A Non-Hydrostatic Non-Dispersive Shallow Water Model

Didier Clamond (1) , Denys Dutykh (2, 3, 4, 5)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 School of Mathematical Sciences [Dublin]
3 LAMA - Laboratoire de Mathématiques
4 USMB [Université de Savoie] [Université de Chambéry] - Université Savoie Mont Blanc
5 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques

An improvement of the nonlinear shallow water (or Saint-Venant) equations is proposed. The new model is designed to take into account the effects resulting from the large spatial 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: Modified Saint-Venant equations; Steep bottom; Varying bathymetry

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

Didier Clamond, Denys Dutykh. A Non-Hydrostatic Non-Dispersive Shallow Water Model. Ph. Gourbesville et al. Advances in Hydroinformatics, Springer Singapore, pp.189-196, 2013, Springer Hydrogeology 2014, 978-981-4451-42-0. ⟨10.1007/978-981-4451-42-0_16⟩. ⟨hal-00907110⟩