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

TL;DR

This paper demonstrates the existence of a self-similar, time-dependent inverse cascade in vibrating elastic plates, challenging previous predictions and showing the formation of long wave structures through wave turbulence dynamics.

Contribution

It provides evidence of a self-similar inverse cascade in elastic plates, revealing new dynamics and structure formation not predicted by earlier theories.

Findings

Existence of a time-dependent inverse cascade in elastic plates

Self-similar spectral density transport from short to large scales

Formation of long wave coherent structures in finite time

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.