Modeling the Coastal Ocean over a Time Period of Several Weeks

Pierre Ailliot (1, 2) , Emmanuel Frenod (1, 3, 4) , Valérie Monbet (1, 2)

1 LEMEL - Laboratoire d'Etude et Modélisation des Environnements littoraux
2 SABRES - Laboratoire de Statistique Appliquée de l'Université de Bretagne-Sud
3 CALVI - Scientific computation and visualization
4 LMAM - Laboratoire de Mathématiques et Applications des Mathématiques, EA 3885

From a scale analysis of hydrodynamic phenomena having a significant action on the drift of an object in coastal ocean waters, we deduce equations modeling the associated hydrodynamic fields over a time period of several weeks. These models are essentially non linear hyperbolic systems of PDE involving a small parameter. Then from the models we extract a simplified and nevertheless typical one for which we prove that its classical solution exists on a time interval which is independent of the small parameter. We then show that the solution weak-* converges as the small parameter goes to zero and we characterize the equation satisfied by the weak-* limit

Mots clés: Hyperbolic PDE; scale analysis; asymptotic analysis; coastal ocean modeling

Domaines: Modélisation et simulation; Equations aux dérivées partielles [math.AP]; Mécanique des fluides [physics.class-ph]; Mécanique des fluides [physics.class-ph]; Interfaces continentales, environnement; Milieux et Changements globaux

Pierre Ailliot, Emmanuel Frenod, Valérie Monbet. Modeling the Coastal Ocean over a Time Period of Several Weeks. Journal of Differential Equations, 2010, 246 (4), pp.639 - 659. ⟨10.1016/j.jde.2009.11.004⟩. ⟨hal-00202638⟩