Skip to main content
SpringerLink
Log in

Freak waves in crossing seas

  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract.

We consider the modulational instability in crossing seas as a potential mechanism for the formation of freak waves. The problem is discussed in terms of a system of two coupled Nonlinear Schröedinger equations. The asymptotic validity of such system is discussed. For some specific angles between the two wave trains, the equations reduce to an integrable system. A stability analysis of these equations is discussed. Furthermore, we present an analytical study of the maximum amplification factor for an unstable plane wave solution. Results indicate that angles between 10∘ and 30∘ are the most probable for establishing a freak wave sea. We show that the theoretical expectations are consistent with numerical simulations of the Euler equations.

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.

Similar content being viewed by others

References

  1. G. Clauss, Appl. Ocean. Res. 24Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 147 (2002)

    Article  Google Scholar 

  2. D.R. Solli, C. Ropers, P. Koonath, B. Jalali, Nature 450Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1054 (2007)

    Article  ADS  Google Scholar 

  3. A. Montina, U. Bortolozzo, S. Residori, F.T. Arecchi, Phys. Rev. Lett. 103Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 173901 (2009)

    Article  ADS  Google Scholar 

  4. A.N. Ganshin, V.B. Efimov, G.V. Kolmakov, L.P. Mezhov-Deglin, P.V.E. McClintock, Phys. Rev. Lett. 101Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 065303 (2008)

    Article  ADS  Google Scholar 

  5. Y.V. Bludov, V.V. Konotop, N. Akhmediev, Phys. Rev. A 80Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 033610 (2009)

    Article  Google Scholar 

  6. A. Maluckov, L. Hadzievski, N. Lazarides, G.P., TsironisPhys. Rev. E 79Discussion & Debate : Rogue Waves - Towards a Unifying Concept? 025601 (2009), ISSN 1539-3755

    Article  ADS  Google Scholar 

  7. C. Kharif, E. Pelinovskij, A. Slunjaev, Rogue Waves in the Ocean (Springer, 2009)

  8. C. Kharif, E. Pelinovsky, Eur. J. Mech./B Fluids 22Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 603 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  9. K. Dysthe, H.E. Krogstad, P. Müller, Ann. Rev. Fluid Mech. 40Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 287 (2008)

    Article  ADS  Google Scholar 

  10. T.B. Benjamin, J.E. Feir, J. Fluid Mech. 27Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 417 (1967)

    Article  MATH  ADS  Google Scholar 

  11. V. Zakharov, J. Appl. Mech. Tech. Phys. 9Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 190 (1968)

    Article  ADS  Google Scholar 

  12. V. Zakharov, A. Dyachenko, A. Prokofiev, Eur. J. Mech./B Fluids 25Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 677 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  13. P.A.E.M. Janssen, J. Phys. Ocean. 33Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 863 (2003)

    Article  ADS  Google Scholar 

  14. M. Onorato, A. Osborne, M. Serio, S. Bertone, Phys. Rev. Lett. 86Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 5831 (2001)

    Article  ADS  Google Scholar 

  15. M. Onorato, A. Osborne, M. Serio, L. Cavaleri, C. Brandini, C. Stansberg, Eur. J. Mech. B/Fluids 25Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 586 (2006)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  16. M. Onorato, A.R. Osborne, M. Serio, Phys. Fluids 14Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 25 (2002)

    Article  MathSciNet  ADS  Google Scholar 

  17. H. Socquet-Juglard, K. Dysthe, K. Trulsen, H. Krogstad, J. Liu, J. Fluid Mech. 542Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 195 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  18. M. Onorato, L. Cavaleri, S. Fouques, O. Gramdstad, P.A.E.M. Janssen, J. Monbaliu, A.R. Osborne, C. Pakozdi, M. Serio, C. Stansberg, et al., J. Fluid Mech. 627Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 235 (2009)

    Article  MATH  ADS  Google Scholar 

  19. M. Onorato, T. Waseda, A. Toffoli, L. Cavaleri, O. Gramdstad, P.A.E.M. Janssen, K. T., J. Monbaliu, N. Mori, A.R. Osborne, et al., Phys. Rev. Lett. 102Discussion & Debate : Rogue Waves - Towards a Unifying Concept? 114502 (2009)

    Article  ADS  Google Scholar 

  20. T. Waseda, T. Kinoshita, H. Tamura, J. Phys. Oceanogr. 39Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 621 (2009)

    Article  ADS  Google Scholar 

  21. A. Toffoli, J. Lefèvre, E. Bitner-Gregersen, J. Monbaliu, Appl. Ocean Res. 27Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 281 (2005)

    Article  Google Scholar 

  22. S. Haver, J. Andersen, Freak waves: rare realizations of a typical population or typical realizations of a rare population?, in Proc. 10-th Int. Offshore and Polar Engineering (ISOPE) Conf. (Seattle, USA, 2000)

  23. S. Lehner, H. Günther, W. Rosenthal, Extreme wave observations from radar data sets, in Ocean Waves Measurements, Analysis, Fifth International Symposium WAVES 2005 (Madrid, Spain, 2005), paper 69

  24. H. Tamura, T. Waseda, Y. Miyazawa, Geophys. Res. Lett. 36Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 01607 (2009)

    Article  Google Scholar 

  25. M. Onorato, A. Osborne, M. Serio, Phys. Rev. Lett. 96Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 014503 (2006)

    Article  ADS  Google Scholar 

  26. P.K. Shukla, I. Kaurakis, B. Eliasson, M. Marklund, L. Stenflo, Phys. Rev. Lett. 97Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 094501 (2006)

    Article  ADS  Google Scholar 

  27. A. Gronlund, B. Eliasson, M. Marklund, EPL 86Discussion & Debate : Rogue Waves - Towards a Unifying Concept? 24001 (2009), ISSN 0295-5075

    Article  ADS  Google Scholar 

  28. J. Hammack, D. Henderson, H. Segur, J. Fluid Mech. 532Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1 (2005)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  29. V. Krasitskii, J. Fluid Mech. 272Discussion & Debate : Rogue Waves - Towards a Unifying Concept? 1 (1994)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  30. N. Akhmediev, V. Korneev, Theor. Math. Phys. 69Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 1089 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  31. B.J. West, K.A. Brueckner, R.S. Jand, D.M. Milder, R.L. Milton, J. Geophys. Res. 92Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 11803 (1987)

    Article  ADS  Google Scholar 

  32. D.G. Dommermuth, D.K. Yue, J. Fluid Mech. 184Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 267 (1987)

    Article  MATH  ADS  Google Scholar 

  33. M. Tanaka, J. Fluid Mech. 444Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 199 (2001)

    Article  MATH  ADS  Google Scholar 

  34. M. Onorato, A.R. Osborne, M. Serio, D. Resio, A. Puskarev, V.E. Zakharov, C. Brandini, Phys. Rev. Lett. 89Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 4.144501 (2002)

    Article  Google Scholar 

  35. G. Ducrozet, D. Bonnefoy, D. Le Touzé, P. Ferrant, Nat. Hazards Earth Syst. Sci. 7Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 109 (2007)

    Article  ADS  Google Scholar 

  36. A. Toffoli, M. Benoit, M. Onorato, E.M. Bitner-Gregersen, Nonlin. Proc. Geophys. 16Discussion & Debate : Rogue Waves - Towards a Unifying Concept?, 131 (2009)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dipartimento di Fisica Generale, Università di Torino, via P. Giuria 1, 10125, Torino, Italy

    M. Onorato & D. Proment

  2. Swinburne University of Technology, PO Box 218, Hawthorn, Victoria, 3122, Australia

    A. Toffoli

  3. INFN, Sezione di Torino, V.P. Giuria 1, 10125, Torino, Italy

    D. Proment

Authors
  1. M. Onorato
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Proment
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Toffoli
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to M. Onorato.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Onorato, M., Proment, D. & Toffoli, A. Freak waves in crossing seas. Eur. Phys. J. Spec. Top. 185, 45–55 (2010). https://doi.org/10.1140/epjst/e2010-01237-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2010-01237-8

Keywords

Search

Navigation