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

The weak turbulence theory has been applied to waves in thin elastic plates obeying the Foppl-Von Karman 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 Foppl-Von Karman equations is performed and reproduces qualitatively and quantitatively the experimental results when the experimentally measured damping rate of waves gamma(k) = a + bk(2) is used. This confirms that the Foppl-Von Karman 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.