An interpretation of the She-Lévêque model based on order statistics
Laboratoire Joliot-Curie, École Normale Supérieure de Lyon,
46 Allée d'Italie, 69364 Lyon Cedex 07, France
Corresponding author: a firstname.lastname@example.org
Published online: 18 August 2005
We present an interpretation of the She-Lévêque model in fully developed turbulence based on order statistics. Turbulent behavior at large values of the Reynolds number is often studied through the scaling behavior of moments of the distribution of the velocity differences and of the energy dissipation. The present interpretation leads to a derivation of the scaling exponents and of these moments, without any postulate about a universal relation over the fluctuation structures such as the one used by She and Lévêque. The interpretation is based on the fact that the hierarchy of fluctuation structures imposes statistical constraints, whereupon the order p itself is seen as a random variable. As proposed by She and Lévêque, the hierarchy of the structures is such that the structures of larger order affect locally lower order structures through an entrainment process. This phenomenon leads to the Fisher-Tippett law, one of three asymptotic distributions for the extreme value of a random sample as the size of the sample grows to infinity.
PACS: 47.27.Jv – High-Reynolds-number turbulence / 02.50.-r – Probability theory, stochastic processes, and statistics
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2005