  Fluid turbulence is a far-from-equilibrium phenomenon and remains one of the
most challenging problems in physics. Two-dimensional, fully developed
turbulence may possess the largest possible symmetry, the conformal symmetry.
We focus on the steady-state solution of two-dimensional bounded turbulent flow
and propose a $c=0$ boundary logarithmic conformal field theory for the inverse
energy cascade and another bulk conformal field theory in the classical limit
$c\rightarrow -\infty$ for the direct enstrophy cascade. We show that these
theories give rise to the Kraichnan-Batchelor scaling $k^{-3}$ and the
Kolmogorov-Kraichnan scaling $k^{-5/3}$ for the enstrophy and the energy
cascades, respectively, with the expected cascade directions, fluxes, and
fractal dimensions. We also made some new predictions for future numerical
simulations and experiments to test.
