Physica A: Statistical Mechanics and its Applications Volume 440, pp. 147-154.

**ISSN/ISBN:** Not available at this time.
**DOI:** 10.1016/j.physa.2015.08.016

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**Abstract:** 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.

**Bibtex:**

```
@Article{biau,
author = {Damien Biau},
title = {The first-digit frequencies in data of turbulent flows},
journal = {Physica A},
year = {2015},
volume = {440},
pages = {297--304}
}
```

**Reference Type:** Journal Article

**Subject Area(s):** Dynamical Systems, Physics