  Considering the first significant digits (noted d) in data sets of
dissipation for turbulent flows, the probability to find a given number (d=1 or
2 or... 9) would be 1/9 for an uniform distribution. Instead the probability
closely follows Newcomb-Benford's law, namely P(d)=log(1+1/d). The
discrepancies between Newcomb-Benford's law and first-digits frequencies in
turbulent data are analysed through Shannon's entropy. The data sets are
obtained with direct numerical simulations for two types of fluid flow: an
isotropic case initialized with a Taylor-Green vortex and a channel flow.
Results are in agreement with Newcomb-Benford's law in nearly homogeneous cases
and the discrepancies are related to intermittent events. Thus the scale
invariance for the first significant digits, which supports Newcomb-Benford's
law, seems to be related to an equilibrium turbulent state, namely with a
significant inertial range. A matlab/octave program is provided in appendix in
such that part of the presented results can easily be replicated.
