  Strong rotation makes an underlying turbulent flow quasi-two-dimensional that
leads to the upscale energy transfer. Recent numerical simulations show that
under certain conditions, the energy is accumulated at the largest scales of
the system, forming coherent vortex structures known as condensates. We
analytically describe the interaction of a strong condensate with weak
small-scale turbulent pulsations and obtain an equation that allows us to
determine the radial velocity profile $U(r)$ of a coherent vortex. When
external rotation is fast, the velocity profiles of cyclones and anticyclones
are identical to each other and are well described by the dependence $U(r)
\propto \pm r \ln (R/r)$, where $R$ is the transverse size of the vortex. As
the external rotation decreases, this symmetry disappears: the maximum velocity
in cyclones is greater and the position of the maximum is closer to the axis of
the vortex in comparison with anticyclones. Besides, our analysis shows that
the size $R$ of the anticyclone cannot exceed a certain critical value, which
depends on the Rossby and Reynolds numbers. The maximum size of the cyclones is
limited only by the system size under the same conditions. Our predictions are
based on the linear evolution of turbulent pulsations on the background of the
coherent vortex flow and are accompanied by estimates following from the
nonlinear Navier-Stokes equation.
