  A turbulent flow is characterized by velocity fluctuations excited in an
extremely broad interval of wave numbers $k> \Lambda_{f}$ where $\Lambda_{f}$
is a relatively small set of the wave-vectors where energy is pumped into fluid
by external forces. Iterative averaging over small-scale velocity fluctuations
from the interval $\Lambda_{f}< k\leq \Lambda_{0}$, where
$\eta=2\pi/\Lambda_{0}$ is the dissipation scale, leads to an infinite number
of "relevant" scale-dependent coupling constants ( Reynolds numbers )
$Re_{n}(k)=O(1)$. It is shown that in the i.r. limit $k\rightarrow
\Lambda_{f}$, the Reynolds numbers $Re(k)\rightarrow Re_{tr}$ where $Re_{tr}$
is the recently numerically and experimentally discovered universal Reynolds
number of "smooth" transition from Gaussian to anomalous statistics of spatial
velocity derivatives. The calculated relation $Re(\Lambda_{f})=Re_{tr}$
"selects" the lowest - order non-linearity as the only relevant one. This means
that in the infra-red limit $k\rightarrow \Lambda_{f}$ all high-order
nonlinearities generated by the scale-elimination sum up to zero.
