Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2002-02-12
Nonlinear Sciences
Chaotic Dynamics
4 pages, 3 figures
Scientific paper
10.1103/PhysRevE.67.046305
We study the nonlinear energy transfer around the peak of the spectrum of surface gravity waves by taking into account nonhomogeneous effects. In the narrow-banded approximation the kinetic equation resulting from a nonhomogeneous wave field is a Vlasov-Poisson type equation which includes at the same time the random version of the Benjamin-Feir instability and the Landau damping phenomenon. We analytically derive the values of the Phillips' constant $\alpha$ and the enhancement factor $\gamma$ for which the narrow-banded approximation of the JONSWAP spectrum is unstable. By performing numerical simulations of the nonlinear Schr\"{o}dinger equation we check the validity of the prediction of the related kinetic equation. We find that the effect of Landau damping is to suppress the formation of coherent structures. The problem of predicting freak waves is briefly discussed.
Fedele Renato
Onorato Miguel
Osborne A.
Serio Manlio
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