  We analytically examine fluctuations of vorticity excited by an external
random force in two-dimensional fluid. We develop the perturbation theory
enabling one to calculate nonlinear corrections to correlation functions of the
flow fluctuations found in the linear approximation. We calculate the
correction to the pair correlation function and the triple correlation
function. It enables us to establish the criterion of validity of the
perturbation theory for different ratios of viscosity and bottom friction. We
find that the corrections to the second moment are anomalously weak in the
cases of small bottom friction and small viscosity and relate the weakness to
the energy and enstrophy balances. We demonstrate that at small bottom friction
the triple correlation function is characterized by universal scaling behavior
in some region of lengths. The developed perturbation method was verified and
confirmed by direct numerical simulations.
