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Account of Occasional Wave Breaking in Numerical Simulations of Irregular Water Waves in the Focus of the Rogue Wave Problem

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Abstract

The issue of accounting of the wave breaking phenomenon in direct numerical simulations of oceanic waves is discussed. It is emphasized that this problem is crucial for the deterministic description of waves, and also for the dynamical calculation of extreme wave statistical characteristics, such as rogue wave height probability, asymmetry, etc. The conditions for accurate simulations of irregular steep waves within the High Order Spectral Method for the potential Euler equations are identified. Such non-dissipative simulations are considered as the reference when comparing with the simulations of occasionally breaking waves which use two kinds of wave breaking regularization. It is shown that the perturbations caused by the wave breaking attenuation may be noticeable within 20 min of the performed simulation of the wave evolution.

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References

  1. Annenkov, S.Y., Shrira, V.I.: Spectral evolution of weakly nonlinear random waves: kinetic description versus direct numerical simulations. J. Fluid Mech. 844, 766–795 (2018)

    Article  MathSciNet  Google Scholar 

  2. Annenkov, S.Y., Shrira, V.I.: On the predictability of evolution of surface gravity and gravity–capillary waves. Phys. D 152, 665–675 (2001)

    Article  MathSciNet  Google Scholar 

  3. Bitner-Gregersen, E.M., Fernandez, L., Lefèvre, J.M., Monbaliu, J., Toffoli, A.: The North Sea Andrea storm and numerical simulations. Nat. Hazards Earth Syst. Sci. 14, 1407–1415 (2014)

    Article  Google Scholar 

  4. Bitner-Gregersen, E.M., Toffoli, A.: Occurrence of rogue sea states and consequences for marine structures. Ocean Dyn. 64, 1457–1468 (2014)

    Article  Google Scholar 

  5. Brennan, J., Dudley, J.M., Dias, F.: Extreme waves in crossing sea states. arXiv: 1802.03547v1 (2018)

  6. Cavaleri, L.: Wave modeling: where to go in the future. Bull. Am. Meteor. Soc. 87, 207–214 (2006)

    Article  Google Scholar 

  7. Chalikov, D.: Statistical properties of nonlinear one-dimensional wave fields. Nonlinear Proc. Geophys. 12, 671–689 (2005)

    Article  Google Scholar 

  8. Chalikov, D.V.: Numerical Modeling of Sea Waves. Springer, New York (2016)

    Book  Google Scholar 

  9. Dommermuth, D., Yue, D.K.P.: A High-Order Spectral Method for the study of nonlinear gravity waves. J. Fluid Mech. 184, 267–288 (1987)

    Article  Google Scholar 

  10. Dommermuth, D.: The initialization of nonlinear waves using an adjustment scheme. Wave Motion 32, 307–317 (2000)

    Article  Google Scholar 

  11. Ducrozet, G., Bonnefoy, F., Le Touze, D., Ferrant, P.: 3-D HOS simulations of extreme waves in open seas. Nat. Hazards Earth Syst. Sci. 7, 109–122 (2007)

    Article  Google Scholar 

  12. Ducrozet, G., Bonnefoy, F., Le Touzé, D., Ferrant, P.: HOS-ocean: open-source solver for nonlinear waves in open ocean based on High-Order Spectral Method. Comput. Phys. Commun. 203, 245–254 (2016)

    Article  Google Scholar 

  13. Ducrozet, G., Bonnefoy, F., Perignon, Y.: Applicability and limitations of highly non-linear potential flow solvers in the context of water waves. Ocean Eng. 142, 233–244 (2017)

    Article  Google Scholar 

  14. Dyachenko, A.I., Kachulin, D.I., Zakharov, V.E.: Super compact equation for water waves. J. Fluid Mech. 828, 661–679 (2017)

    Article  MathSciNet  Google Scholar 

  15. Kharif, C., Pelinovsky, E., Slunyaev, A.: Rogue Waves in the Ocean. Springer, Berlin (2009)

    MATH  Google Scholar 

  16. Köllisch, N., Behrendt, J., Klein, M., Hoffman, N.: Nonlinear real time prediction of ocean surface waves. Ocean Eng. 157, 387–400 (2018)

    Article  Google Scholar 

  17. Onorato, M., Osborne, A.R., Serio, M., Bertone, S.: Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834 (2001)

    Article  Google Scholar 

  18. Onorato, M., Osborne, A.R., Serio, M.: Extreme wave events in directional, random oceanic sea states. Phys. Fluids 14, L25–L28 (2002)

    Article  MathSciNet  Google Scholar 

  19. Ruban, V.P.: Quasiplanar steep water waves. Phys. Rev. E 71, 055303(R) (2005)

    Article  MathSciNet  Google Scholar 

  20. Seiffert, B.R., Ducrozet, G., Bonnefoy, F.: Simulation of breaking waves using the High-Order Spectral Method with laboratory experiments: wave-breaking onset. Ocean Model. 119, 94–104 (2017)

    Article  Google Scholar 

  21. Slunyaev, A.V., Shrira, V.I.: On the highest non-breaking wave in a group: fully nonlinear water wave breathers vs weakly nonlinear theory. J. Fluid Mech. 735, 203–248 (2013)

    Article  MathSciNet  Google Scholar 

  22. Toffoli, A., Bitner-Gregersen, E.M.: Extreme and rogue waves in directional wave fields. The Open Ocean Eng. J. 4, 24–33 (2011)

    Article  Google Scholar 

  23. Toffoli, A., Gramstad, O., Trulsen, K., Monbaliu, J., Bitner-Gregersen, E., Onorato, M.: Evolution of weakly nonlinear random directional waves: laboratory experiments and numerical simulations. J. Fluid Mech. 664, 313–336 (2010)

    Article  MathSciNet  Google Scholar 

  24. Toffoli, A., Onorato, M., Bitner-Gregersen, E., Osborne, A.R., Babanin, A.V.: Surface gravity waves from direct numerical simulations of the Euler equations: a comparison with second-order theory. Ocean Eng. 35, 367–379 (2008)

    Article  Google Scholar 

  25. van Groesen, E., Turnip, P., Kurnia, R.: High waves in Draupner seas—Part 1: numerical simulations and characterization of the seas. J. Ocean Eng. Mar. Energy 3, 233–245 (2017)

    Article  Google Scholar 

  26. van Groesen, E., Wijaya, A.P.: High waves in Draupner seas—Part 2: observation and prediction from synthetic radar images. J. Ocean Eng. Mar. Energy 3, 325–332 (2017)

    Article  Google Scholar 

  27. West, B.J., Brueckner, K.A., Janda, R.S., Milder, D.M., Milton, R.L.: A new numerical method for surface hydrodynamics. J. Geophys. Res. 92, 11803–11824 (1987)

    Article  Google Scholar 

  28. Xiao, W., Liu, Y., Wu, G., Yue, D.K.P.: Rogue wave occurrence and dynamics by direct simulations of nonlinear wave-field evolution. J. Fluid Mech. 720, 357–392 (2013)

    Article  MathSciNet  Google Scholar 

  29. Zakharov, V.: Stability of periodic waves of finite amplitude on a surface of deep fluid. J. Appl. Mech. Tech. Phys. 2, 190–194 (1968)

    Google Scholar 

  30. Zakharov, V.E., Dyachenko, A.I., Vasilyev, O.A.: New method for numerical simulation of a nonstationary potential flow of incompressible fluid with a free surface. Eur. J. Mech. B Fluids 21, 283–291 (2002)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The support from the Russian Foundation for Basic Research (Grants nos. 17-05-00067 and 18-05-80019) is acknowledged by AK. AS is grateful for the support from the Fundamental Research Programme of RAS “Nonlinear Dynamics”.

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Authors and Affiliations

  1. Institute of Applied Physics, Box-120, 46 Ulyanova Street, Nizhny Novgorod, 603950, Russia

    Alexey Slunyaev & Anna Kokorina

  2. Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod, Russia

    Alexey Slunyaev & Anna Kokorina

  3. National Research University – Higher School of Economics, Nizhny Novgorod, Russia

    Alexey Slunyaev

Authors
  1. Alexey Slunyaev
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  2. Anna Kokorina
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Correspondence to Alexey Slunyaev or Anna Kokorina.

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Slunyaev, A., Kokorina, A. Account of Occasional Wave Breaking in Numerical Simulations of Irregular Water Waves in the Focus of the Rogue Wave Problem. Water Waves 2, 243–262 (2020). https://doi.org/10.1007/s42286-019-00014-9

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