Conformal invariance in three-dimensional rotating turbulence

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 $<{\omega }_{\text{z}}{>}_{\text{z}}$ 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.

4 pages, 3 figures, submitted to PRL

References in corpus (4)

• Rotating helical turbulence. Part I. Global evolution and spectral behavior
• Helicity cascades in rotating turbulence
• The Loewner equation: maps and shapes
• Helical rotating turbulence. Part II. Intermittency, scale invariance and structures

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• Theory for helical turbulence under fast rotation
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• Conformal invariance in out-of-equilibrium Bose-Einstein condensates governed by the Gross-Pitaevskii Equation