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Influence of crest and group length on the occurrence of freak waves

Published online by Cambridge University Press:  14 June 2007

ODIN GRAMSTAD  and
KARSTEN TRULSEN
ODIN GRAMSTAD
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway
KARSTEN TRULSEN
Affiliation:
Department of Mathematics, University of Oslo, P.O. Box 1053 Blindern, NO-0316 Oslo, Norway
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Abstract

A large number of simulations have been performed to reveal how the occurrence of freak waves on deep water depends on the group and crest lengths for fixed steepness. It is found that there is a sharp qualitative transition between short- and long-crested sea, for a crest length of approximately ten wavelengths. For short crest lengths the statistics of freak waves deviates little from Gaussian and their occurrence is independent of group length (or Benjamin–Feir index, BFI). For long crest lengths the statistics of freak waves is strongly non-Gaussian and the group length (or BFI) is a good indicator of increased freak wave activity.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 582 , 10 July 2007 , pp. 463 - 472
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Alber, I. E. 1978 The effects of randomness on the stability of two-dimensional surface wavetrains. Proc. R. Soc. Lond. A 363, 525–546.Google Scholar
Benjamin, T. B. 1967 Instability of periodic wavetrains in nonlinear dispersive systems. Proc. R. Soc. Lond. A 299, 59–75.Google Scholar
Clamond, D. & Grue, J. 2002 Interaction beween envelope solitons as a model for freak wave formations. Part i: Long time interaction. C. R. Méc. 330, 575–580.CrossRefGoogle Scholar
Crawford, D. R., Saffman, P. G. & Yuen, H. C. 1980 Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion 2, 1–16.CrossRefGoogle Scholar
Dysthe, K. B. 1979 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105–114.Google Scholar
Dysthe, K. B. & Trulsen, K. 1999 Note on breather type solutions of the NLS as models for freak-waves. Physica Scripta T82, 48–52.CrossRefGoogle Scholar
Janssen, P. A. E. M. 2003 Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863–884.2.0.CO;2>CrossRefGoogle Scholar
Lo, E. & Mei, C. C. 1985 A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation. J. Fluid Mech. 150, 395–416.CrossRefGoogle Scholar
Lo, E. Y. & Mei, C. C. 1987 Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study. Wave Motion 9, 245–259.CrossRefGoogle Scholar
McLean, J. W., Ma, Y. C., Martin, D. U., Saffman, P. G. & Yuen, H. C. 1981 Three-dimensional instability of finite-amplitude water waves. Phys. Rev. Lett. 46, 817–820.CrossRefGoogle Scholar
Mori, N. & Janssen, P. A. E. M. 2006 On kurtosis and occurrence probability of freak waves. J. Phys. Oceanogr. 36, 1471–1483.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R. & Serio, M. 2002 Extreme wave events in directional, random oceanic sea states. Phys. Fluids 14, L25–L28.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R. & Serio, M. 2005 a Modulational instability and non-Gaussian statistics in experimental random water-wave trains. Phys. Fluids 17, 1–4.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R. & Serio, M. 2005 b On deviations from Gaussian statistics for surface gravity waves. In ‘Aha Huliko'a Rogue Waves 2005, pp. 79–83.Google Scholar
Onorato, M., Osborne, A. R. & Serio, M. 2006 Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves. Phys. Rev. Lett. 96, 1–4.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. 2001 Freak waves in random oceanic sea states. Phys. Rev. Lett. 86, 5831–5834.CrossRefGoogle ScholarPubMed
Onorato, M., Osborne, A. R., Serio, M., Cavaleri, L., Brandini, C. & Stansberg, C. T. 2004 Observation of strongly non-Gaussian statistics for random sea surface gravity waves in wave flume experiments. Phys. Rev. E 70, 1–4.Google ScholarPubMed
Osborne, A. R., Onorato, M. & Serio, M. 2000 The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains. Phys. Lett. A 275, 386–393.CrossRefGoogle Scholar
Socquet-Juglard, H., Dysthe, K., Trulsen, K., Krogstad, H. E. & Liu, J. 2005 Probability distributions of surface gravity waves during spectral changes. J. Fluid Mech. 542, 195–216.CrossRefGoogle Scholar
Stansberg, C. T. 1994 Effects from directionality and spectral bandwidth on non-linear spatial modulations of deep-water surface gravity wave trains. In Proc. 24th Intl Conf. on Coastal Engineering, Kobe, Japan, October 23–28, 1994, pp. 579–593. ASCE.Google Scholar
Tayfun, M. A. 1980 Narrow-band nonlinear sea waves. J. Geophys. Res. 85, 1548–1552.CrossRefGoogle Scholar
Trulsen, K. & Dysthe, K. B. 1996 A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281–289.CrossRefGoogle Scholar
Waseda, T 2006 Impact of directionality on the extreme wave occurrence in a discrete random wave system. In 9th Intl Workshop on Wave Hindcasting and Forecasting, Victoria, B.C., Canada, September 24–29, 2006.Google Scholar
Young, I. R. 2006 Directional spectra of hurricane wind waves. J. Geophys. Res. 111 (C08020).Google Scholar