Self-similar gravity wave spectra resulting from the modulation of bound waves

Guillaume Michel, Benoît Semin, Annette Cazaubiel, Florence Haudin, Thomas Humbert, Simon Lepot, Félicien Bonnefoy, Michaël Berhanu, and Éric Falcon
Phys. Rev. Fluids 3, 054801 – Published 15 May 2018

Abstract

We experimentally study the properties of nonlinear surface gravity waves in a large-scale basin. We consider two different configurations: a one-dimensional (1D) monochromatic wave forcing, and a two-dimensional (2D) forcing with bichromatic waves satisfying resonant-wave interaction conditions. For the 1D forcing, we find a discrete wave-energy spectrum dominated at high frequencies by bound waves whose amplitudes decrease as a power law of the frequency. Bound waves (e.g., to the carrier) are harmonics superimposed on the carrier wave propagating with the same phase velocity as the one of the carrier. When a narrow frequency random modulation is applied to this carrier, the high-frequency part of the wave-energy spectrum becomes continuous with the same frequency-power law. Similar results are found for the 2D forcing when a random modulation is also applied to both carrier waves. Our results thus show that all these nonlinear gravity wave spectra are dominated at high frequencies by the presence of bound waves, even in the configuration where resonant interactions occur. Moreover, in all these configurations, the power-law exponent of the spectrum is found to depend on the forcing amplitude with the same trend as the one found in previous gravity wave turbulence experiments. Such a set of bound waves may thus explain this dependence that was previously poorly understood.

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  • Received 19 December 2017

DOI:https://doi.org/10.1103/PhysRevFluids.3.054801

©2018 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsFluid Dynamics

Authors & Affiliations

Guillaume Michel1,*, Benoît Semin1, Annette Cazaubiel2, Florence Haudin2, Thomas Humbert3,†, Simon Lepot3, Félicien Bonnefoy4, Michaël Berhanu2, and Éric Falcon2

  • 1LPS, ENS, CNRS, Univ. Pierre et Marie Curie, Univ. Paris Diderot, F-75 005 Paris, France
  • 2Univ. Paris Diderot, Sorbonne Paris Cité, MSC, UMR 7057 CNRS, F-75 013 Paris, France
  • 3Univ. Paris-Saclay, CEA-Saclay, SPEC, DRF, UMR 3680 CNRS, F-91 191 Gif-sur-Yvette, France
  • 4École Centrale de Nantes, LHEEA, UMR 6598 CNRS, F-44 321 Nantes, France

  • *guillaume.michel@ens.fr
  • Present address: Univ. du Mans, Laboratoire d'Acoustique, UMR 6613 CNRS, F-72 085 Le Mans, France.

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Issue

Vol. 3, Iss. 5 — May 2018

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