https://doi.org/10.1140/epjb/e2005-00273-5
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 philippe.saint-jean@ens-lyon.fr
Received:
25
February
2005
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
