  Exact solutions of conformal turbulence restricted on a upper half plane are
obtained. We show that the inertial range of homogeneous and isotropic
turbulence with constant enstrophy flux develops in a distant region from the
boundary. Thus in the presence of an anisotropic boundary, these exact
solutions of turbulence generalize Kolmogorov's solution consistently and
differ from the Polyakov's bulk case which requires a fine tunning of
coefficients. The simplest solution in our case is given by the minimal model
of $p=2, q=33$ and moreover we find a fixed point of solutions when $p,q$
become large.
