Comptes Rendus
Interaction between envelope solitons as a model for freak wave formations. Part I: Long time interaction
[Interaction de solitons enveloppes comme modèle pour la formation de « freak waves». Partie I : Interaction à long terme]
Comptes Rendus. Mécanique, Volume 330 (2002) no. 8, pp. 575-580.

We are concerned by a special mechanism that can explain the formation of freak waves. We study numerically the long time evolution of a surface gravity wave packet, comparing a fully nonlinear model with Schrödinger-like simplified equations. We observe that the interaction between envelope solitons generates large waves. This is predicted by both models. The fully nonlinear simulations show a qualitative behaviour that differs significantly from the ones preticted by Schrödinger models, however. Indeed, the occurence of freak waves is much more frequent with the fully nonlinear model. This is a consequence of the long-time interaction between envelope solitons, which, in the fully nonlinear model, is totally different from the Schrödinger scenario. The fundamental differences appear for times when the simplified equations cease to be valid. Possible statistical models, based on the latter, should hence under-estimate the probability of freak wave formation.

On s'interresse à un mécanisme particulier pouvant expliquer l'apparition de vagues de grandes amplitudes (freak waves). On étudie numériquement l'évolution à long terme de paquets d'onde de gravité surfaciques. On compare un modèle complètement non linéaire avec des équations simplifiées de type Schrödinger. On observe que l'interaction d'ondes solitaires enveloppes génèrent des vagues de grandes amplitudes. Cela est prédit par tous les modèles. Toutefois, le modèle complètement non linéaire exhibe un comportement à long terme très different des modèles simplifiés. L'apparition de freak waves y est beaucoup plus fréquente. C'est une conséquence de l'interaction à long terme de solitons enveloppes, qui est totalement différente de celle prédite par les scénario dérivés des équations de type Schrödinger. Les différences fondamentales apparaissent pour des temps supérieurs aux domaı̂nes de validité des équations simplifiées. D'envisageable modèles statistiques, basés sur ces dernières, devraient donc sous-estimer la probabilité d'apparition de freak waves.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-0721(02)01496-1
Keywords: waves, freak wave, soliton enveloppe, interaction
Mots-clés : ondes, freak wave, envelope soliton, interaction

Didier Clamond 1 ; John Grue 1

1 Department of Mathematics, University of Oslo, PO Box 1053, Blindern, 0316 Oslo, Norway
@article{CRMECA_2002__330_8_575_0,
     author = {Didier Clamond and John Grue},
     title = {Interaction between envelope solitons as a model for freak wave formations. {Part~I:} {Long} time interaction},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {575--580},
     publisher = {Elsevier},
     volume = {330},
     number = {8},
     year = {2002},
     doi = {10.1016/S1631-0721(02)01496-1},
     language = {en},
}
TY  - JOUR
AU  - Didier Clamond
AU  - John Grue
TI  - Interaction between envelope solitons as a model for freak wave formations. Part I: Long time interaction
JO  - Comptes Rendus. Mécanique
PY  - 2002
SP  - 575
EP  - 580
VL  - 330
IS  - 8
PB  - Elsevier
DO  - 10.1016/S1631-0721(02)01496-1
LA  - en
ID  - CRMECA_2002__330_8_575_0
ER  - 
%0 Journal Article
%A Didier Clamond
%A John Grue
%T Interaction between envelope solitons as a model for freak wave formations. Part I: Long time interaction
%J Comptes Rendus. Mécanique
%D 2002
%P 575-580
%V 330
%N 8
%I Elsevier
%R 10.1016/S1631-0721(02)01496-1
%G en
%F CRMECA_2002__330_8_575_0
Didier Clamond; John Grue. Interaction between envelope solitons as a model for freak wave formations. Part I: Long time interaction. Comptes Rendus. Mécanique, Volume 330 (2002) no. 8, pp. 575-580. doi : 10.1016/S1631-0721(02)01496-1. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/S1631-0721(02)01496-1/

[1] K.B. Dysthe Note on a modification to the nonlinear Schrödinger equation for application to deep water, Proc. Roy Soc. London A, Volume 369 (1979), pp. 105-114

[2] K. Trulsen; I. Kliakhadler; K.B. Dysthe; M.G. Velarde On weakly nonlinear modulation of waves on deep water, Phys. Fluids, Volume 12 (2000) no. 10, pp. 2432-2437

[3] A.R. Osborne; M. Onorato; M. Serio The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains, Phys. Lett. A, Volume 275 (2000), pp. 386-393

[4] C. Kharif; E. Pelinovsky; T. Talipova; A. Slunyaev Focusing of nonlinear wave groups in deep water, JETP Lett., Volume 73 (2001) no. 4, pp. 170-175

[5] M. Onorato; A.R. Osborne; M. Serio Extreme wave events in directional, random oceanic sea states, Phys. Fluids, Volume 14 (2002) no. 4, p. L25-L28

[6] D. Clamond; J. Grue A fast method for fully nonlinear water-wave computations, J. Fluid Mech., Volume 447 (2001), pp. 337-355

[7] M.L. Banner; X. Tian On the determination of the onset of breaking for modulating surface water waves, J. Fluid Mech., Volume 367 (1998), pp. 107-137

[8] J.D. Fenton The numerical solution of steady water wave problems, Computers & Geosciences, Volume 14 (1988) no. 3, pp. 357-368

[9] J. Satsuma; N. Yajima Initial value problems of one-dimensional self-modulation of nonlinear waves in dispersive media, Supp. Prog. Theor. Phys., Volume 55 (1974), pp. 284-306

[10] E. Lo; C.C. Mei A numerical study of water-wave modulation based on a higher-order nonlinear Schrödinger equation, J. Fluid Mech., Volume 150 (1985), pp. 395-416

[11] H.C. Yuen; B.M. Lake Nonlinear dynamics of deep-water gravity waves, Adv. Appl. Mech., Volume 22 (1982), pp. 67-229

  • Daïka Augustin; Mbané Biouélé César Gravity waves’ modulational instability under the effect of drag coefficient in the ocean, Physica Scripta, Volume 98 (2023) no. 12, p. 125014 | DOI:10.1088/1402-4896/ad05a9
  • Weida Xia; Yuxiang Ma; Guohai Dong; Jie Zhang; Xiaozhou Ma Emergence of Solitons from Irregular Waves in Deep Water, Journal of Marine Science and Engineering, Volume 9 (2021) no. 12, p. 1369 | DOI:10.3390/jmse9121369
  • Julien Touboul; Christian Kharif Focusing Wave Group Propagating in Finite Depth in the Presence of Surface Current and Vorticity, Nonlinear Waves and Pattern Dynamics (2018), p. 77 | DOI:10.1007/978-3-319-78193-8_4
  • Lei Wang; Jinxuan Li; Shuxue Li Numerical Simulation of Freak Wave Generation in Irregular Wave Train, Journal of Applied Mathematics and Physics, Volume 03 (2015) no. 08, p. 1044 | DOI:10.4236/jamp.2015.38129
  • Karsten Trulsen; José Carlos Nieto Borge; Odin Gramstad; Lotfi Aouf; Jean–Michel Lefèvre Crossing sea state and rogue wave probability during the Prestige accident, Journal of Geophysical Research: Oceans, Volume 120 (2015) no. 10, p. 7113 | DOI:10.1002/2015jc011161
  • A. Sergeeva; A. Slunyaev Rogue waves, rogue events and extreme wave kinematics in spatio-temporal fields of simulated sea states, Natural Hazards and Earth System Sciences, Volume 13 (2013) no. 7, p. 1759 | DOI:10.5194/nhess-13-1759-2013
  • Tarmo Soomere Solitons Interactions, Mathematics of Complexity and Dynamical Systems (2012), p. 1576 | DOI:10.1007/978-1-4614-1806-1_101
  • A. L. Latifah; E. van Groesen Coherence and predictability of extreme events in irregular waves, Nonlinear Processes in Geophysics, Volume 19 (2012) no. 2, p. 199 | DOI:10.5194/npg-19-199-2012
  • Hae-Jin Choi; Kwang-Hyo Jung; Sung-Bu Suh; Seung-Jae Lee; Hyo-Jae Jo; Han-Suk Choi Experimental Study in Kinematics of Rogue Wave, Journal of Ocean Engineering and Technology, Volume 25 (2011) no. 3, p. 11 | DOI:10.5574/ksoe.2011.25.3.011
  • L H Ying; Z Zhuang; E J Heller; L Kaplan Linear and nonlinear rogue wave statistics in the presence of random currents, Nonlinearity, Volume 24 (2011) no. 11, p. R67 | DOI:10.1088/0951-7715/24/11/r01
  • V. E. Zakharov; A. I. Dyachenko About shape of giant breather, European Journal of Mechanics. B. Fluids, Volume 29 (2010) no. 2, pp. 127-131 | DOI:10.1016/j.euromechflu.2009.10.003 | Zbl:1193.76029
  • Bárður A. Niclasen; Knud Simonsen; Anne Karin Magnusson Wave forecasts and small-vessel safety: A review of operational warning parameters, Marine Structures, Volume 23 (2010) no. 1, p. 1 | DOI:10.1016/j.marstruc.2010.02.001
  • Tarmo Soomere Solitons Interactions, Encyclopedia of Complexity and Systems Science (2009), p. 8479 | DOI:10.1007/978-0-387-30440-3_507
  • Christian Kharif; Efim Pelinovsky; Alexey Slunyaev Rogue Waves in Waters of Infinite and Finite Depths, Rogue Waves in the Ocean (2009), p. 91 | DOI:10.1007/978-3-540-88419-4_5
  • Tarmo Soomere Solitons Interactions, Solitons (2009), p. 257 | DOI:10.1007/978-1-0716-2457-9_507
  • Kristian Dysthe; Harald E. Krogstad; Peter Müller Oceanic Rogue Waves, Annual Review of Fluid Mechanics, Volume 40 (2008) no. 1, p. 287 | DOI:10.1146/annurev.fluid.40.111406.102203
  • V. E. Zakharov; A. I. Dyachenko; A. O. Prokofiev Freak Waves: Peculiarities of Numerical Simulations, Extreme Ocean Waves (2008), p. 1 | DOI:10.1007/978-1-4020-8314-3_1
  • A. I. Dyachenko; V. E. Zakharov On the formation of freak waves on the surface of deep water, JETP Letters, Volume 88 (2008) no. 5, p. 307 | DOI:10.1134/s0021364008170049
  • Tarmo Soomere Nonlinear Components of Ship Wake Waves, Applied Mechanics Reviews, Volume 60 (2007) no. 3, p. 120 | DOI:10.1115/1.2730847
  • Didier Clamond; Dorian Fructus; John Grue A note on time integrators in water-wave simulations, Journal of Engineering Mathematics, Volume 58 (2007) no. 1-4, pp. 149-156 | DOI:10.1007/s10665-006-9106-6 | Zbl:1117.76045
  • ODIN GRAMSTAD; KARSTEN TRULSEN Influence of crest and group length on the occurrence of freak waves, Journal of Fluid Mechanics, Volume 582 (2007), p. 463 | DOI:10.1017/s0022112007006507
  • Atle Jensen; Didier Clamond; Morten Huseby; John Grue On local and convective accelerations in steep wave events, Ocean Engineering, Volume 34 (2007) no. 3-4, p. 426 | DOI:10.1016/j.oceaneng.2006.03.013
  • Christian Kharif On the modelling of huge water waves called rogue waves, Tsunami and Nonlinear Waves (2007), p. 113 | DOI:10.1007/978-3-540-71256-5_6
  • John Grue; Atle Jensen Experimental velocities and accelerations in very steep wave events in deep water, European Journal of Mechanics. B. Fluids, Volume 25 (2006) no. 5, pp. 554-564 | DOI:10.1016/j.euromechflu.2006.03.006 | Zbl:1331.76031
  • J. Touboul; J. P. Giovanangeli; C. Kharif; E. Pelinovsky Freak waves under the action of wind: experiments and simulations, European Journal of Mechanics. B. Fluids, Volume 25 (2006) no. 5, pp. 662-676 | DOI:10.1016/j.euromechflu.2006.02.006 | Zbl:1103.76013
  • V. E. Zakharov; A. I. Dyachenko; A. O. Prokofiev Freak waves as nonlinear stage of Stokes wave modulation instability, European Journal of Mechanics. B. Fluids, Volume 25 (2006) no. 5, pp. 677-692 | DOI:10.1016/j.euromechflu.2006.03.004 | Zbl:1101.76016
  • Didier Clamond; Marc Francius; John Grue; Christian Kharif Long time interaction of envelope solitons and freak wave formations, European Journal of Mechanics. B. Fluids, Volume 25 (2006) no. 5, pp. 536-553 | DOI:10.1016/j.euromechflu.2006.02.007 | Zbl:1331.76027
  • Christian Kharif; Efim Pelinovsky Freak Waves Phenomenon: Physical Mechanisms and Modelling, Waves in Geophysical Fluids, Volume 489 (2006), p. 107 | DOI:10.1007/978-3-211-69356-8_3
  • John Grue Rapid computations of steep surface waves in three dimensions, and comparisons with experiments, Waves in Geophysical Fluids, Volume 489 (2006), p. 173 | DOI:10.1007/978-3-211-69356-8_4
  • A. Slunyaev; E. Pelinovsky; C. Guedes Soares Modeling freak waves from the North Sea, Applied Ocean Research, Volume 27 (2005) no. 1, p. 12 | DOI:10.1016/j.apor.2005.04.002
  • Christian Kharif; Efim Pelinovsky Physical mechanisms of the rogue wave phenomenon., European Journal of Mechanics. B. Fluids, Volume 22 (2003) no. 6, pp. 603-634 | DOI:10.1016/j.euromechflu.2003.09.002 | Zbl:1058.76017

Cité par 31 documents. Sources : Crossref, zbMATH

Commentaires - Politique