https://doi.org/10.1007/s100510050162
Towards log-normal statistics in high Reynolds number turbulence
Centre de Recherche Paul Pascal (CNRS UPR 8641) , Université
Bordeaux I,
avenue Schweitzer, 33600 Pessac, France
Corresponding author: a arneodo@crpp.u-bordeaux.fr
Received:
27
August
1997
Accepted:
8
October
1997
Published online: 15 January 1998
We report on the experimental application of a wavelet based deconvolution
method that has been recently emphasized as a very efficient tool to
extract some underlying multiplicative cascade process from synthetic
turbulent signals.
For high Reynolds number wind tunnel turbulence
(Rλ ≈2000), using large velocity records (about
integral time scales), a cascading process is
identified and found to be log-normal.
This result relies on the Gaussian shape
of the kernel 
that determines the nature of the cascade
from a scale a' to a finer scale a. It is confirmed by investigating
various standard quantities such as the probability density functions of
the wavelet transform coefficients or the scaling exponents 
that characterize the evolution across the scales of the moments of
these distributions. Log-normal
statistics are shown to hold on a well defined range of scales,
that can be further used as an objective definition of the inertial range,
and to depend on the Reynolds number. We comment on the asymptotic
validity of the log-normal multifractal description.
PACS: 02.50.-r – Probability theory, stochastic processes, and statistics / 47.27.Gs – Isotropic turbulence; homogeneous turbulence / 47.27.Jv – High-Reynolds-number turbulence
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 1998
