Low frequency spectra of bending wave turbulence

TL;DR

This study experimentally investigates long-wavelength bending wave turbulence in a vibrating elastic plate, revealing a flat energy spectrum indicative of equipartition and deriving an expression for the effective temperature based on forcing parameters.

Contribution

It provides the first experimental evidence of energy equipartition in bending wave turbulence and formulates a theoretical expression for the effective temperature of the wave field.

Findings

Flat power density spectrum observed for orthogonal velocity.

Energy per mode characterized by an effective temperature.

Derived expression links temperature to forcing frequency, amplitude, and plate properties.

Abstract

We study experimentally the dynamics of long waves among turbulent bending waves in a thin elastic plate set into vibration by a monochromatic forcing at a frequency $f_0$. This frequency is chosen large compared with the characteristic frequencies of bending waves. As a consequence, a range of conservative scales, without energy flux in average, exists for frequencies $f<f_0$. Within this range, we report a flat power density spectrum for the orthogonal velocity, corresponding to energy equipartition between modes. Thus, the average energy per mode $\beta^{-1}$ -- analogous to a temperature -- fully characterizes the large-scale turbulent wave field. We present an expression for $\beta$ as a function of the forcing frequency and amplitude, and of the plate characteristics.