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Numerical Verification of Weakly Turbulent Law of Wind Wave Growth

  • Sergei I. Badulin
  • Alexander V. Babanin
  • Vladimir E. Zakharov
  • Donald T. Resio
Part of the IUTAM Bookseries book series (IUTAMBOOK, volume 6)

Abstract

Numerical solutions of the kinetic equation for deep water wind waves (the Hasselmann equation) for various functions of external forcing are analyzed. For wave growth in spatially homogeneous sea (the so-called duration-limited case) the numerical solutions are related with approximate self-similar solutions of the Hasselmann equation. These self-similar solutions are shown to be considered as a generalization of the classic Kolmogorov-Zakharov solutions in the theory of weak turbulence. Asymptotic law of wave growth that relates total wave energy with net total energy input (energy flux at high frequencies) is proposed. Estimates of self-similarity parameter that links energy and spectral flux and can be considered as an analogue of Kolmogorov-Zakharov constants are obtained numerically.

Keywords

Wind waves kinetic Hasselmann equation weak turbulence Kolmogorov-Zakharov solutions self-similarity 

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Copyright information

© Springer Science + Business Media B.V 2008

Authors and Affiliations

  • Sergei I. Badulin
    • 1
  • Alexander V. Babanin
    • 2
  • Vladimir E. Zakharov
    • 3
    • 4
  • Donald T. Resio
    • 5
  1. 1.P.P. Shirshov Institute of OceanologyRussia
  2. 2.Swinburne University of TechnologyMelbourneAustralia
  3. 3.P.N. Lebedev Physical InstituteRussia
  4. 4.Waves and Solitons, LLCUniversity of ArizonaUSA
  5. 5.Waterways Experimental StationUSA

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