  We expose a hidden scaling symmetry of the Navier-Stokes equations in the
limit of vanishing viscosity, which stems from dynamical space-time rescaling
around suitably defined Lagrangian scaling centers. At a dynamical level, the
hidden symmetry projects solutions which differ up to Galilean invariance and
global temporal scaling onto the same representative flow. At a statistical
level, this projection repairs the scale invariance, which is broken by
intermittency in the original formulation. Following previous work by the first
author, we here postulate and substantiate with numerics that hidden symmetry
statistically holds in the inertial interval of fully developed turbulence. We
show that this symmetry accounts for the scale-invariance of a certain class of
observables, in particular, the Kolmogorov multipliers.
