Dissipative Boussinesq equations

Denys Dutykh (1) , Frédéric Dias (1)

1 CMLA - Centre de Mathématiques et de Leurs Applications

The classical theory of water waves is based on the theory of inviscid flows. However it is important to include viscous effects in some applications. Two models are proposed to add dissipative effects in the context of the Boussinesq equations, which include the effects of weak dispersion and nonlinearity in a shallow water framework. The dissipative Boussinesq equations are then integrated numerically.

Mots clés: Boussinesq equations

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Dynamique des Fluides [physics.flu-dyn]; Physique Numérique [physics.comp-ph]; Physique Atmosphérique et Océanique [physics.ao-ph]; Equations aux dérivées partielles [math.AP]; Systèmes Solubles et Intégrables [nlin.SI]

Denys Dutykh, Frédéric Dias. Dissipative Boussinesq equations. 2007. ⟨hal-00137633v2⟩