tool for mimicking the Navier-Stokes dynamics. In the simplest scalar models, one places velocity variables on a one-dimensional array of wavevectors of the form $k_{n}=k_{0} Q^{n}$, where the integer $n$ labels the shell from 0 to, ideally, $+\infty$ and $Q$ is a scale parameter fixing the step of the cascade. The time evolution of shell-velocities is governed by ordinary differential equations with quadratic non-linearities, whose strength grows like $k_{n}$, deterministic forcing at large scales and viscous dissipation at small ones. The couplings between shells are usually local and chosen in such a way that the total kinetic energy is conserved in the absence of forcing and viscous effects. These hydrodynamic systems display strong departure from the naive scaling expected on the basis of Kolmogorov- like dimensional analysis, which shows up in particular in the higher order moments of velocity. Following the seminal work of Okhitani and Yamada [@YO; @OY], Jensen, Paladin and Vulpiani [@JPV] found in a particular shell model, nowadays referred to as the GOY model, multiscaling properties very close to those of real turbulent flows. Most subsequent studies in this field have therefore concentrated on the GOY model and important progress was made towards a deeper understanding of 