Eur. Phys. J. B 16, 549-561 (2000)
https://doi.org/10.1007/s100510070216

A statistical estimator of turbulence intermittency in physical and numerical experiments

¹ LEGI/IMG - CNRS, BP 53X, 38041 Grenoble Cedex 9, France
² CRTBT/CNRS/UJF et Institut Universitaire de France, BP 166X, 38042 Grenoble Cedex, France

Corresponding author: ^a yann.malecot@ujf-grenoble.fr

Received: 7 January 2000
Revised: 17 March 2000
Published online: 15 August 2000

Abstract

The velocity increments statistic in various turbulent flows is analysed through the hypothesis that different scales are linked by a multiplicative process, of which multiplier is infinitely divisible. This generalisation of the Kolmogorov-Obukhov theory is compatible with the finite Reynolds number value of real flows, thus ensuring safe extrapolation to the infinite Reynolds limit. It exhibits a β estimator universally depending on the Reynolds number of the flow, with the same law either for Direct Numerical Simulations or experiments, both for transverse and longitudinal increments. As an application of this result, the inverse dependence Rλ=ƒ(β) is used to define an unbiased Rλ value for a Large Eddy Simulation from the resolved scales velocity statistics. However, the exact shape of the multiplicative process, though independent of the Reynolds number for a given experimental setup, is found to depend significantly on this setup and on the nature of the increment, longitudinal or transverse. The asymmetry of longitudinal velocity increments probability density functions exhibits similarly a dependence with the experimental setup, but also systematically depends on the Reynolds number.