Conformal invariance in three-dimensional rotating turbulence

Abstract

We examine turbulent flows in the presence of solid-body rotation and helical forcing in the framework of stochastic Schramm-Löwner evolution (SLE) curves. The data stem from a run with 15363 grid 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 ωz 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±0.1. SLE behavior is related to the self-similarity of the direct cascade of energy to small scales and to the partial bidimensionalization of the flow because of rotation. We recover the value of κ with a heuristic argument and show that this is consistent with several nontrivial SLE predictions. © 2011 American Physical Society.