Shallow water equations for large bathymetry variations

Denys Dutykh (1) , Didier Clamond (2)

1 LAMA - Laboratoire de Mathématiques
2 JAD - Laboratoire Jean Alexandre Dieudonné

In this study, we propose an improved version of the nonlinear shallow water (or Saint-Venant) equations. This new model is designed to take into account the effects resulting from the large spacial and/or temporal variations of the seabed. The model is derived from a variational principle by choosing the appropriate shallow water ansatz and imposing suitable constraints. Thus, the derivation procedure does not explicitly involve any small parameter.

Mots clés: Shallow water; Saint-Venant equations; gravity waves; long waves

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

Denys Dutykh, Didier Clamond. Shallow water equations for large bathymetry variations. 2011. ⟨hal-00580310v2⟩