  It is well known that an inverse turbulent cascade in a finite ($2 \pi \times
2 \pi$) two-dimensional periodic domain leads to the emergence of a
system-sized coherent vortex dipole. We report a numerical hyperviscous study
of the spatial vorticity profile inside one of the vortices. The exciting force
was shortly correlated in time, random in space, and had a correlation length
$l_f = 2\pi/k_f$ with $k_f$ ranging from $100$ to $12.5$. Previously, it was
found that in the asymptotic limit of small-scale forcing, the vorticity
exhibits the power-law behavior $\Omega(r) = (3 \epsilon/\alpha)^{1/2} r^{-1}$,
where $r$ is the distance to the vortex center, $\alpha$ is the bottom friction
coefficient, and $\epsilon$ is the inverse energy flux. Now we show that for a
spatially homogeneous forcing with finite $k_f$ the vorticity profile becomes
steeper, with the difference increasing with the pumping scale but decreasing
with the Reynolds number at the forcing scale. Qualitatively, this behaviour is
related to a decrease in the effective pumping of the coherent vortex with
distance from its center. To support this statement, we perform an additional
simulation with spatially localized forcing, in which the effective pumping of
the coherent vortex, on the contrary, increases with $r$ and show for the first
time that in this case the vorticity profile can be flatter than the asymptotic
limit.
