order as inertial ones. Assuming $\phi_{n}=O(1)$, the index $N_{d}$ of the dissipative shell is given by the condition $\displaystyle{{Q^{2N_{d}}
\over R}\sim Q^{2N_{d}\over 3}}$. One should however pay attention to the fact that the stronger the fluctuation, the smaller the scale at which it will be effectively dissipated. Since $\phi_{n}$ can grow at most like $Q^{n\over 3}$ (this corresponds to the extreme case of a fluctuation carrying a constant energy through the cascade), we conclude that $N$ should be an integer between $n_{d}$ and $\displaystyle{{4\over 3} n_{d}}$, where we have defined $n_{d}$ as $$n_{d}={3\over 4} \frac{\mbox{Log} R}{\mbox{Log} Q}
\label{defn_d}$$ In our numerical study of the statistical properties of the model, we took $Q=2$, $R=10^{5}$ and let vary $\beta$ between 0 and 1. The choice of 18 shells ($N=17$) turned out to ensure the absence of any spurious boundary effect.\
Since we shall allude sometimes to the complex GOY model, we close this section by writing down the version of it we used in our computations. With complex variables $\phi_{n}$ rescaled in the way described just before, the equations read :

$$\begin{aligned}
\frac{d}{dt}\phi_{0} & = & (2-\epsilon)[1-\phi^{*}_1\phi^{*}_2]-{\phi_0\over
R}\\
\frac{d}{dt}\phi_{1} & = & Q^{2\over
3}[\phi^{*}_0\phi^{*}_2-\phi^{*}_2\phi^{*}_3]
 -{Q^2\over R} \phi_1\\
\frac{d}{dt}\phi_{n} & = & Q^{2n\over
