Derivation of dissipative Boussinesq equations using the Dirichlet-to-Neumann operator approachReport as inadecuate




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* Corresponding author 1 LAMA - Laboratoire de Mathématiques 2 School of Mathematical Sciences 3 LAMFA - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée

Abstract : The water wave theory traditionally assumes the fluid to be perfect, thus neglecting all effects of the viscosity. However, the explanation of several experimental data sets requires the explicit inclusion of dissipative effects. In order to meet these practical problems, the theory of visco-potential flows has been developed see P.-F. Liu & A. Orfila 2004 and D. Dutykh & F. Dias 2007. Then, usually this formulation is further simplified by developing the potential in an entire series in the vertical coordinate and by introducing thus, the long wave approximation. In the present study we propose a derivation of dissipative Boussinesq equations which is based on asymptotic expansions of the Dirichlet-to-Neumann D2N operator. Both employed methods yield the same system by different ways.

Keywords : Boussinesq equations viscosity dissipation dispersive waves boundary layer





Author: Denys Dutykh - Olivier Goubet -

Source: https://hal.archives-ouvertes.fr/



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