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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, 105-114, 1994
https://doi.org/10.5194/npg-1-105-1994
© 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, 105-114, 1994
https://doi.org/10.5194/npg-1-105-1994
© Author(s) 1994. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.

  30 Sep 1994

30 Sep 1994

Unified multifractal atmospheric dynamics tested in the tropics: part I, horizontal scaling and self criticality

Y. Chigirinskaya*,1, D. Schertzer1, S. Lovejoy1,**, A. Lazarev2, and A. Ordanovich3 Y. Chigirinskaya et al.
  • 1Laboratoire de Météorologie Dynamique, Université Pierre et Marie Curie, 4 Place Jussieu, 75252 Paris Cedex 05, France
  • 2Space Research Institute, Profsoyuznaya pl., 84/32, 117810 Moscow, Russia
  • 3Mathematical and Mechanical Dept., Moscow University, Lenin Hills, 117234 Moscow, Russia
  • *on leave from the Math. and Mech. Dept., Moscow Univ., Russia
  • **on leave from the Physics Dept., McGill Univ., Canada

Abstract. In this paper we test the Unified Mulifractal model of atmospheric dynamics in the tropics. In the first part, we empirically investigate the scaling behaviour along the horizontal, in the second part along the vertical. Here we concentrate on the presentation of basic multifractal notions and techniques and on how they give rise to self-organized critical structures. Indeed, we point out a rather simple and clear characterisation of these structures which may help to clarify both the nature of the oft-cited coherent structures and the generation of cyclones. Using 30 aircraft series of horizontal wind and temperature, we find rather remarkable constancy of the three universal multifractal indices H, C1 and α as well as the value of critical exponents qD, γD associated with multifractal phase transitions and self-organized critical structures. This constancy extends not only from wind tunnel and mid-latitude to the tropics, but also to multifractals generated by Navier-Stokes like equations.

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