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Investigations of the Kaup-Boussinesq model equations for water waves

Juliussen, Bjørn-Sverre Hjelle
Master thesis
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URI
https://hdl.handle.net/1956/8335
Date
2014-06-02
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  • Department of Mathematics [1044]
Abstract
The Kaup-Boussinesq system is a coupled system of nonlinear partial differential equations which has been derived as a model for surface waves in the context of the Boussinesq scaling, and it has also been derived for an internal wave system. In this thesis, modeling properties of the Kaup-Boussinesq water-wave model are under investigation. Differential balance laws for mass, momentum and energy are considered, and we present an exact differential balance for momentum. A Kaup-Boussinesq system describing long internal waves is investigated and compared with the Gardner equation. Finally, a spectral method for the numerical discretization of the Kaup-Boussinesq system for surface waves is put forward, and shown to converge and be stable.
Publisher
The University of Bergen
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