  We perform the stability analysis for a free surface fluid current modeled as
two finite layers of constant vorticity, under the action of gravity and
absence of surface tension. In the same spirit as Taylor ["Effect of variation
in density on the stability of superposed streams of fluid," Proc. R. Soc. A
132, 499 (1931)], a geometrical approach to the problem is proposed, which
allows us to present simple analytical criteria under which the flow is stable.
A strong destabilizing effect of stratification in density is revealed by
comparison with the physical setting where the vorticity interface is also a
density interface separating two immiscible fluids with constant densities.
