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

Research paper by Benjamin B Miquel, Alexandros A Alexakis, Nicolas N Mordant

Indexed on: 16 Jul '14Published on: 16 Jul '14Published in: Physical review. E, Statistical, nonlinear, and soft matter physics



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.