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 $R_łambda=80$ for the wind
tunnel experiment up to $R_łambda=17000$ 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
$\delta$ 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.
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