Circulation Fluctuations of Elementary Turbulent Vortices

TL;DR

This paper investigates the circulation fluctuations of elementary turbulent vortices, revealing a paradoxical fat-tailed distribution explained by Gaussian multiplicative chaos, supported by direct numerical simulations across various Reynolds numbers.

Contribution

It introduces a GMC-based framework to resolve the paradox of vortex circulation distributions in turbulence, linking circulation statistics to spatial distribution fluctuations.

Findings

Circulations of vortices follow fat-tailed distributions.

A coupling exists between vortex circulation and spatial distribution fluctuations.

The GMC framework explains the circulation distribution paradox.

Abstract

Thin vortex tubes, with core sizes within the dissipation range, profuse in a homogeneous and isotropic turbulent flow. Their intersections with an arbitrary plane define, as a mathematical construct, a dilute gas of localized, intermittently distributed, two-dimensional vortex spots. While their planar density fluctuations are described by a field-theoretical extension of log-normal single-point statistics, known as Gaussian multiplicative chaos (GMC), they carry circulations which are Gaussian-correlated throughout the inertial range. It is puzzling, then, to find that the circulations of individual vortices are fat-tailed distributed, an apparent paradox that we fix within the GMC framework. The solution, validated through the examination of direct numerical simulation data for a broad range of Reynolds numbers, unveils, as a surprising phenomenological result, an existing coupling between the circulation of vortex structures and the short-distance properties of their spatial distribution fluctuations at sub-Taylor microscales.