© 1982 by Oxford University Press
GAUSSIAN APPROXIMATION FOR CONTAMINANT DISPERSION
( Department of Applied Mathematics and Theoretical Physics, University of Cambridge )
A Hermite series is used to investigate contaminant dispersion in a parallel shear flow. It is shown that at small times after discharge the skewness of the cross-sectionally averaged concentration is almost entirely an artefact of the averaging process. For example, in a laminar flow with constant diffusivity, the skewness of the cross-sectionally averaged concentration grows as 
, in contrast to the much smaller growth rate 
for the skewness of the three-dimensional concentration distribution. Thus, provided that allowance is made for the non-uniform values across the flow of the centroid and the variance, remarkably accurate results can be obtained with the one-term Gaussian approximation.