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JETP Letters

, Volume 109, Issue 5, pp 309–315 | Cite as

On the Dissipation Rate of Ocean Waves due to White Capping

  • A. O. KorotkevichEmail author
  • A. O. Prokofiev
  • V. E. Zakharov
Plasma, Hydro- and Gas Dynamics
  • 14 Downloads

Abstract

We calculate the rate of ocean wave energy dissipation due to white capping by numerical simulation of deterministic phase resolving model for dynamics of ocean surface. Two independent numerical experiments are performed. First, we solve the 3D Hamiltonian equation that includes three- and four-wave interactions. This model is valid only for moderate values of the surface steepness, μ < 0.09. Then we solve the exact Euler equation for non-stationary potential flow of an ideal fluid with a free surface in 2D geometry. We use the conformal mapping of domain filled with fluid onto the lower half-plane. This model is applicable for arbitrary high levels of the steepness. The results of both experiments are close. The white capping is the threshold process that takes place if the average steepness μ > μcr ≃ 0.055. The rate of energy dissipation grows dramatically with increasing steepness. Comparison of our results with dissipation functions used in the operational models of wave forecasting shows that these models overestimate the rate of wave dissipation by order of magnitude for typical values of the steepness.

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References

  1. 1.
    H. L. Tolman, User Manual and System Documentation of WAVEWATCH III (U. S. Dept. of Commerce, Natl. Ocean. Atmos. Administration, Natl. Weather Service, Natl. Centers for Environmental Prediction, 2009).Google Scholar
  2. 2.
    C. Sulem and P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-Focusing and Wave Collapse (Springer, New York, 1999).zbMATHGoogle Scholar
  3. 3.
    V. E. Zakharov, Sov. Phys. JETP 35, 908 (1972).ADSGoogle Scholar
  4. 4.
    A. Pushkarev and V. E. Zakharov, Ocean Model. 103, 18 (2016).ADSCrossRefGoogle Scholar
  5. 5.
    S. A. Dyachenko and A. C. Newell, Stud. Appl. Math. 137, 199 (2016).MathSciNetCrossRefGoogle Scholar
  6. 6.
    M. L. Banner and X. Tian, J. Fluid Mech. 367, 107 (1998).ADSMathSciNetCrossRefGoogle Scholar
  7. 7.
    M. L. Banner, A. V. Babanin, and I. R. Young, J. Phys. Oceanogr. 30, 3145 (2000).ADSCrossRefGoogle Scholar
  8. 8.
    J.-B. Song and M. L. Banner, J. Phys. Oceanogr. 32, 2541 (2002).ADSMathSciNetCrossRefGoogle Scholar
  9. 9.
    G. J. Komen, L. Cavaleri, M. Donelan, K. Hasselmann, and P. A. E. M. Janssen, Dynamics and Modelling of Ocean Waves (Cambridge Univ. Press, Cambridge, UK, 1994).CrossRefzbMATHGoogle Scholar
  10. 10.
    V. E. Zakharov, A. O. Korotkevich, and A. O. Prokofiev, AIP Conf. Proc. 1168, 1229 (2009).ADSCrossRefGoogle Scholar
  11. 11.
    A. I. Dyachenko, D. I. Kachulin, and V. E. Zakharov, JETP Lett. 102, 513 (2015).ADSCrossRefGoogle Scholar
  12. 12.
    V. E. Zakharov, J. Appl. Mech. Tech. Phys. 9, 190 (1968).ADSCrossRefGoogle Scholar
  13. 13.
    F. Dias, A. I. Dyachenko, and V. E. Zakharov, Phys. Lett. A 372, 1297 (2008).ADSCrossRefGoogle Scholar
  14. 14.
    A. O. Korotkevich, A. I. Dyachenko, and V. E. Zakharov, Phys. D (Amsterdam, Neth.) 321–322, 51 (2016).CrossRefGoogle Scholar
  15. 15.
    A. I. Dyachenko, Dokl. Math. 63, 115 (2001).Google Scholar
  16. 16.
    V. E. Zakharov, A. I. Dyachenko, and A. O. Prokofiev, Eur. J. Mech. B: Fluids 25, 677 (2006).ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, JETP Lett. 77, 546 (2003).ADSCrossRefGoogle Scholar
  18. 18.
    A. I. Dyachenko, A. O. Korotkevich, and V. E. Zakharov, Phys. Rev. Lett. 92, 134501 (2004).ADSCrossRefGoogle Scholar
  19. 19.
    M. A. Donelan, J. Hamilton, and W. H. Hui, Phil. Trans. R. Soc. London, Ser. A 315, 509 (1985).ADSCrossRefGoogle Scholar
  20. 20.
    V. E. Zakharov, A. O. Korotkevich, A. Pushkarev, and A. I. Dyachenko, JETP Lett. 82, 487 (2005).CrossRefGoogle Scholar
  21. 21.
    A. O. Korotkevich, Phys. Rev. Lett. 101, 074504 (2008).ADSCrossRefGoogle Scholar
  22. 22.
    A. O. Korotkevich, Math. Comput. Simul. 82, 1228 (2012).MathSciNetCrossRefGoogle Scholar
  23. 23.
    A. C. Newell and V. E. Zakharov, Phys. Rev. Lett. 69, 1149 (1992).ADSCrossRefGoogle Scholar
  24. 24.
    V. E. Zakharov and S. I. Badulin, arXiv:1212.0963.Google Scholar
  25. 25.
    V. E. Zakharov, Phys. Scripta T 142, 014052 (2010).ADSCrossRefGoogle Scholar
  26. 26.
    Gnuplot, Command-Driven Interactive Function Plotting Program 1986–2018. http://gnuplot.info.

Copyright information

© Pleiades Publishing, Inc. 2019

Authors and Affiliations

  • A. O. Korotkevich
    • 1
    • 2
    Email author
  • A. O. Prokofiev
    • 2
  • V. E. Zakharov
    • 2
    • 3
  1. 1.Department of Mathematics and Statistics, MSC01 11151 University of New MexicoAlbuquerqueUSA
  2. 2.Landau Institute for Theoretical PhysicsRussian Academy of SciencesMoscowRussia
  3. 3.Department of MathematicsThe University of ArizonaTucsonUSA

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