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Empirical study of multifractal phase transitions in atmospheric turbulence

Author(s): F. Schmitt | D. Schertzer | S. Lovejoy | Y. Brunet

Journal: Nonlinear Processes in Geophysics
ISSN 1023-5809

Volume: 1;
Issue: 2/3;
Start page: 95;
Date: 1994;
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We study atmospheric wind turbulence in the framework of universal multifractals, using several medium resolution (10 Hz) time series. We cut these original time series into 704 scale invariant realizations. We then compute the moment scaling exponent of the energy flux K(q) for 4 and 704 realizations, in order to study qualitative difference between strong and weak events associated with multifractal phase transitions. We detect a first order multifractal phase transition of the energy flux at statistical moment of order qD ≈ 2.4 ± 0.2: this means that when the number of realizations increases, moments order q ≥; qD diverge. These results are confirmed by the study of probability distributions, and wind structure functions. A consequence of these findings is that it is no use to compare different cascade models in turbulence by using the high order wind structure functions, because a linear part will always be encountered for high enough order moments. Another important implication for multifractal studies of turbulence is that the asymptotic slope of the scaling moment function is purely a function of sample size and diverges with it; it implies the same for D∞, which has often be considered as finite.
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