of self-similar solutions parameterizing the biggest fluctuations of our hydrodynamic system.\
As a way of checking our numerics, and also in order to get some insight into the differences between the two models, we have performed strictly analogous computations on the complex GOY model for two different values of $\epsilon$ (with $Q=2$, $R=10^{5}$ and $N=17$). The first one, $\epsilon =0.75$, lies far from the transition, which was found in [@BLLP] to occur at $\epsilon^{*}=0.395..$ for a Reynolds number roughly the halfth of ours. The second one is the standard $\epsilon=0.5$, known to lead to scaling properties in good agreement with experiment [@JPV]. Figure \[GOYON1\] shows on the same graph the scaling exponents for the ON model with $\beta =0.28$ and the GOY one for $\epsilon =0.75$. The resemblance is striking, apart from from slightly different asymptotic slopes of the two curves and a cross-over region a bit wider for the GOY model. In Fig. \[GOYON2\], the same comparison is made between the two models, this time for $\beta =0.33$ and $\epsilon =0.5$. Now differences show up, especially at large orders. While a linear monofractal behaviour has definitely set in for $p\geq 7$ in the case of the ON model, the 