Conformal invariance in three-dimensional rotating turbulence

TL;DR

This study provides evidence that zero-value contours of vorticity in three-dimensional rotating turbulence exhibit conformal invariance, belonging to a specific SLE class, linking turbulence self-similarity to conformal field theory concepts.

Contribution

First demonstration of conformal invariance in three-dimensional turbulence via SLE analysis of vorticity contours under rotation.

Findings

Vorticity zero contours are conformal invariant with =3.6b10.

SLE behavior correlates with energy cascade self-similarity.

Flow partial bi-dimensionalization due to rotation is observed.

Abstract

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-L\"owner evolution curves (SLE). The data stems from a run on a grid of $1536^3$ points, with Reynolds and Rossby numbers of respectively 5100 and 0.06. We average the parallel component of the vorticity in the direction parallel to that of rotation, and examine the resulting $<\omega_\textrm{z}>_\textrm{z}$ field for scaling properties of its zero-value contours. We find for the first time for three-dimensional fluid turbulence evidence of nodal curves being conformal invariant, belonging to a SLE class with associated Brownian diffusivity $\kappa=3.6\pm 0.1$. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales in this flow, and to the partial bi-dimensionalization of the flow because of rotation. We recover the value of $\kappa$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.