  We present a numerical study of two-dimensional turbulent flows in the
enstrophy cascade regime, with different large-scale forcings and energy sinks.
In particular, we study the statistics of more-than-differentiable velocity
fluctuations by means of two recently introduced sets of statistical
estimators, namely {\it inverse statistics} and {\it second order differences}.
We show that the 2D turbulent velocity field, $\bm u$, cannot be simply
characterized by its spectrum behavior, $E(k) \propto k^{-\alpha}$. There
exists a whole set of exponents associated to the non-trivial smooth
fluctuations of the velocity field at all scales. We also present a numerical
investigation of the temporal properties of $\bm u$ measured in different
spatial locations.
