  A generalized theory of two-dimensional isotropic turbulence is developed
based on conformal symmetry. A number of minimal models of conformal turbulence
are solved under an extended constraint including both the enstrophy cascade by
Kraichnan and the discontinuity of vorticity by Saffman. There are an infinite
number of solutions which fall into two different categories. An explicit
relation is derived in one of the categories between the central charge of
Virasoro algebra, the lowest anomalous dimension and the power of the energy
spectrum. Some statistical properties such as energy spectrum, skewness,
flatness and Casimir invariants are predicted and compared with numerical
simulation by the pseudospectral method.
