EVOLUTION OF VORTEX STATISTICS IN 2-DIMENSIONAL TURBULENCE

Freely evolving two-dimensional turbulence is dominated by coherent vortices. The density of these vortices decays in time as rho approximately t-xi with xi almost-equal-to 0.75. A new scaling theory is proposed which expresses all statistical properties in terms of xi. Thus the average circulation of the vortices increases as t-xi/2 and their average radius as t-xi/4. The total energy is constant, the enstrophy decreases as t-xi/2, and the vorticity kurtosis increases as t-xi/2. These results are supported both by numerical simulations of the fluid equations and by solutions of a modified point-vortex model.