A mixture model for the PDF of a diffusing scalar in a turbulent flow

This paper offers physical and statistical arguments that lead to the representation of the probability density function of a scalar diffusing in a turbulent flow as a mixture of two probability density functions. Particular attention is given to the high-concentration tails which are consistently observed to be described accurately by a generalized Pareto distribution. A 4-parameter construct, using a mixture of beta densities, is shown to provide an adequate representation of measured concentration distributions of wind-tunnel, grid turbulence, plume data. By using either measured or theoretically predicted moments to conduct statistical inference, it is expected that the proposed model will be flexible enough to apply to a wide variety of experimental data sets, including those obtained from large-scale environmental flows.