Fluctuations of statistics among subregions of a turbulence velocity field

TL;DR

This paper investigates the statistical fluctuations in turbulence velocity fields by analyzing segments of data, revealing lognormal distributions and correlations influenced by large-scale flow, with implications for understanding turbulence dynamics.

Contribution

It introduces a detailed analysis of subregion statistics in turbulence, highlighting fluctuations, distributions, and correlations influenced by large-scale flow effects.

Findings

Statistics fluctuate significantly among subregions.

Distributions of statistics are well approximated by lognormal distributions.

Large-scale flow influences local turbulence statistics.

Abstract

To study subregions of a turbulence velocity field, a long record of velocity data of grid turbulence is divided into smaller segments. For each segment, we calculate statistics such as the mean rate of energy dissipation and the mean energy at each scale. Their values significantly fluctuate, in lognormal distributions at least as a good approximation. Each segment is not under equilibrium between the mean rate of energy dissipation and the mean rate of energy transfer that determines the mean energy. These two rates still correlate among segments when their length exceeds the correlation length. Also between the mean rate of energy dissipation and the mean total energy, there is a correlation characterized by the Reynolds number for the whole record, implying that the large-scale flow affects each of the segments.