title: Role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum.
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 γ_{k}=a+bk{2} 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.
authors.affiliation: Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université Pierre et Marie Curie, CNRS, 24 rue Lhomond, 75005 Paris, France and Aix Marseille Université, CNRS, Centrale Marseille, IRPHE UMR 7342, 13384 Marseille, France.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Miquel
authors.affiliation: Laboratoire de Physique Statistique, Ecole Normale Supérieure, Université Pierre et Marie Curie, CNRS, 24 rue Lhomond, 75005 Paris, France.
authors.forename: Alexandros
authors.initials: A
authors.lastname: Alexakis
authors.affiliation: Laboratoire des Ecoulements Géophysiques et Industriels, Université Grenoble Alpes, Domaine Universitaire, BP53, 38041 Grenoble, France.
authors.forename: Nicolas
authors.initials: N
authors.lastname: Mordant
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004548:Elasticity; D008962:Models, Theoretical; D009038:Motion; D013193:Stainless Steel
chemical_list: D013193:Stainless Steel