  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 $\eta=1/4$ 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.
