Low-frequency spectra of bending wave turbulence

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 fₒ. This frequency is chosen large compared with the characteristic frequencies of bending waves. As a consequence, a range of conservative scales without energy flux on average exists for frequencies f<fₒ. 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 β⁻¹-analogous to a temperature-fully characterizes the large-scale turbulent wave field. We present an expression for β as a function of the forcing frequency, amplitude, and of the plate characteristics.