Identification of a separation wave number between weak and strong turbulence spectra for a vibrating plate.

A weakly nonlinear spectrum and a strongly nonlinear spectrum coexist in a statistically steady state of elastic wave turbulence. The analytical representation of the nonlinear frequency is obtained by evaluating the extended self-nonlinear interactions. The critical wave numbers at which the nonlinear frequencies are comparable with the linear frequencies agree with the separation wave numbers between the weak and strong turbulence spectra. We also confirm the validity of our analytical representation of the separation wave numbers through comparison with the results of direct numerical simulations by changing the material parameters of a vibrating plate.