Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates

Abstract : A phenomenological model describing the time-frequency dependence of the power spectrum of thin plates vibrating in a wave turbulence regime, is introduced. The model equation contains as basic solutions the Rayleigh-Jeans equipartition of energy, as well as the Kolmogorov-Zakharov spectrum of wave turbulence. In the Wave Turbulence Theory framework, the model is used to investigate the self-similar, non-stationary solutions of forced and free turbulent vibrations. Frequency-dependent damping laws can easily be accounted for. Their effects on the characteristics of the stationary spectra of turbulence are then investigated. Thanks to this analysis, self-similar universal solutions are given, relating the power spectrum to both the injected power and the damping law.
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Submitted on : Friday, January 15, 2016 - 5:29:41 PM
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Thomas Humbert, Christophe Josserand, Cyril Touzé, Olivier Cadot. Phenomenological model for predicting stationary and non-stationary spectra of wave turbulence in vibrating plates. Physica D: Nonlinear Phenomena, Elsevier, 2016, 316, pp.34-42. ⟨10.1016/j.physd.2015.11.006⟩. ⟨hal-01257109⟩

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