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A parsimonious and universal description of turbulent velocity increments

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  • O. Barndorff-Nielsen
  • P. Blæsild
  • J. Schmiegel

Abstract

This paper proposes a reformulation and extension of the concept of Extended Self-Similarity. In support of this new hypothesis, 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 different 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 $\delta$ of the normal inverse Gaussian distribution reveals some universal features that are inherent to the pdf of all three data sets. Copyright Springer-Verlag Berlin/Heidelberg 2004

Suggested Citation

  • O. Barndorff-Nielsen & P. Blæsild & J. Schmiegel, 2004. "A parsimonious and universal description of turbulent velocity increments," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(3), pages 345-363, October.
    • Handle: RePEc:spr:eurphb:v:41:y:2004:i:3:p:345-363
    DOI: 10.1140/epjb/e2004-00328-1
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    Citations

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    Cited by:

    1. Korolev, V.Yu. & Chertok, A.V. & Korchagin, A.Yu. & Zeifman, A.I., 2015. "Modeling high-frequency order flow imbalance by functional limit theorems for two-sided risk processes," Applied Mathematics and Computation, Elsevier, vol. 253(C), pages 224-241.
    2. David Scott & Diethelm Würtz & Christine Dong & Thanh Tran, 2011. "Moments of the generalized hyperbolic distribution," Computational Statistics, Springer, vol. 26(3), pages 459-476, September.
    3. Vindel, Jose M. & Trincado, Estrella, 2010. "The timing of information transmission in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(24), pages 5749-5758.
    4. Gravanis, E. & Akylas, E. & Michailides, C. & Livadiotis, G., 2021. "Superstatistics and isotropic turbulence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 567(C).
    5. Ole E. Barndorff-Nielsen, 2016. "Assessing Gamma kernels and BSS/LSS processes," CREATES Research Papers 2016-09, Department of Economics and Business Economics, Aarhus University.
    6. Ole E. Barndorff-Nielsen & Makoto Maejima & Ken-iti Sato, 2006. "Infinite Divisibility for Stochastic Processes and Time Change," Journal of Theoretical Probability, Springer, vol. 19(2), pages 411-446, June.

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