Coherent vortex in a spatially restricted two-dimensional turbulent flow in absence of bottom friction

We investigate the coherent vortex produced by two-dimensional turbulence excited in a finite box. We establish analytically the mean velocity profile of the vortex for the case where the bottom friction is negligible and express its characteristics via the parameters of pumping. Our theoretical predictions are verified and confirmed by direct numerical simulations in the framework of two-dimensional weakly compressible hydrodynamics with zero boundary conditions.