Temporal intermittency and cascades in shell models of turbulence

Abstract

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, $ζ(q)$, 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.