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Lobachevskii Journal of Mathematics

, Volume 38, Issue 5, pp 888–892 | Cite as

Statistics of freak waves in numerical tank

  • A. I. Dyachenko
  • D. I. Kachulin
  • V. E. Zakharov
Article
  • 26 Downloads

Abstract

Presented are the results of experiments on calculation of Probability Distribution Functions for elevations of waters waves in numerical tank. Statistics of waves of anomalous amplitude, or freak-waves were compared both for nonlinear and linear models. Obviously, linear model demonstrates the exact Rayleigh distribution of surface elevations while PDFs for nonlinear equation have tails (for large elevations) similar to Rayleigh distribution, but with larger σ.

Keywords and phrases

Nonlinear water waves Hamiltonian formalism modulational instability freak waves Zakharov equation 

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References

  1. 1.
    A. I. Dyachenko, D. I. Kachulin, and V. E. Zakharov, “About compact equations for water waves,” Nat. Hazards 83, 529–540 (2016).CrossRefGoogle Scholar
  2. 2.
    A. I. Dyachenko, D. I. Kachulin, and V. E. Zakharov, “New compact equation for numerical simulation of freak waves on deep water,” J. Phys.: Conf. Ser. 681, 012028 (2016).Google Scholar
  3. 3.
    A. I. Dyachenko and V. E. Zakharov, “Spatial equation for water waves,” JETP Lett. 103, 181–184 (2016).CrossRefGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  • A. I. Dyachenko
    • 1
    • 2
  • D. I. Kachulin
    • 1
  • V. E. Zakharov
    • 1
    • 2
    • 3
    • 4
  1. 1.Novosibirsk State UniversityNovosibirsk-90Russia
  2. 2.Landau Institute for Theoretical Physics Russian Academy of SciencesChernogolovka, Moscow oblastRussia
  3. 3.Lebedev Physical Institute Russian Academy of SciencesMoscowRussia
  4. 4.Department of MathematicsUniversity of ArizonaTucsonUSA

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