  Venus' atmosphere shows highly variable warm vortices over both of the
planet's poles. The nature of the mechanism behind their formation and
properties is still unknown. Potential vorticity is a conserved quantity when
advective processes dominate over friction and diabatic heating, and is a
quantity frequently used to model balanced flows. As a step toward
understanding the vortices' dynamics, we present maps of Ertel's potential
vorticity (EPV) at Venus' south polar region. We analyze three configurations
of the South Polar Vortex at the upper cloud level ($P\sim 240 mbar$; $z\sim 58
km$), based on our previous analyses of cloud motions and thermal structure
from data acquired by the VIRTIS instrument onboard Venus Express.
Additionally, we tentatively estimate EPV at the lower cloud level ($P\sim 2200
mbar$; $z\sim 43 km$), based on our previous wind measurements and on static
stability data from Pioneer Venus and the VIRA model. Values of EPV are on the
order of $10^{-6}$ and $10^{-8} K m^2 kg^{-1} s^{-1}$ at the upper and lower
cloud levels, respectively, being 3 times larger than the estimated errors. The
morphology observed in EPV maps is mainly determined by the structures of the
vertical component of the relative vorticity. This is in contrast to the
vortex's morphology observed in 3.8 or 5 $\mu m$ images which are related to
the thermal structure of the atmosphere at the cloud top. Some of the EPV maps
point to a weak ringed structure in the upper cloud while a more homogenous EPV
field is found in the lower cloud.
