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arXiv · 1104.1658

Conformal invariance in three-dimensional rotating turbulence

S. Thalabard·D. Rosenberg·A. Pouquet·P. D. Mininni
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Abstract

We examine three--dimensional turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-Löwner 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 $<ω_\textrm{z}>_\textrm{z}$ 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 $κ=3.6\pm 0.1$. 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 $κ$ with a heuristic argument and show that this value is consistent with several non-trivial SLE predictions.

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S. Thalabard, D. Rosenberg, A. Pouquet, P. D. Mininni. 2011-04-08. Conformal invariance in three-dimensional rotating turbulence. https://doi.org/10.1103/physrevlett.106.204503

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