Evolution of vortex statistics in two-dimensional turbulence

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