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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 ,
T. Waseda ,
H. Houtani ,
L. Cavaleri ,
D. Greaves  and
M. Onorato
A. Toffoli*
Affiliation:
Centre for Ocean Engineering Science and Technology, Swinburne University of Technology, P.O. Box 218, Hawthorn, 3122 Vic., Australia
T. Waseda
Affiliation:
Graduate School of Frontier Sciences, University of Tokyo, Kashiwa, Chiba 277-8563, Japan
H. Houtani
Affiliation:
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
Affiliation:
Institute of Marine Sciences, Arsenale, Castello 2737/F, 30122 Venice, Italy
D. Greaves
Affiliation:
School of Marine Science and Engineering, Plymouth University, Plymouth PL4 8AA, UK
M. Onorato
Affiliation:
Department of Physics, University of Turin, Via Pietro Giuria 1, 10125 Turin, Italy INFN, Sezione di Torino, Via Pietro Giuria 1, 10125 Turin, Italy
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Geophysical and Geological Flows: Ocean processes Waves/Free-surface Flows: Surface gravity waves
Type
Papers
Information
Journal of Fluid Mechanics , Volume 769 , 25 April 2015 , pp. 277 - 297
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Copyright
© 2015 Cambridge University Press 

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References

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), 2137–2145.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), 809–818.Google Scholar
Babanin, A., Chalikov, D., Young, I. & Savelyev, I. 2007 Predicting the breaking onset of surface water waves. Geophys. Res. Lett. 34, L07605.Google 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.Google Scholar
Chabchoub, A., Hoffmann, N. P. & Akhmediev, N. 2011 Rogue wave observation in a water wave tank. Phys. Rev. Lett. 106 (20), 204502.Google Scholar
Chawla, A.2000 An experimental study on the dynamics of wave blocking and breaking on opposing currents. PhD thesis, University of Delaware (USA).CrossRefGoogle Scholar
Chawla, A. & Kirby, J. T. 2002 Monochromatic and random wave breaking at blocking points. J. Geophys. Res. 107 (C7), 4-1–4-19.Google Scholar
Dias, F. & Kharif, C. 1999 Nonlinear gravity and capillary–gravity waves. Annu. Rev. Fluid Mech. 31 (1), 301–346.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, 48–52.Google 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, 1–10.Google 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, 311–332.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, 267–284.Google Scholar
Janssen, P. A. E. M. 2003 Nonlinear four-wave interaction and freak waves. J. Phys. Oceanogr. 33 (4), 863–884.2.0.CO;2>CrossRefGoogle Scholar
Johnson, R. S. 1997 A Modern Introduction to the Mathematical Theory of Water Waves. Cambridge University Press.Google 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.Google 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), 16201–16214.Google Scholar
Lavrenov, I. 1998 The wave energy concentration at the Agulhas Current of South Africa. Nat. Hazards 17, 117–127.Google Scholar
Lavrenov, I. & Porubov, A. V. 2006 Three reasons for freak wave generation in the non-uniform current. Eur. J. Mech. (B/Fluids) 25, 574–585.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), 529–549.Google 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, 108–129.Google Scholar
Ma, Y., Ma, X., Perlin, M. & Dong, G. 2013 Extreme waves generated by modulational instability on adverse currents. Phys. Fluids 25 (11), 114109.Google Scholar
Moreira, R. M. & Peregrine, D. H. 2012 Nonlinear interactions between deep-water waves and currents. J. Fluid Mech. 691, 1–25.Google 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.Google Scholar
Ochi, M. K. 1998 Ocean Waves: The Stochastic Approach. Cambridge University Press.Google 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, 235–257.Google 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, 586–601.Google Scholar
Onorato, M., Osborne, A. R., Serio, M. & Bertone, S. 2001 Freak wave in random oceanic sea states. Phys. Rev. Lett. 86 (25), 5831–5834.Google 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 ScholarPubMed
Onorato, M., Proment, D. & Toffoli, A. 2011 Triggering rogue waves in opposing currents. Phys. Rev. Lett. 107, 184502.CrossRefGoogle ScholarPubMed
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.Google 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, 386–393.Google Scholar
Peregrine, D. H. 1976 Interaction of water waves and current. In Advances in Applied Mechanics, pp. 9–117.Google Scholar
Ruban, V. P. 2012 On the nonlinear Schrödinger equation for waves on a nonuniform current. JETP Lett. 95 (9), 486–491.Google 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), 11–22.Google 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), 417–431.Google 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, 195–216.Google Scholar
Stocker, J. D. & Peregrine, D. H. 1999 The current-modified nonlinear Schrödinger equation. J. Fluid Mech. 399, 335–353.Google 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.Google 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, 1–9.Google 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, 281–291.Google 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.Google Scholar
Tulin, M. P. & Waseda, T. 1999 Laboratory observation of wave group evolution, including breaking effects. J. Fluid Mech. 378, 197–232.Google Scholar
Waseda, T., Kinoshita, T. & Tamura, H. 2009 Evolution of a random directional wave and freak wave occurrence. J. Phys. Oceanogr. 39, 621–639.Google 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, 113–138.Google Scholar
Yuen, H. C. & Lake, B. M. 1982 Nonlinear dynamics of deep-water gravity waves. Adv. Appl. Mech. 22, 20–228.Google Scholar
Zakharov, V. E. & Ostrovsky, L. A. 2009 Modulation instability: the beginning. Physica D 238 (5), 540–548.CrossRefGoogle Scholar