Are there waves in elastic wave turbulence ?

TL;DR

This study investigates elastic wave turbulence in a steel plate, confirming the presence of bending waves and examining the applicability of weak turbulence theory, but finds discrepancies between theory and experimental spectra.

Contribution

It provides experimental validation of wave superposition and dispersion relations in elastic turbulence, while highlighting limitations of weak turbulence theory predictions.

Findings

Bending waves follow the theoretical dispersion relation.

Nonlinearities disrupt wave coherence, preventing modal structure.

Experimental spectra do not match weak turbulence theory predictions.

Abstract

An thin elastic steel plate is excited with a vibrator and its local velocity displays a turbulent-like Fourier spectrum. This system is believed to develop elastic wave turbulence. We analyze here the motion of the plate with a two-point measurement in order to check, in our real system, a few hypotheses required for the Zakharov theory of weak turbulence to apply. We show that the motion of the plate is indeed a superposition of bending waves following the theoretical dispersion relation of the linear wave equation. The nonlinearities seem to efficiently break the coherence of the waves so that no modal structure is observed. Several hypotheses of the weak turbulence theory seem to be verified, but nevertheless the theoretical predictions for the wave spectrum are not verified experimentally.