natural frequencies in the approximate ratio 3:1 is considered in this paper. We derive the nonlinear evolution equations of the dominant free-surface modes up to fifth-order in wave amplitude. It is found that the third-order evolution equations are integrable while the fifth-order evolution equations are chaotic, which shows that the fifth-order nonlinearity breaks the integrability of the third-order integrable system.

Original languageEnglish
Pages (from-to)125-140
Number of pages16
JournalWave Motion
Volume35
Issue number2
DOIs
Publication statusPublished - Jan 1 2002

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All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Physics and Astronomy(all)
  • Computational Mathematics
  • Applied Mathematics

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