Multifractality in the statistics of the velocity gradients in turbulence

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Abstract
Using the multifractal approach, we derive the probability distribution function (PDF) of the velocity gradients in fully developed turbulence. The PDF is given by a nontrivial superposition of stretched exponentials, corresponding to the various singularity exponents. The form of the distribution is explicitly dependent on the Reynolds number. The experimental data are in good agreement with the PDF predicted by the same random beta model used to fit the scaling of the velocity structure functions.