Rogue and Shock Waves in Nonlinear Dispersive Media pp 159-178

Part of the Lecture Notes in Physics book series (LNP, volume 926) | Cite as

Modelling Transient Sea States with the Generalised Kinetic Equation

Chapter

Abstract

For historical and technical reasons evolution of random weakly nonlinear wave fields so far has been studied primarily in a quasi-stationary environment, where the main modelling tool is the kinetic equation. In the context of oceanic waves sharp changes of wind do occur quite often and can generate transient sea states with characteristic timescales of up to hundreds of wave periods. It is of great fundamental and practical interest to understand wave field behaviour during short-lived and transient events. At present nothing is known about such ephemeral sea states. One, but not the only, reason was that there were no adequate modelling tools. The generalised kinetic equation (gKE) derived without assumptions of quasi-stationarity seems to fill this gap. Here we study transient events with the gKE aiming to understand what is going during such events and capabilities of the gKE in capturing them. We find how wave spectra evolve being subjected to sharp changes of wind, while tracing in parallel the concomitant evolution of higher moments characterizing the field departure from gaussianity. We demonstrated the capability of the gKE to capture short-lived events, in particular, we found sharp brief increase of kurtosis during squalls, which suggests significant increase of the likelihood of freak waves during such events. Although the study was focussed upon wind wave context the approach is generic and is transferrable to random weakly nonlinear wave fields of other nature.

References

  1. 1.
    Annenkov, S.Y., Shrira, V.I.: Role of non-resonant interactions in the evolution of nonlinear random water wave fields. J. Fluid Mech. 561, 181–207 (2006)ADSMathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Annenkov, S.Y., Shrira, V.I.: Large-time evolution of statistical moments of wind–wave fields. J. Fluid Mech. 726, 517–546 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Autard, L.: Etude de la liaison entre la tension du vent à la surface et les propriétés des champs de vagues de capillarité-gravité developpés. Ph.D. thesis, Université Aix-Marseille I and II (1995)Google Scholar
  4. 4.
    Caulliez, G.: Response of dominant wind wave fields to abrupt wind increase. In: EGU General Assembly Conference Abstracts, vol. 15, p. 11313 (2013)Google Scholar
  5. 5.
    Cavaleri, L.: Wind variability. In: Komen, G. (ed.) Dynamics and Modelling of Ocean Waves, pp. 320–331. Cambridge University Press, Cambridge (1994)Google Scholar
  6. 6.
    Donelan, M.A., Hamilton, J., Hui, W.: Directional spectra of wind-generated waves. Philos. Trans. R. Soc. Lond. A 315 (1534), 509–562 (1985)ADSCrossRefGoogle Scholar
  7. 7.
    Gramstad, O., Babanin, A.: Implementing new nonlinear term in third generation wave models. In: ASME 2014 33rd International Conference on Ocean, Offshore and Arctic Engineering, p. V04BT02A057 (2014)Google Scholar
  8. 8.
    Gramstad, O., Stiassnie, M.: Phase-averaged equation for water waves. J. Fluid Mech. 718, 280–303 (2013)ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    Hasselmann, K.: On the non-linear energy transfer in a gravity-wave spectrum. Part 1: general theory. J. Fluid Mech. 12, 481–500 (1962)Google Scholar
  10. 10.
    Hsiao, S.V., Shemdin, O.H.: Measurements of wind velocity and pressure with a wave follower during MARSEN. J. Geophys. Res. 88, 9841–9849 (1983)ADSCrossRefGoogle Scholar
  11. 11.
    Hwang, P.A., Wang, D.W., Walsh, E.J., Krabill, W.B., Swift, R.N.: Airborne measurements of the wavenumber spectra of ocean surface waves. Part II: directional distribution. J. Phys. Oceanogr. 30, 2768–2787 (2000)Google Scholar
  12. 12.
    Janssen, P.A.E.M.: Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884 (2003)ADSMathSciNetCrossRefGoogle Scholar
  13. 13.
    Janssen, P.A.E.M.: On some consequences of the canonical transformation in the hamiltonian theory of water waves. J. Fluid Mech. 637, 1–44 (2009)ADSMathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Janssen, P.A.E.M.: Hamiltonian description of ocean waves and freak waves. In: Onorato, M. (ed.) Rogue and Shock Waves in Nonlinear Dispersive Media. Springer, Berlin (2016)Google Scholar
  15. 15.
    Nazarenko, S.V.: Wave Turbulence. Lecture Notes in Physics, vol. 825. Springer, Berlin (2011)Google Scholar
  16. 16.
    Onorato, M., Residori, S., Bortolozzo, U., Montina, A., Arecchi, F.: Rogue waves and their generating mechanisms in different physical contexts. Phys. Rep. 528, 47–89 (2013)ADSMathSciNetCrossRefGoogle Scholar
  17. 17.
    Picozzi, A., Garnier, J., Hansson, T., Suret, P., Randoux, S., Millot, G., Christodoulides, D.: Optical wave turbulence: towards a unified nonequilibrium thermodynamic formulation of statistical nonlinear optics. Phys. Rep. 542, 1–132 (2014)ADSMathSciNetCrossRefGoogle Scholar
  18. 18.
    Shrira, V.I., Annenkov, S.Y.: Towards a new picture of wave turbulence. In: Shrira, V., Nazarenko, S. (eds.) Advances in Wave Turbulence. World Scientific Series on Nonlinear Science, vol. 83, pp. 239–281 (World Scientific, Singapore, 2013)Google Scholar
  19. 19.
    van Vledder, G.P., Holthuijsen, L.H.: The directional response of ocean waves to turning winds. J. Phys. Oceanogr. 23, 177–192 (1993)ADSCrossRefGoogle Scholar
  20. 20.
    Waseda, T., Toba, Y., Tulin, M.P.: Adjustment of wind waves to sudden changes of wind speed. J. Oceanogr. 57, 519–533 (2001)CrossRefGoogle Scholar
  21. 21.
    Young, I.R., van Agthoven, A.: The response of waves to a sudden change in wind speed. In: Perrie, W. (ed.) Nonlinear Ocean Waves. Advances in Fluid Mechanics Series, pp. 133–162. WIT Press, Southampton (2013)Google Scholar
  22. 22.
    Zakharov, V.E., L’vov, V.S., Falkovich, G.: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, Berlin (1992)CrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of Computing and MathematicsKeele UniversityKeeleUK

Personalised recommendations