Solitary waves and chaotic twisting in a PDE model of Faraday resonance

S P Decent

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    Abstract

    Standing solitary waves and twisting waves which result from parametric excitation in a narrow rectangular water tank are discussed. We derive a generalized Schrodinger equation, extending the Lagrangian method of Miles [J. Fluid Mech. 148 (1984) 451]. The effects of damping and forcing terms third-order in the wave amplitude, and also the fifth-order conservative frequency shift are investigated. In particular, it is found that constant-phase stationary solitary waves no longer exist when cubic damping and cubic forcing are non-zero: in this case a non-constant phase stationary solution is found which results in a modification of the shape of the standing solitary wave. We also find that non-zero cubic damping can, in some circumstances, give rise to a time-modulated solitary wave and/or coexistent solitary wave solutions. It is also demonstrated that these nonlinear terms greatly effect mode competition between twisting waves, and can cause the twisting waves to evolve chaotically.

    Original languageEnglish
    Pages (from-to)115-137
    Number of pages23
    JournalFluid Dynamics Research
    Volume21
    Issue number2
    DOIs
    Publication statusPublished - Aug 1997

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