On the Determination of Universal Multifractal Parameters in Turbulence

The scaling behavior observed in turbulent flows has lately been the object of growing interest. Scaling exponents are fundamental since they describe the statistical properties over wide ranges of length scales. Multifractals are characterized by their scaling exponents and when generated by canonical cascade processes they generally will belong to specific universal classes. In this case the scaling exponents are specified by two parameters, the Levy index α and the codimension of the mean singularity C 1. In particular, these parameters are believed to characterize the probability distribution of the singularities of the Navier-Stokes equations. The first data analysis technique specifically designed to directly estimate these parameters, the “Double Trace Moment” is described. The methods are then used to analyse the scaling behaviour of turbulent velocity data, providing estimates of their universal multifractal parameters: α ≈ 1.3 ± 0.1 and C 1 ≈ 0.25 ± 0.05.

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