Article

# Weak turbulence of gravity waves

JETP Letters (Impact Factor: 1.52). 08/2003; DOI: 10.1134/1.1595693

Source: arXiv

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**ABSTRACT:**The evolution of the initially random wave field with a Gaussian spectrum shape is studied numerically within the Korteweg–de Vries (KdV) equation. The properties of the KdV random wave field are analyzed: transition to a steady state, equilibrium spectra, statistical moments of a random wave field, and the distribution functions of the wave amplitudes. Numerical simulations are performed for different Ursell parameters and spectrum width. It is shown that the wave field relaxes to the stationary state (in statistical sense) with the almost uniform energy distribution in low frequency range (Rayleigh–Jeans spectrum). The wave field statistics differs from the Gaussian one. The growing of the positive skewness and non-monotonic behavior of the kurtosis with increase of the Ursell parameter are obtained. The probability of a large amplitude wave formation differs from the Rayleigh distribution.European Journal of Mechanics - B/Fluids 07/2006; 25(4):425-434. · 1.64 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We perform full-scale numerical simulation of instability of weakly nonlinear waves on the surface of deep fluid. We show that the instability development leads to chaotization and formation of wave turbulence. We study instability both of propagating and standing waves. We studied separately pure capillary wave unstable due to three-wave interactions and pure gravity waves unstable due to four-wave interactions. The theoretical description of instabilities in all cases is included into the article. The numerical algorithm used in these and many other previous simulations performed by authors is described in details.12/2012; -
##### Article: One-dimensional wave turbulence

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**ABSTRACT:**The problem of turbulence is one of the central problems in theoretical physics. While the theory of fully developed turbulence has been widely studied, the theory of wave turbulence has been less studied, partly because it developed later. Wave turbulence takes place in physical systems of nonlinear dispersive waves. In most applications nonlinearity is small and dispersive wave interactions are weak. The weak turbulence theory is a method for a statistical description of weakly nonlinear interacting waves with random phases. It is not surprising that the theory of weak wave turbulence began to develop in connection with some problems of plasma physics as well as of wind waves. The present review is restricted to one-dimensional wave turbulence, essentially because finer computational grids can be used in numerical computations.Most of the review is devoted to wave turbulence in various wave equations, and in particular in a simple one-dimensional model of wave turbulence introduced by Majda, McLaughlin and Tabak in 1997. All the considered equations are model equations, but consequences on physical systems such as ocean waves are discussed as well. The main conclusion is that the range in which the theory of pure weak turbulence is valid is narrow. In general, wave turbulence is not completely weak. Together with the weak turbulence component, it can include coherent structures, such as solitons, quasisolitons, collapses or broad collapses. As a result, weak and strong turbulence coexist. In situations where coherent structures cannot develop, weak turbulence dominates.Even though this is primarily a review paper, new results are presented as well, especially on self-organized criticality and on quasisolitonic turbulence.Physics Reports 01/2004; 398:1-65. · 22.93 Impact Factor

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