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Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Methods for Measuring the Orientation and Rotation Rate of 3D-printed Particles in Turbulence

Published on: June 24, 2016

Conformal invariance in three-dimensional rotating turbulence.

S Thalabard¹, D Rosenberg, A Pouquet

¹Computational and Information Systems Laboratory, NCAR, P.O. Box 3000, Boulder, Colorado 80307, USA.

Physical Review Letters

|June 15, 2011

Summary

This study reveals that turbulent flows with rotation exhibit nodal curves obeying conformal invariance, a key characteristic of stochastic Schramm-Löwner evolution (SLE) curves in fluid dynamics.

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Area of Science:

Fluid Dynamics
Statistical Physics
Complex Systems

Background:

Turbulent flows are ubiquitous in nature and engineering.
Solid-body rotation and helical forcing significantly alter turbulent flow dynamics.
Stochastic Schramm-Löwner evolution (SLE) describes random fractal curves in 2D conformal field theory.

Purpose of the Study:

To investigate the statistical properties of turbulent flows under solid-body rotation and helical forcing.
To explore the potential connection between the topology of turbulent structures and conformal invariance.
To determine if SLE theory can describe features of three-dimensional fluid turbulence.

Main Methods:

Numerical simulation of turbulent flows using a 1536³ grid.
Analysis of high-resolution data with specific Reynolds (5100) and Rossby (0.06) numbers.
Examination of the scaling properties of zero-value contours of the averaged parallel vorticity component.

Main Results:

First evidence of nodal curves in three-dimensional fluid turbulence exhibiting conformal invariance.
Identification of these curves as belonging to a SLE class with Brownian diffusivity κ = 3.6 ± 0.1.
Correlation of SLE behavior with energy cascade self-similarity and flow bidimensionalization due to rotation.

Conclusions:

The findings suggest a deep connection between turbulence and concepts from 2D statistical physics.
SLE provides a powerful framework for understanding the geometry of turbulent structures.
The study validates theoretical predictions by recovering the SLE parameter κ through heuristic arguments.