Role of dissipation in flexural wave turbulence: From experimental spectrum to Kolmogorov-Zakharov spectrum

Benjamin Miquel, Alexandros Alexakis, and Nicolas Mordant
Phys. Rev. E 89, 062925 – Published 30 June 2014

Abstract

The weak turbulence theory has been applied to waves in thin elastic plates obeying the Föppl-Von Kármán dynamical equations. Subsequent experiments have shown a strong discrepancy between the theoretical predictions and the measurements. Both the dynamical equations and the weak turbulence theory treatment require some restrictive hypotheses. Here a direct numerical simulation of the Föppl-Von Kármán equations is performed and reproduces qualitatively and quantitatively the experimental results when the experimentally measured damping rate of waves γk=a+bk2 is used. This confirms that the Föppl-Von Kármán equations are a valid theoretical framework to describe our experiments. When we progressively tune the dissipation so that to localize it at the smallest scales, we observe a gradual transition between the experimental spectrum and the Kolmogorov-Zakharov prediction. Thus, it is shown that dissipation has a major influence on the scaling properties of stationary solutions of weakly nonlinear wave turbulence.

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  • Received 7 March 2013
  • Revised 24 April 2014

DOI:https://doi.org/10.1103/PhysRevE.89.062925

©2014 American Physical Society

Authors & Affiliations

Benjamin Miquel1,2,*, Alexandros Alexakis1, and Nicolas Mordant3,†

  • 1Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université Pierre et Marie Curie, CNRS, 24 rue Lhomond, 75005 Paris, France
  • 2Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France
  • 3Laboratoire des Ecoulements Géophysiques et Industriels, Université Grenoble Alpes, Domaine Universitaire, BP53, 38041 Grenoble, France

  • *Corresponding author: miquel@irphe.univ-mrs.fr
  • Also at Institut Universitaire de France.

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Issue

Vol. 89, Iss. 6 — June 2014

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