On the Statistical Properties of Two-Dimensional Decaying Turbulence

By high-resolution numerical integration of two-dimensional Navier-Stokes equations we show that the turbulent flow at high Reynolds number is dominated by a simple and weakly unstable Hamiltonian system of pointlike vortices. The large instabilities, typical of the turbulent flow, are found uniquely outside vortices, in the wide dissipative region which results to be only a small perturbation of the vortex system. Moreover, the statistical distribution of vortex sizes determines the slope of the energy spectrum, which is steeper than that predicted by phenomenological theories.