Numerical study of a viscous breaking water wave and the limit of vanishing viscosity

Alan Riquier (1) , Emmanuel Dormy (2, 3)

1 DMA - Département de Mathématiques et Applications - ENS Paris
2 Analyse (DMA)
3 CNRS - Centre National de la Recherche Scientifique

We introduce a numerical strategy to study the evolution of two-dimensional water waves in the presence of a plunging jet. The free-surface Navier–Stokes solution is obtained with a finite, but small, viscosity. We observe the formation of a surface boundary layer where the vorticity is localised. We highlight convergence to the inviscid solution. The effects of dissipation on the development of a singularity at the tip of the wave is also investigated by characterising the vorticity boundary layer appearing near the interface.

Mots clés: Wave Breaking; Gravity Waves; Water Waves; Boundary Layer

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

Alan Riquier, Emmanuel Dormy. Numerical study of a viscous breaking water wave and the limit of vanishing viscosity. Journal of Fluid Mechanics, 2024, 984, pp.R5. ⟨10.1017/jfm.2024.208⟩. ⟨hal-04536467⟩