ON SPECTRAL LAWS OF 2D TURBULENCE IN SHELL MODELS

We consider a class of shell models of 2D turbulence. They conserve inertially the analogues of energy and enstrophy, two quadratic forms in the shell amplitudes. Inertially conserving two quadratic integrals leads to two-spectral ranges. We study in detail the one characterized by a forward cascade of enstrophy and spectrum close to Kraichnan's k-3-law. We find that the spectral slope measured locally increases slowly but smoothly through the inertial range. At the low-k end of the inertial range, the slope changes little, and is well approximated over 15 octaves by k-3.05+/-0.01, with the same slope in all models. At the high-k end of the inertial range, we identify a <<spurious>> intermittency effect, in that the spectrum over a rather wide interval is well approximated by a power law with fall-off significantly steeper than k-3.