  In incompressible viscous flows in a confined domain, vortices are known to
form at the corners and in the vicinity of separation points. The existence of
a sequence of vortices (known as Moffatt vortices) at the corner with
diminishing size and rapidly decreasing intensity has been indicated by
physical experiments as well as mathematical asymptotics. In this work, we
establish the existence of Moffatt vortices for the flow in the famous
Lid-driven square cavity at moderate Reynolds numbers by using an efficient
Navier-Stokes solver on non-uniform space grids. We establish that Moffatt
vortices in succession follow fixed geometric ratios in size and intensities
for a particular Reynolds number. In order to eliminate the possibility of
spurious solutions, we confirm the physical presence of the small scales by
pressure gradient computation along the walls.
