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Descripción
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| An open container of fluid vibrated at high frequency and sufficient amplitude will exhibit subharmonic surface waves. If the vibration is horizontal, these waves are called cross-waves and are strongest near the solid walls acting as wavemakers. In some situations, the waves are sufficiently localized to be modelled by a pair of weakly-coupled parametrically forced oscillators. We analyze such a model in the neighborhood of the primary subharmonic instability and note how both primary and subsequent instabilities depend crucially on the symmetry that remains in the presence of coupling, which, in turn, depends on the relative phases of the parametric forcing terms. A bifurcation study reveals a complex series of transitions organized in part by Bogdanov-Takens points. The case of out-of-phase forcing, which is relevant to horizontally vibrated fluids, is compared with direct numerical simulations and with recent experiments on modulated cross-waves. Both the initial Hopf bifurcation and subsequent saddle-node heteroclinic bifurcation are confirmed. Simulations of vibroequilibria (quasi-steady non-flat surface configurations supported by vibrations) are also discussed. In particular, it is found that subharmonic surface waves may destabilize the underlying vibroequilibria state by driving an odd sloshing motion. The modulated states analyzed in the coupled parametrically forced oscillator model appear to be the key to effective coupling between the high-frequency surface waves and the low-frequency sloshing modes, an interaction with the potential to destabilize/destroy vibroequilibria states. | |
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Internacional
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Si |
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Nombre congreso
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Perspectives in Nonlinear Science |
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Tipo de participación
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730 |
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Lugar del congreso
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Cargèse, Francia |
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Revisores
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Si |
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ISBN o ISSN
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11-1111-111-1 |
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DOI
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Fecha inicio congreso
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26/03/2018 |
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Fecha fin congreso
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30/03/2018 |
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1 |
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Hasta la página
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1 |
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Título de las actas
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x |