Predicting Contaminant Concentration Values In Environmental Flows

A generic, small-time, asymptotic solution for the convective-diffusion equation was expressed as a three-dimensional, Hermite-polynomial expansion. This solution was used in a versatile scheme to describe mean values of concentration of contaminant in environmental flows. An analytical solution and a simple finite difference scheme was used to validate that scheme. The scheme was then used, with empirical information from the flow-field, to describe an elevated line and point source in a region of constant stress within a turbulent boundary-layer where detailed measurements of mean values of concentration of contaminant were used for comparison. The results from that comparison showed the scheme was capable of predicting values of concentration of contaminant in the intermediate region and far-field region of that flow-configuration. Cross-terms in the convective-diffusion equation were shown to be insignificant at large distances from the source. The fluctuating field of concentration was derived, in a simple way, from the mean field of concentration in both the near-source region and far-field region. In the intermediate region, a simple extension of this method was shown to receive support from experimental data. Empirical information extracted from the mean field and mean-squared field were used in a Beta distribution to predict the probability density functions for concentration of contaminant. The results from the Beta distribution were shown to agree with measured probability density functions, except in the near-wall region.