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Article Dans Une Revue Physical Review E : Statistical, Nonlinear, and Soft Matter Physics Année : 2014

The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum

Résumé

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 $\gamma_\mathbf{k}= a + bk^2$ 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 dissipation has a major influence on the scaling properties stationary solutions of weakly non linear wave turbulence.
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hal-01009490 , version 1 (14-09-2023)

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Benjamin Miquel, Alexandros Alexakis, Nicolas Mordant. The role of dissipation in flexural wave turbulence: from experimental spectrum to Kolmogorov-Zakharov spectrum. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 89, pp.062925. ⟨10.1103/PhysRevE.89.062925⟩. ⟨hal-01009490⟩
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