Skip to main content
    • Aa
    • Aa

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


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.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

I. E. Alber 1978 The effects of randomness on the stability of two-dimensional surface wavetrains. Proc. R. Soc. Lond. A 363, 525546.

T. B. Benjamin 1967 Instability of periodic wavetrains in nonlinear dispersive systems. Proc. R. Soc. Lond. A 299, 5975.

D. Clamond & J. Grue 2002 Interaction beween envelope solitons as a model for freak wave formations. Part i: Long time interaction. C. R. Méc. 330, 575580.

D. R. Crawford , P. G. Saffman & H. C. Yuen 1980 Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves. Wave Motion 2, 116.

K. B. Dysthe 1979 Note on a modification to the nonlinear Schrödinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105114.

K. B. Dysthe & K. Trulsen 1999 Note on breather type solutions of the NLS as models for freak-waves. Physica Scripta T82, 4852.

P. A. E. M. Janssen 2003 Nonlinear four-wave interactions and freak waves. J. Phys. Oceanogr. 33, 863884.

E. Lo & C. C. Mei 1985 A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation. J. Fluid Mech. 150, 395416.

E. Y. Lo & C. C. Mei 1987 Slow evolution of nonlinear deep water waves in two horizontal directions: A numerical study. Wave Motion 9, 245259.

J. W. McLean , Y. C. Ma , D. U. Martin , P. G. Saffman & H. C. Yuen 1981 Three-dimensional instability of finite-amplitude water waves. Phys. Rev. Lett. 46, 817820.

N. Mori & P. A. E. M. Janssen 2006 On kurtosis and occurrence probability of freak waves. J. Phys. Oceanogr. 36, 14711483.

M. Onorato , A. R. Osborne & M. Serio 2002 Extreme wave events in directional, random oceanic sea states. Phys. Fluids 14, L25L28.

M. Onorato , A. R. Osborne & M. Serio 2005 aModulational instability and non-Gaussian statistics in experimental random water-wave trains. Phys. Fluids 17, 14.

M. Onorato , A. R. Osborne & M. Serio 2006 Modulational instability in crossing sea states: A possible mechanism for the formation of freak waves. Phys. Rev. Lett. 96, 14.

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

A. R. Osborne , M. Onorato & M. Serio 2000 The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains. Phys. Lett. A 275, 386393.

H. Socquet-Juglard , K. Dysthe , K. Trulsen , H. E. Krogstad & J. Liu 2005 Probability distributions of surface gravity waves during spectral changes. J. Fluid Mech. 542, 195216.

M. A. Tayfun 1980 Narrow-band nonlinear sea waves. J. Geophys. Res. 85, 15481552.

K. Trulsen & K. B. Dysthe 1996 A modified nonlinear Schrödinger equation for broader bandwidth gravity waves on deep water. Wave Motion 24, 281289.

I. R. Young 2006 Directional spectra of hurricane wind waves. J. Geophys. Res. 111 (C08020).

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *


Full text views

Total number of HTML views: 0
Total number of PDF views: 25 *
Loading metrics...

Abstract views

Total abstract views: 102 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th May 2017. This data will be updated every 24 hours.