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 $f_0$. 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.