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Updated: Nov 29, 2025

Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Vortex gas modeling of turbulent circulation statistics
G B Apolinário1, L Moriconi1, R M Pereira2
1Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, CEP: 21945-970, Rio de Janeiro, RJ, Brazil.
Abstract:
Statistical properties of circulation encode relevant information about the multiscale structure of turbulent cascades. Recent massive computational efforts have posed challenging theoretical issues, such 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.
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