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:**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; - [Show abstract] [Hide abstract]

**ABSTRACT:**We report a study of the homogeneous isotropic Boltzmann equation for an open system. We seek for nonequilibrium steady solutions in presence of forcing and dissipation in the case of hard sphere gas. Using the language of weak turbulence theory, we analyze the possibility to observe Kolmogorov- Zakharov steady distributions. We derive a di�erential approximation model and we �nd that the expected nonequilibrium steady solutions have always the form of warm cascades. We propose an analytical prediction for relation between the forcing and dissipation and the thermodynamic quantities of the system. Speci�cally, we �nd that the temperature of the system is independent of the forcing amplitude and determined only by the forcing and dissipation scales. Finally, we perform direct numerical simulations of the Boltzmann equation �nding consistent results with our theoretical predictions.Physica D Nonlinear Phenomena 01/2012; 241:600-615. · 1.67 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**During previous numerical experiments on isotropic turbulence of surface gravity waves we observed formation of the long wave background (condensate). It was shown (Korotkevich, Phys. Rev. Lett. vol. 101 (7), 074504 (2008)), that presence of the condensate changes a spectrum of direct cascade, corresponding to the flux of energy to the small scales from pumping region (large scales). Recent experiments show that the inverse cascade spectrum is also affected by the condensate. In this case mechanism proposed as a cause for the change of direct cascade spectrum cannot work. But inverse cascade is directly influenced by the linear dispersion relation for waves, as a result direct measurement of the dispersion relation in the presence of condensate is necessary. We performed the measurement of this dispersion relation from the direct numerical experiment. The results demonstrate that in the region of inverse cascade influence of the condensate cannot be neglected.JETP Letters 12/2012; 97(3). · 1.52 Impact Factor

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