Comptes Rendus
no. 11
Accurate simple approximation for the solitary wave
[Approximation simple et précise de l'onde solitaire]

Présenté par : Gérard Iooss

Didier Clamond1  ; Dorian Fructus1
1 Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway
Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 727-732.

On traite de l'effet d'une technique de renormalisation sur les approximations d'ordres supérieurs de type eau peu profonde pour les ondes de gravité. La méthode est illustrée pour l'onde solitaire. En renormalisant la solution d'une équation KdV généralisée, il est montré que la précision s'en trouve grandement augmentée.

This Note investigates the effect of a renormalization technique on high-order shallow water approximations of gravity waves. The method is illustrated for the solitary surface wave. Applied to the solution of a generalized KdV equation, it is shown that the renormalization significantly increases the accuracy.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crme.2003.09.001
Keywords: Waves, Shallow water, Solitary wave, Renormalization
Mot clés : Ondes, Eau peu profonde, Onde solitaire, Renormalisation
Didier Clamond 1 ; Dorian Fructus 1

1 Department of Mathematics, University of Oslo, P.O. Box 1053, Blindern, 0316 Oslo, Norway 
@article{CRMECA_2003__331_11_727_0,
     author = {Didier Clamond and Dorian Fructus},
     title = {Accurate simple approximation for the solitary wave},
     journal = {Comptes Rendus. M\'ecanique},
     pages = {727--732},
     publisher = {Elsevier},
     volume = {331},
     number = {11},
     year = {2003},
     doi = {10.1016/j.crme.2003.09.001},
     language = {en},
}
TY  - JOUR
AU  - Didier Clamond
AU  - Dorian Fructus
TI  - Accurate simple approximation for the solitary wave
JO  - Comptes Rendus. Mécanique
PY  - 2003
SP  - 727
EP  - 732
VL  - 331
IS  - 11
PB  - Elsevier
DO  - 10.1016/j.crme.2003.09.001
LA  - en
ID  - CRMECA_2003__331_11_727_0
ER  - 
%0 Journal Article
%A Didier Clamond
%A Dorian Fructus
%T Accurate simple approximation for the solitary wave
%J Comptes Rendus. Mécanique
%D 2003
%P 727-732
%V 331
%N 11
%I Elsevier
%R 10.1016/j.crme.2003.09.001
%G en
%F CRMECA_2003__331_11_727_0
Didier Clamond; Dorian Fructus. Accurate simple approximation for the solitary wave. Comptes Rendus. Mécanique, Volume 331 (2003) no. 11, pp. 727-732. doi : 10.1016/j.crme.2003.09.001. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2003.09.001/

[1] C.C. Mei The Applied Dynamics of Ocean Surface Waves, World Scientific, 1989

[2] D. Clamond Reconstruction of a long wave velocity field, C. R. Acad. Sci. Paris, Ser. IIb, Volume 326 (1998), pp. 91-94 (in French)

[3] D. Clamond Steady finite amplitude waves on a horizontal seabed of arbitrary depth, J. Fluid Mech., Volume 398 (1999), pp. 45-60

[4] D. Clamond Cnoidal type surface wave in deep water, J. Fluid Mech., Volume 489 (2003), pp. 101-120

[5] J.D. Fenton A ninth-order solution for the solitary wave, J. Fluid Mech., Volume 53 (1972) no. 2, pp. 257-271

[6] S.A. Pennell On a series expansion expansion for the solitary wave, J. Fluid Mech., Volume 179 (1987), pp. 557-561

[7] J.-P. Germain, Contribution à l'étude de la houle en eau peu profonde, Thèse d'état, Université de Grenoble, France, 1967 (in French)

[8] J. McCowan On the solitary wave, Phil. Mag. S. 5. 32, Volume 194 (1891), pp. 45-58

[9] D.J. Korteweg; G. de Vries On the change of form of long waves advancing in a rectangular canal and a new type of long stationary waves, Phil. Mag. S. 5., Volume 39 (1895), pp. 422-443

[10] J. Witting On the highest and other solitary waves, SIAM J. Appl. Math., Volume 28 (1975) no. 3, pp. 700-719

[11] R.F. Gwyther The classes of progressive long waves, Phil. Mag. S. 5. 50, Volume 303 (1900), pp. 213-216

[12] R.F. Gwyther An appendix to the paper on the classes of progressive long waves, Phil. Mag. S.5. 50, Volume 303 (1900), pp. 308-312

[13] Lord Rayleigh On waves, Phil. Mag. S. 5., Volume 14 (1876), pp. 257-279

[14] M. Tanaka The stability of solitary waves, Phys. Fluids, Volume 29 (1986) no. 3, pp. 650-655

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

SPH numerical computations of wave impact onto a vertical wall with experimental comparisons

Xuezhou Lu; Jean-Marc Cherfils; Grégory Pinon; ...

C. R. Méca (2021)

On some localized waves described by the extended KdV equation

Alexey V. Porubov; Gérard A. Maugin; Vitaly V. Gursky; ...

C. R. Méca (2005)