Numerical Verification of the Weak Turbulent Model for Swell Evolution

Abstract

The purpose of this article is numerical verification of the theory of weak turbulence. We performed numerical simulation of an ensemble of nonlinearly interacting free gravity waves (swell) by two different methods: solution of primordial dynamical equations describing potential flow of the ideal fluid with a free surface and, solution of the kinetic Hasselmann equation, describing the wave ensemble in the framework of the theory of weak turbulence. In both cases we observed effects predicted by this theory: frequency downshift, angular spreading and formation of Zakharov-Filonenko spectrum $I_{\omega }\sim {\omega }^{-4}$. To achieve quantitative coincidence of the results obtained by different methods, one has to supply the Hasselmann kinetic equation by an empirical dissipation term $S_{diss}$ modeling the coherent effects of white-capping. Using of the standard dissipation terms from operational wave predicting model ({\it WAM}) leads to significant improvement on short times, but not resolve the discrepancy completely, leaving the question about optimal choice of $S_{diss}$ open. In a long run {\it WAM} dissipative terms overestimate dissipation essentially.

41 pages, 37 figures, 1 table. Submitted in European Journal of Mechanics B/Fluids

References in corpus (7)

• Freely decaying weak turbulence for sea surface gravity waves
• Weak Turbulent Kolmogorov Spectrum for Surface Gravity Waves
• Mesoscopic wave turbulence
• Discreteness and its effect on the water-wave turbulence
• Sandpile behaviour in discrete water-wave turbulence
• Weak turbulence of gravity waves
• Decay of the monochromatic capillary wave

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