Shallow water equations for large bathymetry variations

Denys Dutykh (1, 2, 3) , Didier Clamond (4)

1 LAMA - Laboratoire de Mathématiques
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques
3 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
4 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. Journal of Physics A: Mathematical and Theoretical, 2011, 44 (33), pp.332001. ⟨10.1088/1751-8113/44/33/332001⟩. ⟨hal-00580310v3⟩