Weak and strong wave turbulence spectra for elastic thin plate

TL;DR

This study uses numerical simulations of elastic wave turbulence to explore how energy spectra vary with energy levels, revealing weak and strong turbulence regimes and their coexistence.

Contribution

It demonstrates the variability of energy spectra in elastic wave turbulence by systematically changing external force and identifies distinct weak and strong turbulence spectra.

Findings

Weak turbulence spectra match kinetic equation solutions at low energies.

Large-energy wave fields exhibit a different self-similar spectrum.

Coexistence of weak and strong turbulence spectra occurs at moderate energies.

Abstract

Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical simulations according to the F\"{o}ppl--von K\'{a}rm\'{a}n equation, and successfully reproduced the variability of the energy spectra by changing the magnitude of external force systematically. When the total energies in wave fields are small, the energy spectra are close to a statistically steady solution of the kinetic equation in the weak turbulence theory. On the other hand, in large-energy wave fields, another self-similar spectrum is found. Coexistence of the weakly nonlinear spectrum in large wavenumbers and the strongly nonlinear spectrum in small wavenumbers are also found in moderate energy wave fields.