Comptes Rendus
Équations aux dérivées partielles, Analyse numérique
Some quasi-analytical solutions for propagative waves in free surface Euler equations
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1111-1118.

Solutions quasi-analytiques d’ondes propagatives dans les équations d’Euler à surface libre. Cette note décrit des solutions quasi-analytiques correspondant à la propagation d’ondes dans les équations d’Euler et d’Euler linéarisées à surface libre. Les solutions obtenues varient d’une forme sinusoïdale à une forme présentant des singularités. Elles permettent de valider numériquement les codes de simulation des équations d’Euler à surface libre.

This note describes some quasi-analytical solutions for wave propagation in free surface Euler equations and linearized Euler equations. The obtained solutions vary from a sinusoidal form to a form with singularities. They allow a numerical validation of the free-surface Euler codes.

Reçu le :
Accepté le :
Accepté après révision le :
Publié le :
DOI : 10.5802/crmath.63
Marie-Odile Bristeau 1 ; Bernard Di Martino 2 ; Anne Mangeney 1, 3 ; Jacques Sainte-Marie 1 ; Fabien Souille 1

1 ANGE project-team, Inria Paris, 2 rue Simone Iff, CS 42112, 75589 Paris Cedex 12, France; Sorbonne Université, Lab. Jacques-Louis Lions, 4 Place Jussieu, F-75252 Paris cedex 05
2 UMR CNRS 6134 SPE, Université de Corse, Campus Grimaldi, BP 52, 20250 Corte, France
3 Université de Paris, Institut de Physique du Globe de Paris, Seismology Group, 1 rue Jussieu, Paris F-75005, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2020__358_11-12_1111_0,
     author = {Marie-Odile Bristeau and Bernard Di Martino and Anne Mangeney and Jacques Sainte-Marie and Fabien Souille},
     title = {Some quasi-analytical solutions for propagative waves in free surface {Euler} equations},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1111--1118},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {11-12},
     year = {2020},
     doi = {10.5802/crmath.63},
     language = {en},
}
TY  - JOUR
AU  - Marie-Odile Bristeau
AU  - Bernard Di Martino
AU  - Anne Mangeney
AU  - Jacques Sainte-Marie
AU  - Fabien Souille
TI  - Some quasi-analytical solutions for propagative waves in free surface Euler equations
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 1111
EP  - 1118
VL  - 358
IS  - 11-12
PB  - Académie des sciences, Paris
DO  - 10.5802/crmath.63
LA  - en
ID  - CRMATH_2020__358_11-12_1111_0
ER  - 
%0 Journal Article
%A Marie-Odile Bristeau
%A Bernard Di Martino
%A Anne Mangeney
%A Jacques Sainte-Marie
%A Fabien Souille
%T Some quasi-analytical solutions for propagative waves in free surface Euler equations
%J Comptes Rendus. Mathématique
%D 2020
%P 1111-1118
%V 358
%N 11-12
%I Académie des sciences, Paris
%R 10.5802/crmath.63
%G en
%F CRMATH_2020__358_11-12_1111_0
Marie-Odile Bristeau; Bernard Di Martino; Anne Mangeney; Jacques Sainte-Marie; Fabien Souille. Some quasi-analytical solutions for propagative waves in free surface Euler equations. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1111-1118. doi : 10.5802/crmath.63. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.63/

[1] Charles J. Amick Bounds for water waves, Arch. Ration. Mech. Anal., Volume 99 (1987) no. 2, pp. 91-114 | DOI | MR | Zbl

[2] Anne-Cécile Boulanger; Marie-Odile Bristeau; Jacques Sainte-Marie Analytical solutions for the free surface hydrostatic Euler equations, Commun. Math. Sci., Volume 11 (2013) no. 4, pp. 993-1010 | DOI | MR | Zbl

[3] Adrian Constantin; Walter A. Strauss Exact steady periodic water waves with vorticity, Commun. Pure Appl. Math., Volume 57 (2004) no. 4, pp. 481-527 | DOI | MR | Zbl

[4] Robert Malcolm Corless; Gaston H. Gonnet; David E. G. Hare; David J. Jeffrey; Donald E. Knuth On the Lambert w function, Adv. Comput. Math., Volume 5 (1996) no. 4, pp. 329-359 | DOI | MR | Zbl

[5] Alex D. D. Craik The origins of water wave theory, Annual review of fluid mechanics (Annual Review of Fluid Mechanics), Volume 36, Annual Reviews, 2004, pp. 1-28 | DOI | MR | Zbl

[6] D. Daboussy; F. Dias; Jean-Marc Vanden-Broeck On explicite solutions of the free-surface Euler equations in the presence of gravity, Phys. Fluids, Volume 9 (1997) no. 10, pp. 2828-2834 | DOI | Zbl

[7] Marteen W. Dingemans Water wave propagation over uneven bottoms. Part 1: Linear wave propagation. Part 2: Non-linear wave propagation. (2 vol.). (Advanced Series on Ocean Engineering), Volume 13, World Scientific, 1997 (NASA Sti/Recon Technical Report N, pages 171-184, §2.8) | Zbl

[8] David D. Houghton; Akira Kasahara Nonlinear shallow fluid flow over an isolated ridge, Commun. Pure Appl. Math., Volume 21 (1968), pp. 1-23 | DOI | Zbl

[9] Konstantinos Kalimeris Analytical approximation and numerical simulations for periodic travelling water waves, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., Volume 376 (2017) no. 21111, 20170093, 19 pages | DOI | MR | Zbl

[10] David Lannes The water waves problem. Mathematical analysis and asymptotics., Mathematical Surveys and Monographs, 188, American Mathematical Society, 2013 | Zbl

[11] Michael Selwyn Longuet-Higgins A Theory of the Origin of Microseisms, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci., Volume 243 (1950) no. 857, pp. 1-35 | MR | Zbl

[12] James J. Stoker The formation of breakers and bores the theory of nonlinear wave propagation in shallow water and open channels, Commun. Pure Appl. Math., Volume 1 (1948), pp. 1-87 | MR | Zbl

[13] Walter A. Strauss; Miles H. Wheeler Bound on the Slope of Steady Water Waves with Favorable Vorticity, Arch. Ration. Mech. Anal., Volume 222 (2016) no. 3, pp. 1555-1580 | DOI | MR | Zbl

Cité par Sources :

Commentaires - Politique


Ces articles pourraient vous intéresser

A new model of Saint Venant and Savage–Hutter type for gravity driven shallow water flows

François Bouchut; Anne Mangeney-Castelnau; Benoı̂t Perthame; ...

C. R. Math (2003)