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.
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