A note on horizontal dispersion from an instantaneous ground source

Publisher Website
Google Scholar
Abstract
In this paper the shearing advection term, proposed by Lettau (1951), is introduced into an analysis of the diffusion equation discussed recently by Saffman (1962). The case of an instantaneous point source emitted at ground level is considered when the height of diffusion can be assumed to be unlimited; in this case Saffman obtained formulae describing the position of the centroid, x, and the downstream standard deviation, σx, at ground level, of a cloud of marked particles as functions of time, this work being based on a form of analysis which was used initially by Aris in discussing longitudinal diffusion of material in laminar flow through a tube. The introduction of a shearing advection term leads to formulae, for × and σx (excluding the effect of horizontal diffusivity Kx), which predict respectively a 16 per cent and 20 per cent decrease in numerical values compared with those given by Saffman's analysis. If, in addition, eddy diffusivities which are assumed to depend linearly on time are introduced, the respective decreases caused by the shearing advection effect are 19 per cent and 25 per cent.

This publication has 4 references indexed in Scilit: