Elastic wave-turbulence and intermittency

TL;DR

This paper investigates deviations from weak wave turbulence theory in elastic plates, revealing conditions under which intermittency and extreme events occur due to nonlinear effects and energy distribution across scales.

Contribution

It extends wave turbulence theory to elastic plates, analyzing how nonlinearity influences anomalous scaling and intermittency phenomena.

Findings

Mean-field theory applies when linear dynamics dominate all scales.

Intermittency arises when large scales contain significant energy.

Extreme events are sustained at small scales due to nonlinear energy transfer.

Abstract

Weak Wave Turbulence is a powerful theory to predict statistical observables of diverse relevant physical phenomena, such as ocean waves, magnetohydrodynamics and nonlinear optics. The theory is based upon an asymptotic closure permitted in the limit of small nonlinearity. Here, we explore the possible deviations from this mean-field framework, in terms of anomalous scaling, focusing on the case of elastic plates. We establish the picture of the possible behaviors at varying the extent of nonlinearity, and we show that the mean-field theory is appropriate when all excited scales remain dominated by linear dynamics. The other picture is non-trivial and our results suggest that, when large scales contain much energy, the cascade sustains extreme events at small scales and the system displays intermittency.