  The 2d and 3d like Gletzer, Okhitani and Yamada (GOY) shell models are
examined. The 2d like model shows a transition from statistical
quasi-equilibrium to cascade of enstrophy as a function of the spectral ratio
of energy to enstrophy. The transition is related to the ratio of time scales,
corresponding to eddy turnover times, between shells. The anomalous scaling,
giving rise to non-linear scaling functions, is also connected to the ratio of
eddy turnover times. This is illustrated in a simple stochastic model, where
the structure function, $\zeta (q)$, becomes independent of $q$. In the 3d like
model the multiscaling is also influenced by the existence of a second
non-positive definite inviscid invariant, the helicity.
