  We consider perturbations of the non-unitary minimal model solutions of
two-dimensional conformal turbulence proposed by Polyakov. Demanding the
absence of non-integrable singularities in the resulting theories leads to
constraints on the dimension of the perturbing operator. We give some general
solutions of these constraints, illustrating with examples of specific models.
We also examine the effect of such perturbations on the Hopf equation and
derive the interesting result that the latter is invariant under a certain
class of perturbations, to first order in perturbation theory, examples of
which are given in specific cases.
