Editorial Type:
Article
Article Type:
Research Article

Modelling the Impact of Squall on Wind Waves with the Generalized Kinetic Equation

Sergei Annenkov Department of Mathematics, Research Institute for the Environment, Physical Sciences, and Applied Mathematics, Keele University, Keele, United Kingdom

Search for other papers by Sergei Annenkov in
Current site
Google Scholar
PubMed Close
and
Victor Shrira Department of Mathematics, Research Institute for the Environment, Physical Sciences, and Applied Mathematics, Keele University, Keele, United Kingdom

Search for other papers by Victor Shrira in
Current site
Google Scholar
PubMed Close
Print Publication:
01 Mar 2015
DOI:
https://doi.org/10.1175/JPO-D-14-0182.1
Page(s):
807–812
Restricted access

Abstract

This is a first study of short-lived transient sea states, arising from fast variations of wind fields. This study considers the response of a wind-wave field to a sharp increase of wind over a short time interval (a squall). Conventional wind-wave models based on the Hasselmann equation assume quasi stationarity of a random wave field and are a priori inapplicable for such transient states. To describe fast spectral changes, the authors use the generalized kinetic equation (GKE) derived without the quasi-stationarity assumption. A novel efficient highly parallelized algorithm for the numerical simulation of the GKE is presented. Simulations with the GKE and the Hasselmann equation are examined and compared. While under steady wind, the spectral evolution in both cases is shown to be practically identical, but after the squall the qualitative difference emerges: the GKE predicts formation of a transient sea state with a considerably narrower peak.

Corresponding author address: Sergei Annenkov, Department of Mathematics, EPSAM, Keele University, Keele ST5 5BG, United Kingdom. E-mail: s.annenkov@keele.ac.uk

Abstract

This is a first study of short-lived transient sea states, arising from fast variations of wind fields. This study considers the response of a wind-wave field to a sharp increase of wind over a short time interval (a squall). Conventional wind-wave models based on the Hasselmann equation assume quasi stationarity of a random wave field and are a priori inapplicable for such transient states. To describe fast spectral changes, the authors use the generalized kinetic equation (GKE) derived without the quasi-stationarity assumption. A novel efficient highly parallelized algorithm for the numerical simulation of the GKE is presented. Simulations with the GKE and the Hasselmann equation are examined and compared. While under steady wind, the spectral evolution in both cases is shown to be practically identical, but after the squall the qualitative difference emerges: the GKE predicts formation of a transient sea state with a considerably narrower peak.

Corresponding author address: Sergei Annenkov, Department of Mathematics, EPSAM, Keele University, Keele ST5 5BG, United Kingdom. E-mail: s.annenkov@keele.ac.uk
Save
Cover Journal of Physical Oceanography
Journal of Physical Oceanography

  • Annenkov, S. Y., and V. I. Shrira, 2006: Role of non-resonant interactions in the evolution of nonlinear random water wave fields. J. Fluid Mech., 561, 181–207, doi:10.1017/S0022112006000632.

    • Search Google Scholar
    • Export Citation

  • Annenkov, S. Y., and V. I. Shrira, 2009: “Fast” nonlinear evolution in wave turbulence. Phys. Rev. Lett.,102, 024502, doi:10.1103/PhysRevLett.102.024502.

  • Autard, L., 1995: 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, 181 pp.

  • Bastianini, M., L. Cavaleri, and T. L. Rocca, 2012: An extreme meteorological event at the ISMAR oceanographic tower. Nat. Hazards Earth Syst. Sci., 12, 281–285, doi:10.5194/nhess-12-281-2012.

    • Search Google Scholar
    • Export Citation

  • Donelan, M. A., J. Hamilton, and W. Hui, 1985: Directional spectra of wind-generated waves. Philos. Trans. Roy. Soc. London, A315, 509–562, doi:10.1098/rsta.1985.0054.

    • Search Google Scholar
    • Export Citation

  • Gramstad, O., and M. Stiassnie, 2013: Phase-averaged equation for water waves. J. Fluid Mech., 718, 280–303, doi:10.1017/jfm.2012.609.

    • Search Google Scholar
    • Export Citation

  • Gramstad, O., and A. Babanin, 2014: Implementing new nonlinear term in third-generation wave models. Proc. ASME 2014 33rd Int. Conf. on Ocean, Offshore and Arctic Engineering, Paper OMAE2014–24 677, San Francisco, CA, Ocean, Offshore and Arctic Engineering Division, doi:10.1115/OMAE2014-24677.

  • Hasselmann, K., 1962: On the non-linear energy transfer in a gravity-wave spectrum. Part 1. General theory. J. Fluid Mech., 12, 481–500, doi:10.1017/S0022112062000373.

    • Search Google Scholar
    • Export Citation

  • Hsiao, S. V., and O. H. Shemdin, 1983: Measurements of wind velocity and pressure with a wave follower during Marsen. J. Geophys. Res., 88, 9841–9849, doi:10.1029/JC088iC14p09841.

    • Search Google Scholar
    • Export Citation

  • Janssen, P. A. E. M., 2004: The Interaction of Ocean Waves and Wind. Cambridge University Press, 300 pp.

  • Komen, G. J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen, 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 532 pp.

  • Krasitskii, V. P., 1994: On reduced equations in the Hamiltonian theory of weakly nonlinear surface waves. J. Fluid Mech., 272, 1–20, doi:10.1017/S0022112094004350.

    • Search Google Scholar
    • Export Citation

  • van Vledder, G. P., 2006: The WRT method for the computation of non-linear four-wave interactions in discrete spectral wave models. Coastal Eng., 53, 223–242, doi:10.1016/j.coastaleng.2005.10.011.

    • Search Google Scholar
    • Export Citation

  • van Vledder, G. P., and L. H. Holthuijsen, 1993: The directional response of ocean waves to turning winds. J. Phys. Oceanogr., 23, 177–192, doi:10.1175/1520-0485(1993)023<0177:TDROOW>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Waseda, T., Y. Toba, and M. Tulin, 2001: Adjustment of wind waves to sudden changes of wind speed. J. Oceanogr., 57, 519–533, doi:10.1023/A:1021287032271.

    • Search Google Scholar
    • Export Citation

  • Young, I. R., and A. van Agthoven, 1998: The response of waves to a sudden change in wind speed. Adv. Fluid Mech., 17, 133–162.

  • Zakharov, V. E., and S. I. Badulin, 2011: On energy balance in wind-driven seas. Dokl. Earth Sci., 440, 1440–1444, doi:10.1134/S1028334X11100175.

    • Search Google Scholar
    • Export Citation

  • Zakharov, V. E., V. S. L’vov, and G. Falkovich, 1992: Kolmogorov Spectra of Turbulence I: Wave Turbulence. Springer, 264 pp.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 126 47 5
PDF Downloads 89 38 10