Empirical determination of universal multifractal exponents in turbulent velocity fields
1992; American Physical Society; Volume: 68; Issue: 3 Linguagem: Inglês
10.1103/physrevlett.68.305
ISSN1092-0145
AutoresFrançois G. Schmitt, La Vallée D, Daniel Schertzer, S. Lovejoy,
Tópico(s)Complex Systems and Time Series Analysis
ResumoIt 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.
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