  We compute the solutions of Prandtl's and Navier-Stokes equations for the two
dimensional flow induced by a rectilinear vortex interacting with a boundary in
the half plane. For this initial datum Prandtl's equation develops, in a finite
time, a separation singularity. We investigate the different stages of unsteady
separation for Navier-Stokes solution at different Reynolds numbers
$Re=10^3-10^5$, and we show the presence of a large-scale interaction between
the viscous boundary layer and the inviscid outer flow. We also see a
subsequent stage, characterized by the presence of a small-scale interaction,
which is visible only for moderate-high Re numbers $Re=10^4-10^5$. We also
investigate the asymptotic validity of boundary layer theory by comparing
Prandtl's solution to Navier-Stokes solutions during the various stages of
unsteady separation.
