Large-scale lognormal fluctuations in turbulence velocity fields

TL;DR

This study reveals that in laboratory turbulence, fluctuations of velocity-related quantities are universally lognormal across various flows, likely due to multiplicative stochastic processes in energy transfer among scales.

Contribution

It demonstrates the universality of lognormal fluctuations in turbulence velocity fields across different flow configurations and Reynolds numbers.

Findings

Fluctuations are lognormal within large-scale ranges.

Lognormality is consistent across different turbulence setups.

Fluctuations are linked to multiplicative stochastic processes.

Abstract

For several flows of laboratory turbulence, we obtain long records of velocity data. These records are divided into numerous segments. In each segment, we calculate the mean rate of energy dissipation, the mean energy at each scale, and the mean total energy. Their values fluctuate significantly among the segments. The fluctuations are lognormal, if the segment length lies within the range of large scales where the velocity correlations are weak but not yet absent. Since the lognormality is observed regardless of the Reynolds number and the configuration for turbulence production, it is expected to be universal. The likely origin is some multiplicative stochastic process related to interactions among scales through the energy transfer.