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Updated: Aug 5, 2026
04:35
Preparation of Free-Surface Hyperbolic Water Vortices
Published on: July 28, 2023
Circulation fluctuations of elementary turbulent vortices
Luca Moriconi1, Rodrigo M Pereira2
1Physics, Universidade Federal do Rio de Janeiro , Rio de Janeiro, Brazil.
Summary
Individual vortex circulations in turbulent flows exhibit fat-tailed distributions, a paradox resolved by Gaussian multiplicative chaos (GMC). This framework reveals a coupling between vortex circulation and spatial distribution at small scales.
Area of Science:
- Fluid dynamics
- Statistical physics
- Turbulence research
Background:
- Turbulent flows contain profuse thin vortex tubes.
- Vortex tube intersections with a plane form a dilute gas of 2D vortex spots.
- Planar density fluctuations follow Gaussian multiplicative chaos (GMC), but circulations are Gaussian-correlated.
Purpose of the Study:
- Resolve the paradox of fat-tailed vortex circulation distributions.
- Investigate the relationship between vortex circulation and spatial distribution.
- Validate findings using direct numerical simulation data.
Main Methods:
- Utilized a field-theoretical extension of lognormal statistics (GMC).
- Analyzed direct numerical simulation data across various Reynolds numbers.
- Examined vortex core sizes within the dissipation range.
Main Results:
- Resolved the apparent paradox of fat-tailed vortex circulation distributions within the GMC framework.
- Demonstrated that individual vortex circulations are fat-tailed distributed.
- Unveiled a coupling between vortex circulation and short-distance spatial distribution properties at sub-Taylor microscales.
Conclusions:
- The GMC framework successfully explains the fat-tailed distribution of vortex circulations.
- A novel coupling exists between vortex circulation and spatial distribution at small scales.
- Findings are robust across a range of Reynolds numbers and validated by simulation data.
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