Two-dimensional turbulence

An inequality demonstrating the growth in the differential scale of isotropic two-dimensional turbulence is obtained. It is shown that the spectrum has a delta-form asymptotics, which is not realized physically owing to limitations imposed by the law of conservation of angular momentum. A consequence of this is either a breakdown of the isotropic structure of the turbulence ('phase transition') or a transition to stochastic motion not possessing correlation characteristics. The properties of inhomogeneous two-dimensional turbulence are briefly discussed.