Derivation of a viscous Boussinesq system for surface water waves

Hervé Le Meur (1)

1 LM-Orsay - Laboratoire de Mathématiques d'Orsay

In this article, we derive a viscous Boussinesq system for surface water waves from Navier-Stokes equations. We use neither the irrotationality assumption, nor the Zakharov-Craig-Sulem formulation. During the derivation, we find the bottom shear stress, and also the decay rate for shallow water. In order to justify our derivation, we derive the viscous Korteweg-de Vries equation from our viscous Boussinesq system and compare it to the ones found in the bibliography. We also extend the system to the 3-D case.

Mots clés: water waves; shallow water; Boussinesq system; viscosity; KdV equation

Domaines: Equations aux dérivées partielles [math.AP]; Analyse numérique [math.NA]

Hervé Le Meur. Derivation of a viscous Boussinesq system for surface water waves. Asymptotic Analysis, 2015, 94 (3-4), pp.309-345. ⟨hal-00826564v2⟩