Empirical determination of universal multifractal exponents in turbulent velocity fields

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 \ensuremath{\alpha}=0 and 2, respectively. Using a technique called double trace moment analysis, and turbulent velocity data, we empirically obtain \ensuremath{\alpha}\ensuremath{\approxeq}1.3\ifmmode\pm\else\textpm\fi{}0.1: As has long been suspected, turbulence really is ``in between'' the \ensuremath{\beta} and lognormal models. This describes the entire hierarchy of singularities of the Navier-Stokes equations.