Intermittency and emergence of coherent structures in wave turbulence of a vibrating plate

TL;DR

This paper investigates wave turbulence in a vibrating elastic plate through numerical simulations, revealing the emergence of coherent structures and intermittency at higher forcing levels, contrasting with weak turbulence predictions.

Contribution

It demonstrates the formation of dynamic coherent structures and intermittency in wave turbulence of a vibrating plate under strong forcing, extending understanding beyond weak turbulence theory.

Findings

Coherent structures resemble crumpled paper folds and D-cones.

Intermittency correlates with the emergence of nonlinear structures.

Numerical simulations reveal a transition from weak to strong turbulence.

Abstract

We report numerical investigations of wave turbulence in a vibrating plate. The possibility to implement advanced measurement techniques and long time numerical simulations makes this system extremely valuable for wave turbulence studies. The purely 2D character of dynamics of the elastic plate makes it much simpler to handle compared to much more complex 3D physical systems that are typical of geo- and astrophysical issues (ocean surface or internal waves, magnetized plasmas or strongly rotating and/or stratified flows). When the forcing is small the observed wave turbulence is consistent with the predictions of the Weak Turbulent Theory. Here we focus on the case of stronger forcing for which coherent structures can be observed. These structures look similar to the folds and D-cones that are commonly observed for strongly deformed static thin elastic sheets (crumpled paper) except that they evolve dynamically in our forced system. We describe their evolution and show that their emergence is associated with statistical intermittency (lack of self similarity) of strongly nonlinear wave turbulence. This behavior is reminiscent of intermittency in Navier-Stokes turbulence. Experimental data show hints of the weak to strong turbulence transition. However, due to technical limitations and dissipation, the strong nonlinear regime remains out of reach of experiments and therefore has been explored numerically.