A simple model for the probability density function of concentration fluctuations in atmospheric plumes

Simple closure hypotheses for the conditional pseudo-diffusion and pseudo-dissipation terms given a fixed concentration level in a dispersing plume are formulated, and used to obtain a simple functional form for the one-point probability density function (PDF) of concentration. These closure assumptions lead to a left-shifted and clipped-gamma PDF. A simple parametric expression for the observed relationship between the intermittency factor (i.e. the probability of non-zero concentrations) and the normalized second concentration moment is incorporated in the specification of the clipped-gamma PDF. This expression allows the form of the clipped-gamma PDF to be completely specified in terms of only two parameters; namely, the mean concentration and concentration variance. Comparisons of the clipped-gamma PDF to some atmospheric and large-eddy simulation concentration data show good agreement over a wide range of plume locations and atmospheric conditions.