Skip to main content
SpringerLink
Log in

Contributions of Nonlinear Spectral Components to the Probability Distribution of Rogue Waves Based on the Results of Numerical Simulation of the Euler Equations

  • Published:
Izvestiya, Atmospheric and Oceanic Physics Aims and scope Submit manuscript

Abstract

Based on the direct numerical modeling results of irregular nonlinear waves on the surface of deep water within the framework of three-dimensional potential equations of hydrodynamics, the contributions of various wave components (second, third, and difference harmonics) to the formation of probability distributions of extreme wave heights, as well as the amplitudes of crests and troughs, are determined. The simulation results are analyzed taking into account four- and five-wave nonlinear interactions. Various nonlinear harmonics participate in the formation of probability distributions in a nontrivial way, which is essentially not amenable to the principles of linear addition and the contribution of ordering by a small nonlinearity parameter.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.

Similar content being viewed by others

REFERENCES

  1. Adcock, T.A.A., Taylor, P.H., Yan, S., Ma, Q.W., and Janssen, P.A.E.M., Did the Draupner wave occur in a crossing sea?, Proc. R. Soc. A, 2011, vol. 467, pp. 3004–3021.

    Article  Google Scholar 

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

    Article  Google Scholar 

  3. Annenkov, S.Y. and Shrira, V.I., Effects of finite non-Gaussianity on evolution of a random wind wave field, Phys. Rev. E, 2022, vol. 106, p. L042102.

    Article  Google Scholar 

  4. Chalikov, D.V., Numerical Modeling of Sea Waves, Springer, 2016.

    Book  Google Scholar 

  5. Chalikov, D. and Bulgakov, K., Estimation of wave height probability based on the statistics of significant wave height, J. Ocean Eng. Mar. Energy, 2017, vol. 3, pp. 417–423.

    Article  Google Scholar 

  6. Christou, M. and Evans, K., Field measurements of rogue water waves, J. Phys. Oceanogr., 2014, vol. 44, pp. 2317–2335.

    Article  Google Scholar 

  7. Dalzell, J.F., A note on finite depth second-order wave-wave interactions, Appl. Ocean Res., 1999, vol. 21, pp. 105–111.

    Article  Google Scholar 

  8. Dommermuth, D. and Yue, D.K.P., A high-order spectral method for the study of nonlinear gravity waves, J. Fluid Mech., 1987, vol. 184, pp. 267–288.

    Article  Google Scholar 

  9. Dommermuth, D., The initialization of nonlinear waves using an adjustment scheme, Wave Motion, 2000, vol. 32, pp. 307–317.

    Article  Google Scholar 

  10. Ducrozet, G., Bonnefoy, F., Le Touzé, D., and Ferrant, P., HOS-ocean: Open-source solver for nonlinear waves in open ocean based on high-order spectral method, Comput. Phys. Commun., 2016, vol. 203, pp. 245–254.

    Article  Google Scholar 

  11. Dyachenko, A.I., Kachulin, D.I., and Zakharov, V.E., Freak-waves: Compact equation versus fully nonlinear one, in Extreme Ocean Waves, Pelinovsky, E. and Kharif, C., Eds., Springer, 2016, pp. 23–44.

    Google Scholar 

  12. Fedele, F., Brennan, J., Ponce de Léon, S., Dudley, J., and Dias, F., Real world ocean rogue waves explained without the modulational instability, Sci. Rep., 2016, vol. 6, p. 27715.

    Article  Google Scholar 

  13. Holthuijsen, L.H., Waves in Oceanic and Coastal Waters, Cambridge: Cambridge Univ. Press, 2007.

    Book  Google Scholar 

  14. Kachulin, D., Dyachenko, A., and Gelash, A., Interactions of coherent structures on the surface of deep water, Fluids, 2019, vol. 4, p. 83.

    Article  Google Scholar 

  15. Kharif, C., Pelinovsky, E., and Slunyaev, A., Rogue Waves in the Ocean, Berlin–Heidelberg: Springer, 2009.

    Google Scholar 

  16. Massel, S.R., Ocean Surface Waves: Their Physics and Prediction, Singapore: World Scientific, 1996.

    Book  Google Scholar 

  17. Onorato, M., Osborne, R., and Serio, M., On the relation between two numerical methods for the computation of random surface gravity waves, Eur. J. Mech., 2007, vol. 26, pp. 43–48.

    Article  Google Scholar 

  18. Sergeeva, A. and Slunyaev, A., Rogue waves, rogue events and extreme wave kinematics in spatio–temporal fields of simulated sea states, Nat. Hazards Earth Syst. Sci., 2013, vol. 13, pp. 1759–1771.

    Article  Google Scholar 

  19. Slunyaev, A.V., A high-order nonlinear envelope equation for gravity waves in finite-depth water, J. Exp. Theor. Phys., 2005, vol. 101, pp. 926–941.

    Article  Google Scholar 

  20. Slunyaev, A.V., Effects of coherent dynamics of stochastic deep-water waves, Phys. Rev. E, 2020, vol. 101, p. 062214.

    Article  Google Scholar 

  21. Slunyaev, A.V., Persistence of hydrodynamic envelope solitons: Detection and rogue wave occurrence, Phys. Fluids, 2021, vol. 33, p. 036606.

    Article  Google Scholar 

  22. Slunyaev, A.V. and Kokorina, A.V., Soliton groups as the reason for extreme statistics of unidirectional sea waves, J. Ocean Eng. Mar. Energy, 2017, vol. 3, pp. 395–408.

    Article  Google Scholar 

  23. Slunyaev, A.V. and Kokorina, A.V., Numerical simulation of the sea surface rogue waves within the framework of the potential Euler equations, Izv., Atmos. Ocean. Phys., 2020a, vol. 56, no. 2, pp. 179–190.

    Article  Google Scholar 

  24. Slunyaev, A. and Kokorina, A., Account of occasional wave breaking in numerical simulations of irregular water waves in the focus of the rogue wave problem, Water Waves, 2020b, vol. 2, pp. 243–262.

    Article  Google Scholar 

  25. Slunyaev, A.V., Sergeeva, A.V., and Didenkulova, I., Rogue events in spatiotemporal numerical simulations of unidirectional waves in basins of different depth, Nat. Hazards, 2016, vol. 84, pp. 549–565.

    Article  Google Scholar 

  26. Slunyaev, A., Klein, M., and Clauss, G.F., Laboratory and numerical study of intense envelope solitons of water waves: Generation, reflection from a wall and collisions, Phys. Fluids, 2017, vol. 29, p. 047103.

    Article  Google Scholar 

  27. Slunyaev, A.V., Pelinovsky, D.E., and Pelinovsky, E.N., Rogue waves in the sea: Observations, physics, and mathematics, Phys.-Usp., 2023, vol. 66, no. 2, pp. 148–172.

    Article  Google Scholar 

  28. Tanaka, M., A method of studying nonlinear random field of surface gravity waves by direct numerical simulation, Fluid Dyn. Res., 2001a, vol. 28, pp. 41–60.

    Article  Google Scholar 

  29. Tanaka, M., Verification of Hasselmann’s energy transfer among surface gravity waves by direct numerical simulations of primitive equations, J. Fluid Mech., 2001b, vol. 444, pp. 199–221.

    Article  Google Scholar 

  30. West, B.J., Brueckner, K., Janda, R.S., Milder, D.M., and Milton, R.L., A new numerical method for surface hydrodynamics, J. Geophys. Res., 1987, vol. 92, pp. 11803–11824.

    Article  Google Scholar 

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

    Article  Google Scholar 

  32. Zakharov, V.E., Stability of periodic waves on the surface of a deep liquid, Zh. Prikl. Mekh. Tekh. Fiz., 1968, vol. 9, pp. 86–94.

    Google Scholar 

Download references

Funding

This work was supported by the Laboratory of Nonlinear Hydrophysics and Natural Hazards of V.I. Il’ichev Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Sciences under a grant from the Ministry of Science and Higher Education of the Russian Federation, agreement no. 075-15-2022-1127 dated July 1, 2022.

Author information

Authors and Affiliations

  1. Institute of Applied Physics, Russian Academy of Sciences, 603950, Nizhny Novgorod, Russia

    A. V. Slunyaev

  2. Il’ichev Pacific Oceanological Institute, Far Eastern Branch, Russian Academy of Sciences, 690041, Vladivostok, Russia

    A. V. Slunyaev

  3. National Research University, Higher School of Economics, Nizhny Novgorod Branch, 603155, Nizhny Novgorod, Russia

    A. V. Slunyaev

Authors
  1. A. V. Slunyaev
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Slunyaev.

Ethics declarations

The author of this work declares that he has no conflicts of interest.

Additional information

Translated by V. Selikhanovich

Publisher’s Note.

Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

The article was prepared on the basis of an oral report presented at the IV All-Russian Conference with international participation “Turbulence, Dynamics of the Atmosphere and Climate,” dedicated to the memory of Academician A.M. Obukhov (Moscow, November 22–24, 2022).

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Slunyaev, A.V. Contributions of Nonlinear Spectral Components to the Probability Distribution of Rogue Waves Based on the Results of Numerical Simulation of the Euler Equations. Izv. Atmos. Ocean. Phys. 59, 701–721 (2023). https://doi.org/10.1134/S0001433823060105

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001433823060105

Keywords:

Search

Navigation