Title :

Autocorrelation function of velocity increments time series in fully developed turbulence

Author(s) :

Huang, Yongxiang [Auteur]
Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187 [LOG]
Schmitt, François G [Auteur]
Laboratoire d’Océanologie et de Géosciences (LOG) - UMR 8187 [LOG]
Lu, Zhiming [Auteur]
Liu, Yulu [Auteur]

Journal title :

EPL - Europhysics Letters

Pages :

40010

Publisher :

European Physical Society / EDP Sciences / Società Italiana di Fisica / IOP Publishing

Publication date :

2009-05

ISSN :

0295-5075

English keyword(s) :

Time series analysis
Stochastic analysis
Isotropic turbulence
homogeneous turbulence

HAL domain(s) :

Physique [physics]/Physique [physics]/Analyse de données, Statistiques et Probabilités [physics.data-an]
Physique [physics]/Mécanique [physics]/Mécanique des fluides [physics.class-ph]
Sciences de l'ingénieur [physics]/Mécanique [physics.med-ph]/Mécanique des fluides [physics.class-ph]
Physique [physics]/Physique [physics]/Dynamique des Fluides [physics.flu-dyn]

English abstract : [en]

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 $\Delta ...
Show more >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 $\Delta u_{\ell}(t)$ at separation time $\ell$. Anselmet et al. [Anselmet et al. J. Fluid Mech. \textbf{140}, 63 (1984)] have found that the autocorrelation function of velocity increment has a minimum value, whose location is approximately equal to $\ell$. 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 $\ell$ when the scaling of the power spectrum of the original variable belongs to the range $0<\beta<2$. 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.Show less >

Language :

Anglais

Peer reviewed article :

Oui

Audience :

Internationale

Popular science :

Non

Collections :

• Laboratoire d'Océanologie et de Géosciences (LOG) - UMR 8187

Source :

Harvested from HAL