close to the transition, and one has with a very good accuracy, for all integers $n$ and $p$, $\langle \phi_{n}^{p}(t)\rangle =(\phi_{n}^{e})^{p}$ (where $\langle  \ldots \rangle$ denotes a temporal average).\
The behaviour in the chaotic phase is rather simple to understand, far from the transition. For values of $\beta$ not greater than say 0.28, the dynamics consists in well isolated pulses emitted from the forced shell, after it has reached a significant level. The pulse propagates down the scales, through almost inactive shells, leaving behind a finite amount of energy. After being stopped by dissipation, it gives rise to a rather well characterized pulse of negative amplitude, which carries back to the large scales most of the energy that dissipation failed to absorb. This is quite close to what is observed in the Obukhov limit, although here things repeat themselves in a slightly disordered manner. The picture gets more complicated as $\beta$ gets closer to $\beta^{*}$ (typically for $0.30\leq \beta \leq 0.349$). Shells in the inertial range remain almost always active and they form a noisy background out of which only the biggest fluctuations develop like singular pulses. Negative excursions of variables, triggering backflow of energy, occur very rarely. Splitting of 