Universal Velocity Profile for Coherent Vortices in Two-Dimensional Turbulence

Two-dimensional turbulence generated in a finite box produces large-scale coherent vortices coexisting with small-scale fluctuations. We present a rigorous theory explaining the $\eta =1\mathrm{/}4$ scaling in the $V\propto r^{-\eta }$ law of the velocity spatial profile within a vortex, where $r$ is the distance from the vortex center. This scaling, consistent with earlier numerical and laboratory measurements, is universal in its independence of details of the small-scale injection of turbulent fluctuations and details of the shape of the box.