  High resolution direct numerical simulations of two-dimensional turbulence in
stationary conditions are presented. The development of an energy-enstrophy
double cascade is studied and found to be compatible with the classical
Kraichnan theory in the limit of extended inertial ranges. The analysis of the
joint distribution of energy and enstrophy fluxes in physical space reveals a
small value of cross correlation. This result supports many experimental and
numerical studies where only one cascade is generated.
