Some quasi-analytical solutions for propagative waves in free surface Euler equations

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. Résumé. 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. Funding. The work presented in this paper was supported in part by the ANR Mimosa (ANR-14-CE01-0012) and ERC contract ERC-CG-2013-PE10-617472 SLIDEQUAKES.. Manuscript received 5th December 2019, revised 29th September 2020, accepted 26th April 2020. ∗Corresponding author. ISSN (electronic) : 1778-3569 https://comptes-rendus.academie-sciences.fr/mathematique/ 1112 Marie-Odile Bristeau, Bernard Di Martino, Ange Mangeney, Jacques Sainte-Marie and Fabien Souille

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