Evidence for the double cascade scenario in two-dimensional turbulence

Statistical features of homogeneous, isotropic, two-dimensional turbulence is discussed on the basis of a set of direct numerical simulations up to the unprecedented resolution 32768(2). By forcing the system at intermediate scales, narrow but clear inertial ranges develop both for the inverse and for direct cascades where the two Kolmogorov laws for structure functions are simultaneously observed. The inverse cascade spectrum is found to be consistent with Kolmogorov-Kraichnan prediction and is robust with respect the presence of an enstrophy flux. The direct cascade is found to be more sensible to finite size effects: the exponent of the spectrum has a correction with respect theoretical prediction which vanishes by increasing the resolution.