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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Volume 1, issue 2/3
Nonlin. Processes Geophys., 1, 95-104, 1994
https://doi.org/10.5194/npg-1-95-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

Special issue: Including papers presented at the EGS Richardson - AGU Chapman...

Nonlin. Processes Geophys., 1, 95-104, 1994
https://doi.org/10.5194/npg-1-95-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  30 Sep 1994

30 Sep 1994

Empirical study of multifractal phase transitions in atmospheric turbulence

F. Schmitt1, D. Schertzer1, S. Lovejoy2,*, and Y. Brunet3 F. Schmitt et al.
  • 1Laboratoire de Météorologie Dynamique (CNRS), Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
  • 2Département de Physique, Université McGill, 3600 rue Université, Montréal, (Québec), H3A 2T8, Canada
  • *present address L.M.D., Paris, France
  • 3INRA Bioclimatologie, 71, Avenue Edouard-Bourleaux, BP 81, 33883 Villenave d'Ornon Cedex, France

Abstract. 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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