Probability law of concentration in plumes dispersing in an urban area

Abstract

The relationships between various normalized higher-order concentration moments in plumes dispersing in a built-up (urban) environment have been investigated using a large concentration data set obtained in a boundary-layer water channel. This data set consists of measurements of plume dispersion in a number of idealized obstacle arrays (e.g., cubical and non-cubical obstacles in aligned and staggered arrangements with uniform, random and alternating heights). A remarkably robust feature of all the concentration data was the observed collapse of the third- and fourth-order normalized concentration moments on the second-order normalized concentration moment. The data are shown to collapse to a series of universal curves (independent of the geometry of the obstacle array) and these curves were found to be identical to those observed previously for open-terrain plumes. The results imply that the probability law of concentration in a plume dispersing in either a built-up environment or open terrain has a universal form that can be specified by at most two independent parameters. The universal functions representing the relationships between the normalized concentration moments were found to be well modeled (approximated) using a two-parameter clipped-gamma probability law for the concentration. Finally, the clipped-gamma distribution was found to be in very good conformance with the measured probability distribution of concentration for plumes dispersing in a built-up environment.