Energy and enstrophy fluxes in the double cascade of two-dimensional turbulence

High-resolution direct numerical simulations of two-dimensional turbulence in stationary conditions are presented. The development of an energy-enstrophy double cascade is investigated and its statistics 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.