Mathematical modelling of tsunami waves

Abstract : This thesis is devoted to tsunami wave modelling. The life of tsunami waves can be conditionally divided into three parts: generation, propagation and inundation (or run-up). In the first part of the manuscript we consider the generation process of such extreme waves. We examine various existing approaches to its modelling. Then we propose a few alternatives. The main conclusion is that the seismology/hydrodynamics coupling is poorly understood at the present time.

The second chapter essentially deals with Boussinesq equations which are often used to model tsunami propagation and sometimes even run-up. More precisely, we discuss the importance, nature and inclusion of dissipative effects in long wave models.

In the third chapter we slightly change the subject and turn to two-phase flows. The main purpose of this chapter is to propose an operational and simple set of equations in order to model wave impacts on coastal structures. Another important application includes wave sloshing in liquified natural gas carriers. Then, we discuss the numerical discretization of governing equations in the finite volume framework on unstructured meshes.

Finally, this thesis deals with a topic which should be present in any textbook on hydrodynamics but it is not. We mean visco-potential flows. We propose a novel and sufficiently simple approach for weakly viscous flow modelling. We succeeded in keeping the simplicity of the classical potential flow formulation with the addition of viscous effects. In the case of finite depth we derive a correction term due to the presence of the bottom boundary layer. This term is nonlocal in time. Hence, the bottom boundary layer introduces a memory effect to the governing equations.
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Contributor : Denys Dutykh <>
Submitted on : Monday, January 21, 2008 - 1:18:10 PM
Last modification on : Thursday, January 11, 2018 - 6:12:26 AM
Long-term archiving on : Tuesday, September 21, 2010 - 4:03:16 PM

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  • HAL Id : tel-00194763, version 2

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Denys Dutykh. Mathematical modelling of tsunami waves. Mathematics [math]. École normale supérieure de Cachan - ENS Cachan, 2007. English. ⟨tel-00194763v2⟩

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