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**Time change and universality in turbulence.** / Barndorff-Nielsen, Ole Eiler; Schmiegel, Jürgen.

Research output: Working paper/Preprint › Working paper › Research

Barndorff-Nielsen, OE & Schmiegel, J 2006 'Time change and universality in turbulence' Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet.

Barndorff-Nielsen, O. E., & Schmiegel, J. (2006). *Time change and universality in turbulence*. Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet.

Barndorff-Nielsen OE, Schmiegel J. 2006. Time change and universality in turbulence. Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet.

Barndorff-Nielsen, Ole Eiler and Jürgen Schmiegel *Time change and universality in turbulence*. Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet. 2006., 21 p.

Barndorff-Nielsen OE, Schmiegel J. Time change and universality in turbulence. Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet. 2006 Sep 15.

Barndorff-Nielsen, Ole Eiler ; Schmiegel, Jürgen. / **Time change and universality in turbulence**. Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet, 2006.

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title = "Time change and universality in turbulence",

abstract = "We discuss a unifying description of the probability densities of turbulent velocity increments for a large number of turbulent data sets that include data from low temperature gaseous helium jet experiments, a wind tunnel experiment, an atmospheric boundary layer experiment and a free air jet experiment. Taylor Reynolds numbers range from Rλ = 80 for the wind tunnel experiment up to Rλ = 17000 for the atmospheric boundary layer experiment. Empirical findings strongly support the appropriateness of normal inverse Gaussian distributions for a parsimonious and universal description of the probability densities of turbulent velocity increments. Furthermore, the application of a time change in terms of the scale parameter δ of the normal inverse Gaussian distribution results in a collapse of the densities of velocity increments onto Reynolds number independent distributions. We discuss this kind of universality in terms of a stochastic equivalence class that reformulates and extends the concept of Generalized Extended Self-Similarity.",

keywords = "generalized extended self-similarity, hierarchical models, normal inverse Gaussian distribution, stochastic equivalence class, turbulence",

author = "Barndorff-Nielsen, {Ole Eiler} and J{\"u}rgen Schmiegel",

year = "2006",

month = sep,

day = "15",

language = "English",

publisher = "Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet",

type = "WorkingPaper",

institution = "Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet",

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TY - UNPB

T1 - Time change and universality in turbulence

AU - Barndorff-Nielsen, Ole Eiler

AU - Schmiegel, Jürgen

PY - 2006/9/15

Y1 - 2006/9/15

N2 - We discuss a unifying description of the probability densities of turbulent velocity increments for a large number of turbulent data sets that include data from low temperature gaseous helium jet experiments, a wind tunnel experiment, an atmospheric boundary layer experiment and a free air jet experiment. Taylor Reynolds numbers range from Rλ = 80 for the wind tunnel experiment up to Rλ = 17000 for the atmospheric boundary layer experiment. Empirical findings strongly support the appropriateness of normal inverse Gaussian distributions for a parsimonious and universal description of the probability densities of turbulent velocity increments. Furthermore, the application of a time change in terms of the scale parameter δ of the normal inverse Gaussian distribution results in a collapse of the densities of velocity increments onto Reynolds number independent distributions. We discuss this kind of universality in terms of a stochastic equivalence class that reformulates and extends the concept of Generalized Extended Self-Similarity.

AB - We discuss a unifying description of the probability densities of turbulent velocity increments for a large number of turbulent data sets that include data from low temperature gaseous helium jet experiments, a wind tunnel experiment, an atmospheric boundary layer experiment and a free air jet experiment. Taylor Reynolds numbers range from Rλ = 80 for the wind tunnel experiment up to Rλ = 17000 for the atmospheric boundary layer experiment. Empirical findings strongly support the appropriateness of normal inverse Gaussian distributions for a parsimonious and universal description of the probability densities of turbulent velocity increments. Furthermore, the application of a time change in terms of the scale parameter δ of the normal inverse Gaussian distribution results in a collapse of the densities of velocity increments onto Reynolds number independent distributions. We discuss this kind of universality in terms of a stochastic equivalence class that reformulates and extends the concept of Generalized Extended Self-Similarity.

KW - generalized extended self-similarity

KW - hierarchical models

KW - normal inverse Gaussian distribution

KW - stochastic equivalence class

KW - turbulence

M3 - Working paper

BT - Time change and universality in turbulence

PB - Thiele Centre, Institut for Matematiske Fag, Aarhus Universitet

ER -