Theory of two-dimensional turbulence

The two-dimensional Navier-Stokes equation and the drift approximation to the Vlasov equation are equivalent. An analytical theory of the turbulent state of this system is developed which contains no ad hoc assumptions. The theory is not strictly valid for the largest eddies and in the inertial range is restricted to large Reynolds numbers. A vorticity flow to large wavenumbers and an energy flow to small wavenumbers is predicted. In the inertial range the theory has a similarity solution whose spectrum agrees with that obtained from dimensional arguments. Diffusion coefficients are derived and the extension to shear turbulence and more general plasma turbulence is discussed.