Empirical determination of universal multifractal exponents in turbulent velocity fields

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.