NDLI: The Relationship between Skewness and Kurtosis of A Diffusing Scalar

Content Provider	Springer Nature Link
Author	Schopflocher, T. P. Sullivan, P. J.
Copyright Year	2005
Abstract	It has been demonstrated that in turbulent dispersion, there exists a quadratic relationship between the skewness (S) and kurtosis (K) statistics obtained from continuous, elevated sources of scalar contaminant released into both convective and stable atmospheric boundary layers. Specifically, one observes that $$K = A S^2 + B,$$ where A and B are empirically fitted constants that depend on the flow. For two reasons, this is potentially useful information in regard to modelling the probability density function (PDF) of a diffusing scalar. First, since many PDFs have a signature relationship between their skewness and kurtosis, candidate models can immediately be either accepted or rejected depending upon whether they conform to the quadratic curve that is observed experimentally. Second, if one intends to model the PDF by inverting a limited number of moments, the task is reduced when there is a functional relationship between the standardized third and fourth moments. The aforementioned relationship has been corroborated by others who have examined data over a wide range of experimental configurations. However, from one flow to another, there appears to be a non-negligible variability in the two fitting constants of the quadratic curve. In this paper we put forth a framework to help explain this phenomenon, and we also attempt to predict how these parameters vary in space and/or time. Our point is illustrated with well-resolved data from a wind-tunnel, grid-turbulence, plume experiment.
Starting Page	341
Ending Page	358
Page Count	18
File Format	PDF
ISSN	00068314
Journal	Boundary-Layer Meteorology
Volume Number	115
Issue Number	3
e-ISSN	15731472
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2005-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Concentration Kurtosis Probability density Skewness Turbulent diffusion. Meteorology/Climatology Atmospheric Protection/Air Quality Control/Air Pollution
Content Type	Text
Resource Type	Article
Subject	Atmospheric Science

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