  We consider the correlation functions of two-dimensional turbulence in the
presence and absence of a three-dimensional perturbation, by means of conformal
field theory. In the persence of three dimensional perturbation, we show that
in the strong coupling limit of a small scale random force, there is some
logarithmic factor in the correlation functions of velocity stream functions.
We show that the logarithmic conformal field theory $c_{8,1}$ describes the 2D-
turbulence both in the absence and the presence of the perturbation. We obtain
the following energy spectrum $E(k) \sim k^{-5.125 } \ln(k )$ for perturbed 2D
- turbulence and $E(k) \sim k^{-5 } \ln(k )$ for unperturbed turbulence. Recent
numerical simulation and experimental results confirm our prediction.
