A new model for large amplitude long internal waves

Walter Craig; Philippe Guyenne; Henrik Kalisch

doi:10.1016/j.crme.2004.02.026

A new model for large amplitude long internal waves

Presented by: Yves Meyer

Walter Craig ¹; Philippe Guyenne ¹ ; Henrik Kalisch ²

¹ Department of Mathematics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
² Centre for Mathematical Sciences, Lund University, Lund 221 00, Sweden

Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 525-530.

Abstract
Résumé

We derive a new model for the description of large amplitude internal waves in a two-fluid system. The displacement of the interface between the two fluids is assumed to be of small slope, but no smallness assumption is made on the wave amplitude. The derivation of the model is based on the perturbation theory for Hamiltonian systems. In the case of a single fluid layer, the model reduces to the classical shallow water regime for surface water waves.

Nous établissons un nouveau modèle pour la description des ondes internes de grande amplitude dans un système à deux fluides. On suppose que le déplacement de l'interface entre les deux fluides est de faible pente, mais on ne fait aucune hypothèse de faible amplitude pour les ondes. L'écriture du modèle est basée sur la théorie des perturbations pour les systèmes hamiltoniens. Dans le cas d'une seule couche de fluide, le modèle se réduit au régime classique en eau peu profonde pour les ondes de surface.

Received: 2003-12-02
Accepted: 2004-02-18
Published online: 2004-05-13

DOI: 10.1016/j.crme.2004.02.026

Keywords: Fluid mechanics, Internal waves, Hamiltonian systems, Dirichlet–Neumann operators
Mots-clés : Mécanique des fluides, Ondes internes, Systèmes hamiltoniens, Opérateurs Dirichlet–Neumann

Author's affiliations:

Walter Craig ¹; Philippe Guyenne ¹; Henrik Kalisch ²

¹ Department of Mathematics, McMaster University, 1280 Main Street West, Hamilton, Ontario L8S 4K1, Canada
² Centre for Mathematical Sciences, Lund University, Lund 221 00, Sweden

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     author = {Walter Craig and Philippe Guyenne and Henrik Kalisch},
     title = {A new model for large amplitude long internal waves},
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     number = {7},
     year = {2004},
     doi = {10.1016/j.crme.2004.02.026},
     language = {en},
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Walter Craig; Philippe Guyenne; Henrik Kalisch. A new model for large amplitude long internal waves. Comptes Rendus. Mécanique, Volume 332 (2004) no. 7, pp. 525-530. doi : 10.1016/j.crme.2004.02.026. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.02.026/

References
Cited by

[1] T.B. Benjamin; T.J. Bridges Reappraisal of the Kelvin–Helmholtz problem. I. Hamiltonian structure, J. Fluid Mech., Volume 333 (1997), pp. 301-325

[2] W. Craig; M.D. Groves Normal forms for wave motion in fluid interfaces, Wave Motion, Volume 31 (2000), pp. 21-41

[3] R. Coifman; Y. Meyer Nonlinear harmonic analysis and analytic dependence, Pseudodifferential Operators and Applications, Notre Dame, IN, 1984, American Mathematical Society, 1985, pp. 71-78

[4] W. Craig; C. Sulem Numerical simulation of gravity waves, J. Comput. Phys., Volume 108 (1993), pp. 73-83

[5] W. Choi; R. Camassa Fully nonlinear internal waves in a two-fluid system, J. Fluid Mech., Volume 386 (1999), pp. 1-36

[6] H. Lamb Hydrodynamics, Dover, New York, 1932 (p. 738)

[7] W. Craig; M.D. Groves Hamiltonian long-wave scaling limits of the water-wave problem, Wave Motion, Volume 19 (1994), pp. 367-389

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