Circulation Fluctuations of Elementary Turbulent Vortices

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.