  We present a search for conformal invariance in vorticity isolines of
two-dimensional compressible turbulence. The vorticity is measured by tracking
the motion of particles that float at the surface of a turbulent tank of water.
The three-dimensional turbulence in the tank has a Taylor microscale
$Re_\lambda \simeq 160$. The conformal invariance theory being tested here is
related to the behavior of equilibrium systems near a critical point. This
theory is associated with the work of L\"owner, Schramm and others and is
usually referred to as Schramm-L\"owner Evolution (SLE). The system was exposed
to several tests of SLE. The results of these tests suggest that zero-vorticity
isolines exhibit noticeable departures from this type of conformal invariance.
