Weak turbulence of gravity waves

JETP Letters (Impact Factor: 1.36). 08/2003; 77(10). DOI: 10.1134/1.1595693
Source: arXiv


For the first time weak turbulent theory was demonstrated for the surface gravity waves. Direct numerical simulation of the dynamical equations shows Kolmogorov turbulent spectra as predicted by analytical analysis from kinetic equation.

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Available from: Alexander O. Korotkevich, Sep 04, 2015
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    • "In Chapter 4 we give a detailed description of the numerical code which we used for solution of the Hamiltonian Euler equation. This code was used in many papers but never was described in details [13] [14] [15] [16] [17] [18] [19] [20]. "
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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.
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    • "These solutions, named cascade solutions, become important when considering an open system, i.e. with forcing and dissipation terms. They have been studied for a great variety of weakly nonlinear dispersive models: examples can be found in water waves [8] [9] [10], internal waves [11], nonlinear optics [12], Bose-Einstein condensation [13] [14] [15], magnetohydrodynamics [16]. An out of equilibrium description of the Boltzmann equation using the KZ solutions was first devised in [17] considering different types of interaction potential between particles. "
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    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 03/2012; 241(5):600-615. DOI:10.1016/j.physd.2011.11.019 · 1.64 Impact Factor
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    • "Author follows previous works in theoretical description of the system under consideration [20] [21] [19] [24] "
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    ABSTRACT: During direct numerical simulation of the isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations formation of the long wave background or condensate was observed. Exponents of the direct cascade spectra at the different levels of an artificial condensate suppression show a tendency to become closer to the prediction of the wave turbulence theory at lower levels of condensate. A simple qualitative explanation of the mechanism of this phenomenon is proposed.
    Mathematics and Computers in Simulation 11/2009; 82(7). DOI:10.1016/j.matcom.2010.07.009 · 0.95 Impact Factor
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