  Iterative coarse-graining procedure based on Wyld's perturbation expansion is
applied to the problem of Navier-Stokes turbulence. It is shown that the
low-order calculation gives the fixed-point Reynolds number $ Re_{fp}$
(coupling constant) almost identical to the Reynolds number of the recently
discovered transition to anomalous scaling of the moments of {\bf "velocity
derivatives"}. Using this result as a dynamic constraint, it is argued that in
the vicinity of the fixed point (integral scale) the high-order
non-linearities, generated by the procedure, are irrelevant. The infra-red
divergencies do not disappear but are are contained in the derived equations
for the symmetry-breaking large-scale flows (turbulence models or
"condensates"), which are source of the small-scale turbulence.
