Empirical determination of universal multifractal exponents in turbulent velocity fields

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Abstract
It is now apparent that the two principal models of turbulence (the ‘‘beta’’ and ‘‘lognormal’’ models) and the extremes of a continuous family of (stable, attractive, hence ‘‘universal’’) multifractals characterized by Levy indices α=0 and 2, respectively. Using a technique called double trace moment analysis, and turbulent velocity data, we empirically obtain α≊1.3±0.1: As has long been suspected, turbulence really is ‘‘in between’’ the β and lognormal models. This describes the entire hierarchy of singularities of the Navier-Stokes equations.