Self-similar formation of an inverse cascade in vibrating elastic plates

Abstract

The dynamics of random weakly nonlinear waves is studied in the framework of vibrating thin elastic plates. Although it has been previously predicted that no stationary inverse cascade of constant wave action flux could exist in the framework of wave turbulence for elastic plates, we present substantial evidence of the existence of {\gr a time dependent} inverse cascade, opening up the possibility of self organization for a larger class of systems. This inverse cascade transports the spectral density of the amplitude of the waves from short up to large scales, increasing the distribution of long waves despite the short wave fluctuations. This dynamics appears to be self-similar and possesses a power law behaviour in the short wavelength limit which is significantly different from the exponent obtained via a Kolmogorov dimensional analysis argument. Finally, we show explicitly a tendency to build a long wave coherent structure in finite time.

References in corpus (6)

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Cited by in corpus (5)

• Saturation of the inverse cascade in surface gravity wave turbulence
• Low frequency spectra of bending wave turbulence
• The Structure of Fluctuating Thin Sheets Under Random Forcing
• Thermally driven elastic membranes are quasi-linear across all scales
• Dynamics of Fluctuating Thin Sheets Under Random Forcing