Skip to main content Accessibility help
Hostname: page-component-78dcdb465f-nbrzn Total loading time: 0.492 Render date: 2021-04-16T12:26:50.561Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Rogue waves in opposing currents: an experimental study on deterministic and stochastic wave trains

Published online by Cambridge University Press:  16 March 2015

A. Toffoli
Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, 3122 Vic., Australia
T. Waseda
Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8563, Japan
H. Houtani
Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8563, Japan National Maritime Research Institute, Shinkawa, Mitaka-shi, Tokyo 181-0004, Japan
L. Cavaleri
Institute of Marine Sciences, Arsenale, Castello 2737/F, 30122 Venice, Italy
D. Greaves
School of Marine Science and Engineering, Plymouth University, Plymouth PL4 8AA, UK
M. Onorato
Department of Physics, University of Turin, Via Pietro Giuria 1, 10125 Turin, Italy INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Turin, Italy


Interaction with an opposing current amplifies wave modulation and accelerates nonlinear wave focusing in regular wavepackets. This results in large-amplitude waves, usually known as rogue waves, even if the wave conditions are less prone to extremes. Laboratory experiments in three independent facilities are presented here to assess the role of opposing currents in changing the statistical properties of unidirectional and directional mechanically generated random wavefields. The results demonstrate in a consistent and robust manner that opposing currents induce a sharp and rapid transition from weakly to strongly non-Gaussian properties. This is associated with a substantial increase in the probability of occurrence of rogue waves for unidirectional and directional sea states, for which the occurrence of extreme and rogue waves is normally the least expected.

© 2015 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below.


Akhmediev, N., Soto-Crespo, J. M. & Ankiewicz, A. 2009 Extreme waves that appear from nowhere: on the nature of rogue waves. Phys. Lett. A 373 (25), 21372145.CrossRefGoogle Scholar
Akhmediev, N. N., Eleonskii, V. M. & Kulagin, N. E. 1987 Exact first-order solutions of the nonlinear Schrödinger equation. Theor. Math. Phys. 72 (2), 809818.CrossRefGoogle Scholar
Babanin, A., Chalikov, D., Young, I. & Savelyev, I. 2007 Predicting the breaking onset of surface water waves. Geophys. Res. Lett. 34, L07605.CrossRefGoogle Scholar
Chabchoub, A., Hoffmann, N., Onorato, M., Slunyaev, A., Sergeeva, A., Pelinovsky, E. & Akhmediev, N. 2012 Observation of a hierarchy of up to fifth-order rogue waves in a water tank. Phys. Rev. E 86 (5), 056601.CrossRefGoogle Scholar
Chabchoub, A., Hoffmann, N. P. & Akhmediev, N. 2011 Rogue wave observation in a water wave tank. Phys. Rev. Lett. 106 (20), 204502.CrossRefGoogle Scholar
Chawla, A.2000 An experimental study on the dynamics of wave blocking and breaking on opposing currents. PhD thesis, University of Delaware (USA).Google Scholar
Chawla, A. & Kirby, J. T. 2002 Monochromatic and random wave breaking at blocking points. J. Geophys. Res. 107 (C7), 4-1–4-19.CrossRefGoogle Scholar
Dias, F. & Kharif, C. 1999 Nonlinear gravity and capillary–gravity waves. Annu. Rev. Fluid Mech. 31 (1), 301346.CrossRefGoogle Scholar
Dysthe, K. B. & Trulsen, K. 1999 Note on breather type solutions of the NLS as models for freak-waves. Phys. Scr. T 82, 4852.CrossRefGoogle Scholar
Dysthe, K. B., Trulsen, K., Krogstad, H. E. & Socquet-Juglard, H. 2003 Evolution of a narrow-band spectrum of random surface gravity waves. J. Fluid Mech. 478, 110.CrossRefGoogle Scholar
Gerber, M. 1987 The Benjamin–Feir instability of a deep water Stokes wavepacket in the presence of a non-uniform medium. J. Fluid Mech. 176, 311332.CrossRefGoogle Scholar
Hauser, D., Kahma, K. K., Krogstad, H. E., Lehner, S., Monbaliu, J. & Wyatt, L. W.(Eds) 2005 Measuring and Analysing the Directional Spectrum of Ocean Waves. Cost Office.Google Scholar
Hjelmervik, K. B. & Trulsen, K. 2009 Freak wave statistics on collinear currents. J. Fluid Mech. 637, 267284.CrossRefGoogle Scholar
Janssen, P. A. E. M. 2003 Nonlinear four-wave interaction and freak waves. J. Phys. Oceanogr. 33 (4), 863884.2.0.CO;2>CrossRefGoogle Scholar
Johnson, R. S. 1997 A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge University Press.CrossRefGoogle Scholar
Kharif, C., Pelinovsky, E. & Slunyaev, A. 2009 Rogue Waves in the Ocean. Springer.Google Scholar
Komen, G. J., Cavaleri, L., Donelan, M., Hasselmann, K., Hasselmann, H. & Janssen, P. A. E. M. 1994 Dynamics and Modeling of Ocean Waves. Cambridge University Press.CrossRefGoogle Scholar
Lai, R. J., Long, S. R. & Huang, N. 1989 Laboratory studies of wave–current interaction: kinematics of the strong interaction. J. Geophys. Res. 94 (C11), 1620116214.CrossRefGoogle Scholar
Lavrenov, I. 1998 The wave energy concentration at the Agulhas Current of South Africa. Nat. Hazards 17, 117127.CrossRefGoogle Scholar
Lavrenov, I. & Porubov, A. V. 2006 Three reasons for freak wave generation in the non-uniform current. Eur. J. Mech. (B/Fluids) 25, 574585.CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1961 The changes in amplitude of short gravity waves on steady non-uniform currents. J. Fluid Mech. 10 (4), 529549.CrossRefGoogle Scholar
Ma, Y., Dong, G., Perlin, M., Ma, X., Wang, G. & Xu, J. 2010 Laboratory observations of wave evolution, modulation and blocking due to spatially varying opposing currents. J. Fluid Mech. 661, 108129.CrossRefGoogle Scholar
Ma, Y., Ma, X., Perlin, M. & Dong, G. 2013 Extreme waves generated by modulational instability on adverse currents. Phys. Fluids 25 (11), 114109.CrossRefGoogle Scholar
Moreira, R. M. & Peregrine, D. H. 2012 Nonlinear interactions between deep-water waves and currents. J. Fluid Mech. 691, 125.CrossRefGoogle Scholar
Mori, N., Onorato, M., Janssen, P. A. E. M., Osborne, A. R. & Serio, M. 2007 On the extreme statistics of long-crested deep water waves: theory and experiments. J. Geophys. Res. 112, C09011.CrossRefGoogle Scholar
Ochi, M. K. 1998 Ocean Waves: The Stochastic Approach. Cambridge University Press.CrossRefGoogle Scholar
Onorato, M., Cavaleri, L., Fouques, S., Gramstad, O., Janssen, P. A. E. M., Monbaliu, J., Osborne, A. R., Pakozdi, C., Serio, M., Stansberg, C. T., Toffoli, A. & Trulsen, K. 2009a Statistical properties of mechanically generated surface gravity waves: a laboratory experiment in a 3D wave basin. J. Fluid Mech. 627, 235257.CrossRefGoogle Scholar
Onorato, M., Osborne, A., Serio, M., Cavaleri, L., Brandini, C. & Stansberg, C. T. 2006 Extreme waves, modulational instability and second order theory: wave flume experiments on irregular waves. Eur. J. Mech. (B/Fluids) 25, 586601.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. 2001 Freak wave in random oceanic sea states. Phys. Rev. Lett. 86 (25), 58315834.CrossRefGoogle Scholar
Onorato, M., Osborne, A. R., Serio, M., 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, 067302.CrossRefGoogle Scholar
Onorato, M., Proment, D. & Toffoli, A. 2011 Triggering rogue waves in opposing currents. Phys. Rev. Lett. 107, 184502.CrossRefGoogle Scholar
Onorato, M., Waseda, T., Toffoli, A., Cavaleri, L., Gramstad, O., Janssen, P. A. E. M., Kinoshita, T., Monbaliu, J., Mori, N., Osborne, A. R., Serio, M., Stansberg, C. T., Tamura, H. & Trulsen, K. 2009b Statistical properties of directional ocean waves: the role of the modulational instability in the formation of extreme events. Phys. Rev. Lett. 102, 114502.CrossRefGoogle Scholar
Osborne, A. R., Onorato, M. & Serio, M. 2000 The nonlinear dynamics of rogue waves and holes in deep-water gravity wave train. Phys. Lett. A 275, 386393.CrossRefGoogle Scholar
Peregrine, D. H. 1976 Interaction of water waves and current. In Advances in Applied Mechanics, pp. 9117.Google Scholar
Ruban, V. P. 2012 On the nonlinear Schrödinger equation for waves on a nonuniform current. JETP Lett. 95 (9), 486491.CrossRefGoogle Scholar
Shrira, V. I. & Geogjaev, V. V. 2010 What makes the Peregrine soliton so special as a prototype of freak waves? J. Engng Maths 67 (1), 1122.CrossRefGoogle Scholar
Shrira, V. I. & Slunyaev, A. V. 2014 Nonlinear dynamics of trapped waves on jet currents and rogue waves. Phys. Rev. E 89, 041002.CrossRefGoogle ScholarPubMed
Smith, R. 1976 Giant waves. J. Fluid Mech. 77 (3), 417431.CrossRefGoogle Scholar
Socquet-Juglard, H., Dysthe, K., Trulsen, K., Krogstad, H. E. & Liu, J. 2005 Distribution of surface gravity waves during spectral changes. J. Fluid Mech. 542, 195216.CrossRefGoogle Scholar
Stocker, J. D. & Peregrine, D. H. 1999 The current-modified nonlinear Schrödinger equation. J. Fluid Mech. 399, 335353.CrossRefGoogle Scholar
Suastika, I. K.2004 Wave blocking. PhD thesis, Technische Universiteit Delft, The Netherlands.Google Scholar
Thomas, R., Kharif, C. & Manna, M. 2012 A nonlinear Schrödinger equation for water waves on finite depth with constant vorticity. Phys. Fluids 24 (12), 127102.CrossRefGoogle Scholar
Toffoli, A., Cavaleri, L., Babanin, A. V., Benoit, M., Bitner-Gregersen, E. M., Monbaliu, J., Onorato, M., Osborne, A. R. & Stansberg, C. T. 2011 Occurrence of extreme waves in three-dimensional mechanically generated wavefields propagating over an oblique current. Nat. Hazards Earth Syst. Sci. 11, 19.CrossRefGoogle Scholar
Toffoli, A., Lefèvre, J. M., Bitner-Gregersen, E. & Monbaliu, J. 2005 Towards the identification of warning criteria: analysis of a ship accident database. Appl. Ocean Res. 27, 281291.CrossRefGoogle Scholar
Toffoli, A., Waseda, T., Houtani, H., Kinoshita, T., Collins, K., Proment, D. & Onorato, M. 2013 Excitation of rogue waves in a variable medium: an experimental study on the interaction of water waves and currents. Phys. Rev. E 87, 051201.CrossRefGoogle Scholar
Tulin, M. P. & Waseda, T. 1999 Laboratory observation of wave group evolution, including breaking effects. J. Fluid Mech. 378, 197232.CrossRefGoogle Scholar
Waseda, T., Kinoshita, T. & Tamura, H. 2009 Evolution of a random directional wave and freak wave occurrence. J. Phys. Oceanogr. 39, 621639.CrossRefGoogle Scholar
Waseda, T., Rheem, C. K., Sawamura, J., Yuhara, T., Kinoshita, T., Tanizawa, K. & Tomita, H.2005 Extreme wave generation in laboratory wave tank. In Proceedings of the 15th ISOPE, Seoul, Korea, June pp. 19–24.Google Scholar
White, B. S. & Fornberg, B. 1998 On the chance of freak waves at the sea. J. Fluid Mech. 255, 113138.CrossRefGoogle Scholar
Yuen, H. C. & Lake, B. M. 1982 Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech. 22, 20228.Google Scholar
Zakharov, V. E. & Ostrovsky, L. A. 2009 Modulation instability: the beginning. Physica D 238 (5), 540548.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 31
Total number of PDF views: 237 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 16th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the or variations. ‘’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Rogue waves in opposing currents: an experimental study on deterministic and stochastic wave trains
Available formats

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Rogue waves in opposing currents: an experimental study on deterministic and stochastic wave trains
Available formats

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Rogue waves in opposing currents: an experimental study on deterministic and stochastic wave trains
Available formats

Reply to: Submit a response

Your details

Conflicting interests

Do you have any conflicting interests? *