Vortex Gas Modeling of Turbulent Circulation Statistics

TL;DR

This paper introduces a vortex gas model to analyze turbulent circulation statistics, successfully capturing key features and heavy-tailed distributions observed in high-resolution simulations.

Contribution

It presents a novel vortex gas modeling approach that combines structural turbulence ideas with intermittency phenomenology to explain circulation statistics.

Findings

Reproduces circulation distribution shapes consistent with simulations

Captures Reynolds number dependence of circulation moments

Aligns well with empirical data from DNS studies

Abstract

Statistical properties of circulation encode relevant information about the multi-scale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, as the dependence of circulation moments upon Reynolds numbers and length scales, and the specific shape of the heavy-tailed circulation probability distribution functions. We address these focal points in an investigation of circulation statistics for planar cuts of three-dimensional flows. The model introduced here borrows ideas from the structural approach to turbulence, whereby turbulent flows are depicted as dilute vortex gases, combined with the standard Obukhov-Kolmogorov phenomenological framework of small-scale intermittency. We are able to reproduce, in this way, key statistical features of circulation, in close agreement with empirical observations compiled from direct numerical simulations.