  We investigate various boundary conditions in two dimensional turbulence
systematically in the context of conformal field theory. Keeping the conformal
invariance, we can either change the shape of boundaries through finite
conformal transformations, or insert boundary operators so as to handle more
general cases. Effects of such operations will be reflected in physically
measurable quantities such as the energy power spectrum $E(k)$ or the average
velocity profiles. We propose that these effects can be used as a possible test
of conformal turbulence in an experimental setting. We also study the periodic
boundary conditions, i.e. turbulence on a torus geometry. The dependence of
moduli parameter $q$ appears explictly in the one point functions in the
theory, which can also be tested.
