Influence of friction on the direct cascade of the 2d forced turbulence

We discuss two possible scenarios for the direct cascade in two-dimensional turbulent systems in the presence of friction which differ by the presence or not of enstrophy dissipation in the inviscid limit. They are distinguished by the existence or not of a constant enstrophy transfer and by the presence of leading anomalous scaling in the velocity three-point functions. We also point out that the velocity statistics becomes Gaussian in the approximation consisting in neglecting odd-order correlations in front of even-order ones.