Issue |
EPL
Volume 86, Number 4, May 2009
|
|
---|---|---|
Article Number | 40010 | |
Number of page(s) | 6 | |
Section | General | |
DOI | https://doi.org/10.1209/0295-5075/86/40010 | |
Published online | 04 June 2009 |
Autocorrelation function of velocity increments time series in fully developed turbulence
1
Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University - 200072 Shanghai, China
2
Université des Sciences et Technologies de Lille - Lille 1, CNRS, Laboratory of Oceanology and Geosciences, UMR 8187 LOG - 62930 Wimereux, France, EU
Corresponding author: francois.schmitt@univ-lille1.fr
Received:
12
February
2009
Accepted:
5
May
2009
In fully developed turbulence, the velocity field possesses
long-range correlations, denoted by a scaling power spectrum or structure
functions. Here we consider the autocorrelation function of velocity increment
at separation
time
. Anselmet et al.
(J. Fluid Mech., 140 (1984)
63) have found that the autocorrelation function of velocity increment has a minimum value,
whose location is approximately equal to
.
Taking statistical stationary assumption, we link the velocity increment and the autocorrelation
function with the power spectrum of the original variable. We then propose an analytical
model of the autocorrelation function. With this model, we prove that the location of
the minimum autocorrelation function is exactly equal to the separation time
when the scaling of the power
spectrum of the original variable belongs to the range 0 < β < 2. This model also suggests a power law expression for the minimum
autocorrelation. Considering the cumulative function of the autocorrelation function, it is
shown that the main contribution to the autocorrelation function comes from the large scale
part. Finally we argue that the autocorrelation function is a better indicator of the inertial
range than the second-order structure function.
PACS: 05.45.Tp – Time series analysis / 02.50.Fz – Stochastic analysis / 47.27.Gs – Isotropic turbulence; homogeneous turbulence
© EPLA, 2009
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