  We introduce a numerical strategy to study the evolution of 2D 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.
