Large-amplitude internal solitary waves in a two-fluid model

Philippe Guyenne

doi:10.1016/j.crme.2006.05.001

Large-amplitude internal solitary waves in a two-fluid model
[Ondes solitaires internes de grande amplitude dans un modèle à deux fluides]

Présenté par : Gérard Iooss

Philippe Guyenne ¹

¹ Department of Mathematical Sciences, 501 Ewing Hall, University of Delaware, Newark, DE 19716-2553, USA

Comptes Rendus. Mécanique, Volume 334 (2006) no. 6, pp. 341-346.

Résumé
Abstract

Nous calculons numériquement des solutions en ondes solitaires d'un modèle hamiltonien décrivant les ondes internes longues de grande amplitude dans un milieu stratifié à deux couches. Ces solutions numériques sont calculées pour des valeurs de rapports de densité et de profondeur proches des conditions océaniques, et sont comparées avec les solutions de modèles faiblement et pleinement non-linéaires. Les résultats montrent que le modèle reproduit bien les caractéristiques des ondes solitaires fortement non-linéaires telles que le phénomène d'élargissement.

We compute solitary wave solutions of a Hamiltonian model for large-amplitude long internal waves in a two-layer stratification. Computations are performed for values of the density and depth ratios close to oceanic conditions, and comparisons are made with solutions of both weakly and fully nonlinear models. It is shown that characteristic features of highly nonlinear solitary waves such as broadening are reproduced well by the present model.

Reçu le : 2006-04-10
Accepté le : 2006-04-25
Publié le : 2006-06-01

DOI : 10.1016/j.crme.2006.05.001

Keywords: Fluid mechanics, Internal waves, Solitary waves, Hamiltonian systems
Mot clés : Mécanique des fluides, Ondes internes, Ondes solitaires, Systèmes hamiltoniens

Affiliations des auteurs :

Philippe Guyenne ¹

¹ Department of Mathematical Sciences, 501 Ewing Hall, University of Delaware, Newark, DE 19716-2553, USA

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     title = {Large-amplitude internal solitary waves in a two-fluid model},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {341--346},
     publisher = {Elsevier},
     volume = {334},
     number = {6},
     year = {2006},
     doi = {10.1016/j.crme.2006.05.001},
     language = {en},
}

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Philippe Guyenne. Large-amplitude internal solitary waves in a two-fluid model. Comptes Rendus. Mécanique, Volume 334 (2006) no. 6, pp. 341-346. doi : 10.1016/j.crme.2006.05.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2006.05.001/

Bibliographie
Cité par

[1] K.R. Helfrich; W.K. Melville Long nonlinear internal waves, Annu. Rev. Fluid Mech., Volume 38 (2006), pp. 395-425

[2] W.A.B. Evans; M.J. Ford An integral equation approach to internal (2-layer) solitary waves, Phys. Fluids, Volume 8 (1996), pp. 2032-2047

[3] O. Laget; F. Dias Numerical computation of capillary-gravity interfacial solitary waves, J. Fluid Mech., Volume 349 (1997), pp. 221-251

[4] H. Michallet; E. Barthélémy Experimental study of interfacial solitary waves, J. Fluid Mech., Volume 366 (1998), pp. 159-177

[5] J. Grue; A. Jensen; P.-O. Rusås; J.K. Sveen Properties of large-amplitude internal waves, J. Fluid Mech., Volume 380 (1999), pp. 257-278

[6] P.-O. Rusås; J. Grue Solitary waves and conjugate flows in a three-layer fluid, Eur. J. Mech. B/Fluids, Volume 21 (2002), pp. 185-206

[7] F. Dias; J.-M. Vanden-Broeck On internal fronts, J. Fluid Mech., Volume 479 (2003), pp. 145-154

[8] W. Choi; R. Camassa Fully nonlinear internal waves in a two-fluid system, J. Fluid Mech., Volume 396 (1999), pp. 1-36

[9] L.A. Ostrovsky; J. Grue Evolution equations for strongly nonlinear internal waves, Phys. Fluids, Volume 15 (2003), pp. 2934-2948

[10] R. Camassa; W. Choi; H. Michallet; P.-O. Rusås; J.K. Sveen On the realm of validity of strongly nonlinear asymptotic approximations for internal waves, J. Fluid Mech., Volume 549 (2006), pp. 1-23

[11] W. Craig; P. Guyenne; H. Kalisch A new model for large amplitude long internal waves, C. R. Mecanique, Volume 332 (2004), pp. 525-530

[12] W. Craig; P. Guyenne; H. Kalisch Hamiltonian long wave expansions for free surfaces and interfaces, Comm. Pure Appl. Math., Volume 58 (2005), pp. 1587-1641

[13] T.P. Stanton; L.A. Ostrovsky Observations of highly nonlinear internal solitons over the continental shelf, Geophys. Res. Lett., Volume 25 (1998), pp. 2696-2698

[14] R. Grimshaw; D. Pelinovsky; E. Pelinovsky; A. Slunyaev Generation of large-amplitude solitons in the extended Korteweg–de Vries equation, Chaos, Volume 12 (2002), pp. 1070-1076

[15] R. Grimshaw; D. Pullin Extreme interfacial waves, Phys. Fluids, Volume 29 (1986), pp. 2802-2807

[16] R.E.L. Turner; J.-M. Vanden-Broeck Broadening of interfacial solitary waves, Phys. Fluids, Volume 31 (1988), pp. 2486-2490

[17] K.G. Lamb; B. Wan Conjugate flows and flat solitary waves for a continuously stratified fluid, Phys. Fluids, Volume 10 (1998), pp. 2061-2079

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