Two-dimensional turbulence in the inverse cascade range

Numerical and physical experiments on forced two-dimensional Navier-Stokes equations show that transverse velocity differences are described by "nonna l" Kolmogorov scaling ((Delta nu)(2n))alpha r(2n/3) and obey Gaussian stati stics. Since nontrivial scaling is a sign of the strong nonlinearity of the problem, these two results seem to contradict each other. A theory explain ing these observations is presented in this paper. The derived self-consist ent expression for the pressure gradient contributions leads to the conclus ion that small-scale transverse velocity differences are governed by a Line ar Langevin-like equation, stirred by a nonlocal, universal, solution-depen dent Gaussian random force. This explains the experimentally observed Gauss ian statistics of transverse velocity differences and their Kolmogorov scal ing. The solution for the PDF of longitudinal velocity differences is based on the numerical smallness of the energy flux in two-dimensional turbulenc e. The theory makes a few quantitative predictions that can be tested exper imentally. [S1063-651X(99)13011-3].