Log-Poisson Cascade Description of Turbulent Velocity Gradient Statistics

TL;DR

This paper applies the Log-Poisson model to describe turbulence velocity gradients, showing that low Reynolds number simulations can effectively predict high Reynolds number behaviors, aiding experimental analysis.

Contribution

It introduces a Log-Poisson phenomenological framework for turbulence, linking low and high Reynolds number statistics of velocity derivatives.

Findings

Theoretical predictions are confirmed by numerical solutions.

Low Reynolds number data can predict high Reynolds number turbulence statistics.

The approach enhances understanding of small-scale turbulence fluctuations.

Abstract

The Log-Poisson phenomenological description of the turbulent energy cascade is evoked to discuss high-order statistics of velocity derivatives and the mapping between their probability distribution functions at different Reynolds numbers. The striking confirmation of theoretical predictions suggests that numerical solutions of the flow, obtained at low/moderate Reynolds numbers can play an important quantitative role in the analysis of experimental high Reynolds number phenomena, where small scales fluctuations are in general inaccessible from direct numerical simulations.