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Influence de la topographie sur les ondes de surface

Abstract : This work deals with the water waves problem for uneven bottoms in the long-wave framework. We aim here at constructing, justifying and comparing new asymptotic models taking into account the bottom topography. First, two new classes of symmetric Boussinesq-like models are rigorously derived for two different topographical regimes, one for small bathymetrical variations and one for strong variations. In a second part, we recover and discuss the classical Korteweg-de Vries approximation in the regime of small topographical variations. A new approximation is then proposed by adding correcting terms linked to the bathymetry. In the last part, all the previous models are integrated and compared numerically on two classical examples of bathymetry. Finally, we present a numerical study of the Green-Naghdi equations, whose range of validity is wider, and this model is compared numerically to the previous ones on specific bathymetries.
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Contributor : Florent Chazel Connect in order to contact the contributor
Submitted on : Friday, December 21, 2007 - 3:22:07 PM
Last modification on : Thursday, March 5, 2020 - 3:23:54 PM
Long-term archiving on: : Tuesday, September 21, 2010 - 3:46:02 PM


  • HAL Id : tel-00200419, version 2



Florent Chazel. Influence de la topographie sur les ondes de surface. Mathématiques [math]. Université Sciences et Technologies - Bordeaux I, 2007. Français. ⟨tel-00200419v2⟩



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