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Faraday waves: their dispersion relation, nature of bifurcation and wavenumber selection revisited

Published online by Cambridge University Press:  15 July 2015

Jean Rajchenbach  and
Didier Clamond
Jean Rajchenbach*
Affiliation:
Laboratoire de Physique de la Mati\`ere Condensée, CNRS UMR 7336, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice CEDEX 2, France
Didier Clamond
Affiliation:
Laboratoire J. A. Dieudonné, CNRS UMR 7351, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice CEDEX 2, France
*
†Email address for correspondence: Jean.Rajchenbach@unice.fr
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Abstract

In the current literature, the dispersion relation of parametrically forced surface waves is often identified with that of free unforced waves. We revisit here the theoretical description of Faraday waves, showing that forcing and dissipation play a significant role in the dispersion relation, rendering it bi-valued. We then determine the instability thresholds and the wavenumber selection in cases of both short and long waves. We show that the bifurcation can be either supercritical or subcritical, depending on the depth.

JFM classification

Nonlinear Dynamical Systems: Bifurcation Waves/Free-surface Flows: Faraday waves Instability: Parametric instability
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 777 , 25 August 2015 , R2
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Copyright
© 2015 Cambridge University Press 

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