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Truncated Lévy laws and 2D turbulence

type de publication      article dans une revue internationale avec comité de lecture
date de publication 1998
auteur(s) Dubrulle Bérengère; Laval Jean-Philippe
journal (abréviation) The Europeen Physical Journal B (Eur. Phys. J. B)
volume (numéro) 4
  
pages 143 – 146
résumé Lévy laws were introduced by Paul Lévy in his search of stable laws (stable by convolution). They also arise in the context of generalization of the Central Limit Theorem, for variables with infinite variance. Lévy laws are characterized by one or two algebraic wings. They have therefore attracted special attention in systems where the probability distribution function displays an algebraic behavior in part of its wings, like financial markets or more recently 2D turbulence. The main physical explanation of the importance of Lévy laws in turbulence was given some times ago by Takayasu. The idea is to decompose the velocity into contribution coming from individual vortices, with singular cores (see e.g. Farge 1996). If the vortices are statistically independent and ``fractal", the probability distribution of their properly renormalized sum is in the basin of attraction of a stable law, i.e.a Lévy law, whose index depending on the index of singularity of individual vortices.
mots clés turbulence, levy laws
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