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 $\eta =1/4$ 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.

Figure 1

(Color online) Average vorticity profile vs distance from the vortex center observed in simulations ((A), Fig. 2(C) from [10]) and experiment ((B), Fig. 3 from [9]). On both plots straight lines correspond to $\Omega \left(r\right)\sim r^{-5/4}$.