\label{nlphi_n}$$ We still have the freedom to set to unity the forcing amplitude and the coefficient in front of $\vec N$ by non-dimensionalizing in the proper way time and velocities. The final form of the equations (as they were used in the numerical investigations reported in Section 3) is $$\frac{d}{dt} \phi_{n} =N_{n}[\vec{\phi}] +\delta_{n,0}-
{1\over R} Q^{2n} \phi_{n}
\label{equphi_n}$$ The Reynolds number $R$ has been defined as $\displaystyle{R={1\over \nu} \sqrt{{f Q^{2\over 3}}\over k_{0}^{3}}}$. Equations (\[nlphi\_n\]) and (\[equphi\_n\]) make energy conservation quite obvious. Indeed, in the limit $R=+\infty$ and for $n\geq 1$, the energy $E_{n}=\displaystyle{u_{n}^{2}\over 2}=
\displaystyle{{1\over 2}{\phi_{n}^{2} Q^{-{2n\over 3}}}}$ carried by the $n^{th}$ shell obeys the equation $$\frac{d}{dt} E_{n}= \epsilon_{n}-\epsilon_{n+1}$$ where $$\epsilon_{n}= \phi_{n-1} \phi_{n} (\alpha \phi_{n} +\beta \phi_{n-1})
\label{flux_n}$$ is the energy flux from the $(n-1)^{th}$ to the $n^{th}$ shell. Kolmogorov scaling corresponds to $\phi_{n}=C^{te}$ or more fundamentally to $\epsilon_{n}=C^{te}$ throughout the cascade.\
The physics of the model, as defined by equation (\[equphi\_n\]), depends on three parameters, namely : the step of the cascade Q, the proportion of Novikov interactions $\beta$, and the Reynolds number $R$. The number of shells will not matter, provided the truncation is done far beyond the Kolmogorov dissipative scale, where viscous effects become of the same 