Two-dimensional turbulence in a finite box

Abstract: We present theory of two-dimensional turbulence excited by an external force in thin fluid films on scales larger than the film thickness. The principal feature of two-dimensional turbulence is the tendency of producing motions of larger and larger scales thanks to the nonlinear interaction. The tendency leads to formation of the so-called inverse cascade and, at some conditions, of big coherent vortices. We discuss the mean velocity profile of the coherent vortices and the flow fluctuations on the background of the mean velocity for different regimes. We demonstrate that the regime of strongly interacting fluctuations leads to an anisotropic scaling inside the coherent vortices.