Circulation Statistics and the Mutually Excluding Behavior of Turbulent Vortex Structures

TL;DR

This paper investigates the statistical properties of velocity circulation in turbulent flows, revealing that vortex structures behave like a two-dimensional gas with short-range repulsive correlations, supported by modeling and numerical simulations.

Contribution

It introduces a novel model combining cascade and structural turbulence descriptions, proposing vortex hard disk behavior supported by numerical evidence.

Findings

Vortex structures exhibit short-distance repulsive correlations.

The effective vortices behave like a two-dimensional gas with hard disk interactions.

Numerical simulations support the proposed vortex behavior model.

Abstract

The small-scale statistical properties of velocity circulation in classical homogeneous and isotropic turbulent flows are assessed through a modeling framework that brings together the multiplicative cascade and the structural descriptions of turbulence. We find that vortex structures exhibit short-distance repulsive correlations, which is evidenced when they are "tomographically" investigated, by means of planar cuts of the flow, as two-dimensional vortex gases. This phenomenon is suggested from model improvements which allow us to obtain an accurate multiscale description of the intermittent fluctuations of circulation. Its crucial new ingredient, the conjectured hard disk behavior of the effective planar vortices, is then found to be strongly supported from a study of their spatial distributions in direct numerical simulations of the Navier-Stokes equations.