Shallow water equations for large topographies

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 nonlinear shallow water or Saint-Venant equations. The improvement is achieved by including the fluid particles vertical acceleration effect due to the variable bathymetry. More precisely, our model is not hydrostatic at the bottom. This modification is particularly pertinent when the bottom undergoes strong variations in space and/or in time. The model is derived from the relaxed variational principle by choosing the appropriate shallow water ansatz and imposing some constraints. Our 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 topographies. 2011. ⟨hal-00580310v1⟩