  Numerical and physical experiments on the forced two-dimensional
Navier-Stokes equations show that transverse velocity differences are described
by ``normal'' Kolmogorov scaling $<(\Delta v)^{2n}> \propto r^{2n/3}$ and obey
a gaussian statistics. Since the non-trivial scaling is a sign of a strong
non-linearity of the problem, these two results seem to contradict each other.
A theory, explaining this result is presented in this paper. Strong
time-dependence of the large-scale features of the flow ($\bar{u^2}\propto t$)
results in decoupling of the large-scale dynamics from statistically
steady-state small-scale random processes. This time-dependence is also a
reason for the localness of the pressure-gradient terms in the equations
governing the small-scale velocity difference PDF's. The derived
self-consistent expression for the pressure gradient contributions lead to the
conclusion that the small-scale transverse velocity differences are governed by
a linear Langevin-like equation, strirred by a non-local, universal,
solution-depending gaussian random force. This explains the experimentally
observed gaussian statistics of transverse velocity differences and their
Kolmogorov scaling. The solution for the PDF of longitudinal velocity
differences is based on a smallness of the energy flux in two-dimensional
turbulence. The theory makes a few quantitative predictions which can be tested
experimentally.
