A new approach to handle wave breaking in fully non-linear Boussinesq models.

Fabien Marche (1) , Florent Chazel (2) , Philippe Bonneton (3) , David Lannes (4) , Marion Tissier (3)

1 I3M - Institut de Mathématiques et de Modélisation de Montpellier
2 IMT - Institut de Mathématiques de Toulouse UMR5219
3 EPOC - Environnements et Paléoenvironnements OCéaniques
4 DMA - Département de Mathématiques et Applications - ENS Paris

In this paper, a new method to handle wave breaking in fully non-linear Boussinesq-type models is presented. The strategy developed to treat wave breaking is based on a reformulation of the set of governing equations (namely Serre Green-Naghdi equations) that allows us to split them into a hyperbolic part in the conservative form and a dispersive part. When a wave is ready to break, we switch locally from Serre Green-Naghdi equations to Non-linear Shallow Water equations by suppressing the dispersive terms in the vicinity of the wave front. Thus, the breaking wave front is handled as a shock by the Non-linear Shallow Water equations, and its energy dissipation is implicitly evaluated from the mathematical shock-wave theory. A simple methodology to characterize the wave fronts at each time step is first described, as well as appropriate criteria for the initiation and termination of breaking. Extensive validations using laboratory data are then presented, demonstrating the efficiency of our simple treatment for wave breaking.

Domaines: Analyse numérique [math.NA]; Océan, Atmosphère

Fabien Marche, Florent Chazel, Philippe Bonneton, David Lannes, Marion Tissier. A new approach to handle wave breaking in fully non-linear Boussinesq models.. Coastal Engineering, 2012, 67, pp.54--66. ⟨10.1016/j.coastaleng.2012.04.004⟩. ⟨hal-00798996⟩