MaPhySto
The Danish National Research Foundation:
Network in Mathematical Physics and Stochastics

MPS-RR 2004-4
February 2004

# A Parsimonious and Universal Description of Turbulent Velocity Increments

by: Ole E. Barndorff-Nielsen, Preben Blæsild , Jürgen Schmiegel

## Abstract

We discuss an analysis of the probability density function (pdf) of turbulent velocity increments based on the class of normal inverse Gaussian distributions. It allows for a parsimonious description of velocity increments that covers the whole range of amplitudes and all accessible scales from the finest resolution up to the integral scale. The analysis is performed for three di erent data sets obtained from a wind tunnel experiment, a free-jet experiment and an atmospheric boundary layer experiment with Taylor-Reynolds numbers $R_\lambda = 80, 190, 17000$, respectively. The application of a time change in terms of the scale parameter of the normal inverse Gaussian distribution reveals some universal features that are inherent to the pdf of all three data sets.

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