  We study the time irreversibility of the direct cascade in two-dimensional
turbulence by looking at the time derivative of the square vorticity along
Lagrangian trajectories, a quantity which we call metenstrophy. By means of
extensive numerical simulations we measure the time irreversibility from the
asymmetry of the PDF of the metenstrophy and we find that it increases with the
Reynolds number of the cascade, similarly to what found in three-dimensional
turbulence. A detailed analysis of the different contributions to the enstrophy
budget reveals a remarkable difference with respect to what observed for the
direct cascade, in particular the role of the statistics of the forcing to
determine the degree of irreversibility.
