MELINAND, Benjamin

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MELINAND, Benjamin
Institut de Mathématiques de Bordeaux [IMB]

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Article de revue

Ce document a été publié dans

Nonlinearity. 2015-03, vol. 28, n° 11

IOP Publishing

Résumé en anglais

In this paper, we want to understand the Proudman resonance. It is a resonant respond in shallow waters of a water body on a traveling atmospheric disturbance when the speed of the disturbance is close to the typical water wave velocity. We show here that the same kind of resonance exists for landslide tsunamis and we propose a mathematical approach to investigate these phenomena based on the derivation, justification and analysis of relevant asymptotic models. This approach allows us to investigate more complex phenomena that are not dealt with in the physics literature such as the influence of a variable bottom or the generalization of the Proudman resonance in deeper waters. First, we prove a local well-posedness of the water waves equations with a moving bottom and a non constant pressure at the surface taking into account the dependence of small physical parameters and we show that these equations are a Hamiltonian system (which extend the result of Zakharov [33]). Then, we justify some linear asymptotic models in order to study the Proudman resonance and submarine landslide tsunamis; we study the linear water waves equations and dispersion estimates allow us to investigate the amplitude of the sea level. To complete these asymptotic models, we add some numerical simulations.< Réduire

Mots clés en anglais

quasilinear hyperbolic system

asymptotic models

water waves equations

URI

https://oskar-bordeaux.fr/handle/20.500.12278/194001

Project ANR

DYnamique des Fluides, Couches Limites, Tourbillons et Interfaces - ANR-13-BS01-0003

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Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251