Wave turbulence in vibrating plates : the effect of damping

TL;DR

This paper investigates how damping affects wave turbulence in vibrating plates, showing that increased damping alters spectral slopes but turbulence persists with a damping-independent cutoff frequency.

Contribution

It introduces an experimental method to measure dissipation at all scales and demonstrates the impact of damping on spectral behavior in wave turbulence.

Findings

Damping modifies the slope of the power spectral density.

Turbulence persists despite increased damping.

Cut-off frequency depends on injected power, not damping.

Abstract

The effect of damping in the wave turbulence regime for thin vibrating plates is studied. An experimental method, allowing measurements of dissipation in the system at all scales, is first introduced. Practical experimental devices for increasing the dissipation are used. The main observable consequence of increasing the damping is a significant modification in the slope of the power spectral density, so that the observed power laws are not in a pure inertial regime. However, the system still displays a turbulent behavior with a cut-off frequency that is determined by the injected power which does not depend on damping. By using the measured damping power-law in numerical simulations, similar conclusions are drawn out.