Spectral evolution of random wave fields: Kinetic equations vs. direct numerical simulations (INVITED)

Abstract eng:
We examine how accurately the kinetic equations describe evolution of random weakly nonlinear waves in fluids and solids. To this end we simulate numerically long-term evolution of wave spectra without forcing using three different models: (i) the classical kinetic equation (KE); (ii) the generalised kinetic equation (gKE) valid also when the wave spectrum is changing rapidly; (iii) the DNS based on the Zakharov integrodifferential equation for water waves (DNS-ZE). (DNS-ZE does not rely on any statistical assumptions. As the initial conditions we choose two spectra with the same frequency distribution and different degrees of directionality. All three approaches demonstrate very close evolution of integral characteristics of spectra. However, there are notable systematic differences (e.g. the broadening of angular spectra is much faster for the kinetic equations), which suggests the presence and significance of coherent interactions not accounted for by the established closure for the kinetic equations.

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