The Fractal Dimension of Iso-Vorticity Structures in 3-Dimensional Turbulence

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Abstract
The fractal dimension of iso-vorticity surfaces is estimated from a 3-dimensional simulation of homogeneous turbulence at moderate Reynolds numbers, performed by Vincent and Meneguzzi. The results are found to be compatible with a recently proposed theory which predicts a crossover from a 2-dimensional geometry at small scales to a fractal geometry at larger scales, with a dimension D = 2.5 + ζ/2, with ζ being the exponent characterizing the scaling of velocity differences.