On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast

Vincent Duchêne (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

The rigid-lid approximation is a commonly used simplification in the study of density-stratified fluids in oceanography. One assumes that the displacements of the surface are negligible compared with internal displacements. We offer a rigorous justification of this approximation in the case of two shallow layers of immiscible fluid with constant and quasi-equal mass densities. More precisely, we control the difference between the solutions of the Cauchy problem predicted by the shallow-water (Saint-Venant) system in the rigid-lid and free-surface configuration. We also describe explicitly the first-order behavior of the deformation of the surface in the latter situation.

Mots clés: Internal waves; Rigid-lid approximation; Boussinesq approximation; Asymptotic analysis; Hyperbolic system

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Vincent Duchêne. On the rigid-lid approximation for two shallow layers of immiscible fluids with small density contrast. 2013. ⟨hal-00861093v1⟩