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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 λ = 80, 190, 17000, respectively. The application of a time change in terms of the scale parameter δ 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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Cumulative curves of grain-size against frequency often show segmented shapes. These shapes have been interpreted as resulting from a combination of normally distributed populations each of which should reflect a mode of transport. The present study deals with samples in motion as bedload, pure saltation load and suspended load. All of these exhibited segmented shapes on cumulative curves. An explanation of this is that the populations are better described as log-hyperbolic distributions rather than as a mixture of log-normal distributions. The log-hyperbolic distribution when plotted on probability paper has a shape which can be misinterpreted as consisting of segments.

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