Skip to main content
    • Aa
    • Aa
  • Get access
    Check if you have access via personal or institutional login
  • Cited by 18
  • Cited by
    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Li, Jinxuan Yang, Jiqing Liu, Shuxue and Ji, Xinran 2015. Wave groupiness analysis of the process of 2D freak wave generation in random wave trains. Ocean Engineering, Vol. 104, p. 480.

    Shermeneva, M. A. Shugan, I. V. and Hwung, H. -H. 2015. Effect of internal waves on the sea surface in two-dimensional case. Physics of Wave Phenomena, Vol. 23, Issue. 1, p. 68.

    Wang, Lei Li, Jinxuan and Li, Shuxue 2015. Numerical Simulation of Freak Wave Generation in Irregular Wave Train. Journal of Applied Mathematics and Physics, Vol. 03, Issue. 08, p. 1044.

    Adcock, Thomas A A and Taylor, Paul H 2014. The physics of anomalous (‘rogue’) ocean waves. Reports on Progress in Physics, Vol. 77, Issue. 10, p. 105901.

    Eliasson, B. and Haas, F. 2014. Trapping and instability of directional gravity waves in localized water currents. Physical Review E, Vol. 89, Issue. 6,

    Shrira, V. I. and Slunyaev, A. V. 2014. Nonlinear dynamics of trapped waves on jet currents and rogue waves. Physical Review E, Vol. 89, Issue. 4,

    Gramstad, O. Zeng, H. Trulsen, K. and Pedersen, G. K. 2013. Freak waves in weakly nonlinear unidirectional wave trains over a sloping bottom in shallow water. Physics of Fluids, Vol. 25, Issue. 12, p. 122103.

    Kundu, Sumana Debsarma, S. and Das, K. P. 2013. Modulational instability in crossing sea states over finite depth water. Physics of Fluids, Vol. 25, Issue. 6, p. 066605.

    Li, Jin-xuan Li, Peng-fei and Liu, Shu-xue 2013. Observations of freak waves in random wave field in 2D experimental wave flume. China Ocean Engineering, Vol. 27, Issue. 5, p. 659.

    Lynge, Birgit Kjoss Hjelmervik, Karina and Gjevik, Bjørn 2013. Storm surge and tidal interaction in the Tjeldsund channel, northern Norway. Ocean Dynamics, Vol. 63, Issue. 7, p. 723.

    Ma, Yuxiang Ma, Xiaozhou Perlin, Marc and Dong, Guohai 2013. Extreme waves generated by modulational instability on adverse currents. Physics of Fluids, Vol. 25, Issue. 11, p. 114109.

    Onorato, M. Residori, S. Bortolozzo, U. Montina, A. and Arecchi, F.T. 2013. Rogue waves and their generating mechanisms in different physical contexts. Physics Reports, Vol. 528, Issue. 2, p. 47.

    Ruban, V. P. 2013. On the modulation instability of surface waves on a large-scale shear flow. JETP Letters, Vol. 97, Issue. 4, p. 188.

    Toffoli, A. Waseda, T. Houtani, H. Kinoshita, T. Collins, K. Proment, D. and Onorato, M. 2013. Excitation of rogue waves in a variable medium: An experimental study on the interaction of water waves and currents. Physical Review E, Vol. 87, Issue. 5,

    Ruban, V. P. 2012. On the nonlinear Schrödinger equation for waves on a nonuniform current. JETP Letters, Vol. 95, Issue. 9, p. 486.

    Trulsen, K. Zeng, H. and Gramstad, O. 2012. Laboratory evidence of freak waves provoked by non-uniform bathymetry. Physics of Fluids, Vol. 24, Issue. 9, p. 097101.

    Adcock, T. A. A. Taylor, P. H. Yan, S. Ma, Q. W. and Janssen, P. A. E. M. 2011. Did the Draupner wave occur in a crossing sea?. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 467, Issue. 2134, p. 3004.

    Onorato, Miguel Proment, Davide and Toffoli, Alessandro 2011. Triggering Rogue Waves in Opposing Currents. Physical Review Letters, Vol. 107, Issue. 18,

  • Journal of Fluid Mechanics, Volume 637
  • October 2009, pp. 267-284

Freak wave statistics on collinear currents

  • DOI:
  • Published online: 17 September 2009

Linear refraction of waves on inhomogeneous current is known to provoke extreme waves. We investigate the effect of nonlinearity on this phenomenon, with respect to the variation of significant wave height, kurtosis and occurrence of freak waves. Monte Carlo simulations are performed employing a modified nonlinear Schrödinger equation that includes the effects of a prescribed non-potential current. We recommend that freak waves should be defined by a local criterion according to the wave distribution at each location of constant current, not by a global criterion that is either averaged over, or insensitive to, inhomogeneities of the current. Nonlinearity can reduce the modulation of significant wave height. Depending on the configuration of current and waves, the kurtosis and probability of freak waves can either grow or decrease when the wave height increases due to linear refraction. At the centre of an opposing current jet where waves are known to become large, we find that freak waves should be more rare than in the open ocean away from currents. The largest amount of freak waves on an opposing current jet is found at the jet sides where the significant wave height is small.

Corresponding author
Email address for correspondence:
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.

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

K. B. Dysthe , H. E. Krogstad & P. Müller 2008 Oceanic rogue waves. Annu. Rev. Fluid Mech. 40, 287310.

F. I. González 1984 A case study of wave–current-bathymetry interactions at the Columbia river entrance. J. Phys. Oceanogr. 14, 10651078.

C. Kharif & E. Pelinovsky 2003 Physical mechanisms of the rogue wave phenomenon. Eur. J. Mech. B/Fluids 22, 603634.

I. V. Lavrenov 1998 The wave energy concentration at the Agulhas current off South Africa. Nat. Hazards 17, 117127.

I. V. Lavrenov & A. V. Porubov 2006 Three reasons for freak wave generation in the non-uniform current. Eur. J. Mech. B/Fluids 25, 574585.

R. D. MacIver , R. R. Simons & G. P. Thomas 2006 Gravity waves interacting with narrow jet-like current. J. Geophys. Res. 111, C03009.

J. H. MacMahan , E. B. Thornton & A. J. H. M. Reniers 2006 Rip current review. Coast. Engng 53, 191208.

N. Mori , P. C. Liu & T. Yasuda 2002 Analysis of freak wave measurements in the sea of Japan. Ocean Engng 29, 13991414.

G. M. Muslu & H. A. Erbay 2004 Higher-order split-step Fourier schemes for the generalized nonlinear Schrödinger equation. Math. Comput. Simul. 67, 581595.

M. Onorato , A. R. Osborne , M. Serio , D. Resio , A. Pushkarev , V. E. Zakharov & C. Brandini Freely decaying weak turbulence for sea surface gravity waves. Phys. Rev. Lett. 89, 144501.

D. H. Peregrine 1976 Interaction of water waves and currents. Adv. Appl. Mech. 16, 9117.

D. H. Peregrine & R. Smith 1979 Nonlinear effects upon waves near caustics. Phil. Trans. R. Soc. Lond. A 292, 341370.

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.

C. H. Wu & A. Yao 2004 Laboratory measurements of limiting freak waves on currents. J. Geophys. Res. 109, C12002.

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? *