Abstract
We show that a recent proposal for “log-Poisson” multifractality in turbulence is in fact a weak hypothesis of universality of turbulent cascades. By using the Lévy canonical measure, we relate this weak universality to the classical strong multifractal universality involving stable Lévy multifractal generators. Finally, using high Reynolds number atmospheric data, we show that for both weak and strong events, the data are inconsistent with Log-Poisson multifractality, whereas—when multifractal phase transitions are taken into account—it is extremely close to the strong universality over the entire range of singularities.
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Schertzer, D., Lovejoy, S., Schmitt, F. (1995). Structures in turbulence and multifractal universality. In: Meneguzzi, M., Pouquet, A., Sulem, PL. (eds) Small-Scale Structures in Three-Dimensional Hydrodynamic and Magnetohydrodynamic Turbulence. Lecture Notes in Physics, vol 462. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0102409
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DOI: https://doi.org/10.1007/BFb0102409
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