• Alber, I., 1978: The effects of randomness of the stability of two-dimensional surface wavetrains. Proc. Roy. Soc. London, 363A , 525546.

    • Search Google Scholar
    • Export Citation
  • Alber, I., , and P. Saffman, 1978: Stability of random nonlinear deepwater waves with finite bandwidth spectra. Tech. Rep. 31326-6035-RU-00, TRW Defense and Space System Group.

  • Benjamin, T., , and J. Feir, 1967: The disintegration of wavetrains on deep water. Part 1. Theory. J. Fluid Mech., 27 , 417430.

  • Caponi, E., , P. Saffman, , and H. Yuen, 1982: Instability and confined chaos in a nonlinear dispersive wave system. Phys. Fluids, 25 , 21592166.

    • Search Google Scholar
    • Export Citation
  • Dean, R., 1990: Freak waves: A possible explanation. Water Wave Kinematics, A Tørum and O. Gudmestad, Eds., Kluwer Academic, 609–612.

    • Search Google Scholar
    • Export Citation
  • Dysthe, K., 1979: Note on modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. Roy. Soc. London, 369A , 105114.

    • Search Google Scholar
    • Export Citation
  • Forristall, G., 2000: Wave crest distributions: Observation and second-order theory. J. Phys. Oceanogr., 30 , 19311942.

  • Goda, Y., 2000: Random Seas and Design of Maritime Structures. 2d ed. World Scientific, 464 pp.

  • Hasselmann, K., 1962: On the nonlinear energy transfer in gravity-wave spectrum. I. General theory. J. Fluid Mech., 12 , 481500.

  • Haver, S., 2001: Evidences of the existence of freak waves. Rogue Waves, M. Olagnon and G. Atanassoulis, Eds., 129–140.

  • Janssen, P., 2003: Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr., 33 , 20012018.

  • Krasitskii, V., 1990: Canonical transformation in a theory of weakly nonlinear waves with a nondecay dispersion law. Soviet Phys. JETP, 71 , 921927.

    • Search Google Scholar
    • Export Citation
  • Lavrenov, I., 1998: The wave energy concentration at the Agulhas current off South Africa. Nat. Hazard, 17 , 117127.

  • Longuet-Higgins, M., 1957: The statistical analysis of a random moving surface. Philos. Trans. Roy. Soc. London, 249A , 321387.

  • Mori, N., 2003: Effects of wave breaking on wave statistics for deep-water random wave train. Ocean Eng., 30 , 205220.

  • Mori, N., , and T. Yasuda, 2002: A weakly non-Gaussian model of wave height distribution for random wave train. Ocean Eng., 29 , 12191231.

    • Search Google Scholar
    • Export Citation
  • Mori, N., , P. Liu, , and T. Yasuda, 2002: Analysis of freak wave measurements in the Sea of Japan. Ocean Eng., 29 , 13991414.

  • Olagnon, M., 2004: Rogue Waves 2004. IFREMER, 200 pp.

  • Olagnon, M., , and G. Athanassoulis, 2000: Rogue Waves 2000. IFREMER, 395 pp.

  • Onorato, M., , A. Osborne, , M. Serio, , and S. Bertone, 2001: Freak waves in random oceanic sea states. Phys. Rev. Lett., 86 , 58315834.

  • Osborne, A., , M. Onorato, , M. Serio, , and S. Bertone, 2000: The nonlinear dynamics of rogue waves and holes in deep water gravity wave trains. Phys. Lett., 275A , 386393.

    • Search Google Scholar
    • Export Citation
  • Srokosz, M., , and M. Longuet-Higgins, 1986: On the skewness of sea-surface elevation. J. Fluid Mech., 164 , 487497.

  • Stansberg, C., 1990: Extreme waves in laboratory generated irregular wave trains. Water Wave Kinematics, A. Tørum and O. Gudmestad, Eds., Kluwer Academic, 573–590.

    • Search Google Scholar
    • Export Citation
  • Stiassnie, M., , and L. Shemer, 1987: Energy computations for evolution of class I and II instabilities of Stokes waves. J. Fluid Mech., 174 , 299312.

    • Search Google Scholar
    • Export Citation
  • Su, M., 1982: Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric patterns. J. Fluid Mech., 124 , 73108.

    • Search Google Scholar
    • Export Citation
  • Trulsen, K., , and K. Dysthe, 1997: Freak waves—A three-dimensional wave simulation. Proceedings of the 21st Symposium on Naval Hydrodynamics, National Academy Press, 550–558.

    • Search Google Scholar
    • Export Citation
  • Vinje, T., 1989: The statistical distribution of wave heights in a random seaway. Appl. Ocean Res., 11 , 143152.

  • Whitham, G., 1974: Linear and Nonlinear Waves. John Wiley and Sons, 656 pp.

  • Yasuda, T., , and N. Mori, 1994: High order nonlinear effects on deep-water random wave trains. Int. Symp. on Waves—Physical and Numerical Modelling, Vol. 2. Vancouver, BC, Canada, International Association of Hydraulic Engineering and Research, 823–332.

  • Yasuda, T., , and N. Mori, 1997: Roles of sideband instability and mode coupling in forming a water wave chaos. Wave Motion, 26 , 163185.

    • Search Google Scholar
    • Export Citation
  • Yasuda, T., , N. Mori, , and K. Ito, 1992: Freak waves in a unidirectional wave train and their kinematics. Proc. 23d Int. Conf. on Coastal Engineering, Vol. 1, Venice, Italy, American Society of Civil Engineers, 751–764.

  • Yuen, H., , and W. Ferguson, 1978: Relationship between Benjamin–Feir instability and recurrence in the nonlinear schrödinger equation. Phys. Fluids, 21 , 12751278.

    • Search Google Scholar
    • Export Citation
  • Yuen, H., , and B. Lake, 1982: Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech., 22 , 67229.

  • Zakharov, V., 1968: Stability of periodic waves of finite amplitude on the surface of a deep fluid. J. Appl. Tech. Phys., 9 , 190194.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 224 224 27
PDF Downloads 184 184 26

On Kurtosis and Occurrence Probability of Freak Waves

View More View Less
  • 1 Graduate School of Engineering, Osaka City University, Osaka, Japan
  • | 2 European Centre for Medium-Range Weather Forecasts, Shinfield Park, Reading, United Kingdom
© Get Permissions Rent on DeepDyve
Restricted access

Abstract

Based on a weakly non-Gaussian theory, the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis. Finite kurtosis gives rise to a significant enhancement of freak wave generation in comparison with the linear narrowbanded wave theory. For a fixed number of waves, the estimated amplification ratio of freak wave occurrence due to the deviation from the Gaussian theory is 50%–300%. The results of the theory are compared with laboratory and field data.

Corresponding author address: Nobuhito Mori, Graduate School of Engineering, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan. Email: mori@urban.eng.osaka-cu.ac.jp

Abstract

Based on a weakly non-Gaussian theory, the occurrence probability of freak waves is formulated in terms of the number of waves in a time series and the surface elevation kurtosis. Finite kurtosis gives rise to a significant enhancement of freak wave generation in comparison with the linear narrowbanded wave theory. For a fixed number of waves, the estimated amplification ratio of freak wave occurrence due to the deviation from the Gaussian theory is 50%–300%. The results of the theory are compared with laboratory and field data.

Corresponding author address: Nobuhito Mori, Graduate School of Engineering, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan. Email: mori@urban.eng.osaka-cu.ac.jp

Save