  We show that some statistical properties of forced two-dimensional turbulence
have an important sensitivity to the form of large-scale dissipation which is
required to damp the inverse cascade. We consider three models of large-scale
dissipation: linear "Ekman" drag, non-linear quadratic drag, and scale
selective hypo-drag that damps only low-wavenumber modes. In all cases, the
statistically steady vorticity field is dominated by almost axisymmetric
vortices, and the probability density function of vorticity is non-Gaussian.
However, in the case of linear and quadratic drag, we find that the velocity
statistics is close to Gaussian, with non-negligible contribution coming from
the background turbulent flow. On the other hand, with hypo-drag, the
probability density function of velocity is non-Gaussian and is predominantly
determined by the properties of the vortices. With hypo-drag, the relative
positions of the vortices and the exponential distribution of the vortex
extremum are important factors responsible for the non-Gaussian velocity
statistics.
