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A 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 perform direct numerical simulations according to the Föppl-von Kármán equation, and successfully reproduce 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. The coexistence of the weakly nonlinear spectrum in large wave numbers and the strongly nonlinear spectrum in small wave numbers is also found in moderate energy wave fields. [ABSTRACT FROM AUTHOR]

Abstract: In wave turbulence, which is made by nonlinear interactions among waves, it has been believed that statistical properties are well described by the weak turbulence theory, where separation of linear and nonlinear time scales derived from weak nonlinearity is assumed. However, the separation of the time scales is often violated. To get rid of this inconsistency, closed equations are derived in wave turbulence without assuming the weak nonlinearity according to Direct-Interaction Approximation (DIA), which has been successful in Navier–Stokes turbulence. The DIA equations is a natural extension of the conventional kinetic equation to not-necessarily-weak wave turbulence. [Copyright &y& Elsevier]

Abstract: A series of numerical studies has been performed to investigate the statistical characteristics of fluctuations of energy of each component wave and its time derivative in a wave turbulence for a Hamiltonian system with a non-decay type dispersion relation. It has been found that the probability density functions (PDF) of and evaluated among independent realizations are almost equivalent to the PDF’s evaluated among nearby modes in the space in a single realization. Therefore, the averaging over the realizations and that over the nearby modes in a single realization are interchangeable. It has also been found that the PDF of evolves in time toward the distribution with two degrees of freedom, while that of evolves toward the Laplace distribution (or the two-sided exponential distribution) at any wavenumber , both in the peripheral of the spectrum (large region) and in the energy-containing range (small region). [Copyright &y& Elsevier]