Physical mechanisms for sporadic wind wave horse-shoe patterns (original) (raw)
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On the kinetic equation in Zakharov's wave turbulence theory for capillary waves
2017
The wave turbulence equation is an effective kinetic equation that describes the dynamics of wave spectrum in weakly nonlinear and dispersive media. Such a kinetic model has been derived by physicists in the sixties, though the well-posedness theory remains open, due to the complexity of resonant interaction kernels. In this paper, we provide a global unique radial strong solution, the first such a result, to the wave turbulence equation for capillary waves.
Journal of Fluid Mechanics, 2018
Kinetic equations are widely used in many branches of science to describe the evolution of random wave spectra. To examine the validity of these equations, we study numerically the long-term evolution of water wave spectra without wind input using three different models. The first model is the classical kinetic (Hasselmann) equation (KE). The second model is the generalised kinetic equation (gKE), derived employing the same statistical closure as the KE but without the assumption of quasistationarity. The third model, which we refer to as the DNS-ZE, is a direct numerical simulation algorithm based on the Zakharov integrodifferential equation, which plays the role of the primitive equation for a weakly nonlinear wave field. It does not employ any statistical assumptions. We perform a comparison of the spectral evolution of the same initial distributions without forcing, with/without a statistical closure and with/without the quasistationarity assumption. For the initial conditions, ...