Recent advances in Serre-Green Naghdi modelling for wave transformation, breaking and runup processes

Philippe Bonneton (1) , Eric Barthélemy (2) , Florent Chazel (3) , Rodrigo Cienfuegos (4) , David Lannes (5) , Fabien Marche (6) , Marion Tissier (1)

1 EPOC - Environnements et Paléoenvironnements OCéaniques
2 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]
3 IMT - Institut de Mathématiques de Toulouse UMR5219
4 Departamento de Ingenierıa Hidraulica y Ambiental
5 DMA - Département de Mathématiques et Applications - ENS Paris
6 I3M - Institut de Mathématiques et de Modélisation de Montpellier

To describe the strongly nonlinear dynamics of waves propagating in the final stages of shoaling and in the surf and swash zones, fully nonlinear models are required. The ability of the Serre or Green Naghdi (S-GN) equations to reproduce this nonlinear processes is reviewed. Two high-order methods for solving S-GN equations, based on Finite Volume approaches, are presented. The first one is based on a quasi-conservative form of the S-GN equations, and the second on a hybrid Finite Volume/Finite Difference method. We show the ability of these two approaches to accurately simulate nonlinear shoaling, breaking and runup processes.

Domaines: Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]

Philippe Bonneton, Eric Barthélemy, Florent Chazel, Rodrigo Cienfuegos, David Lannes, et al.. Recent advances in Serre-Green Naghdi modelling for wave transformation, breaking and runup processes. European Journal of Mechanics - B/Fluids, 2011, pp.doi:10.1016/j.euromechflu.2011.02.005. ⟨10.1016/j.euromechflu.2011.02.005⟩. ⟨hal-00606543⟩