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Diffusion from a continuous source near a surface in steady reversing shear flow

The dispersion of continuous emissions from a line-source in a reversed-flow layer is analysed by means of diffusion equations; a family of exact solutions is found in the form of infinite series and/or integrals. It is shown that the concentration within the layer decays exponentially with the streamwise distance in the direction of reversed flow. The ground-level concentration near the source is found to be governed largely by the local mean flow; the value of the diffusivity affects the position of the maximum of ground-level concentration, but has little influence upon its magnitude. A useful upper limit is deduced for the background concentration due to recirculation effects. Further, a simple formula is given for the maximum value of the ground-level concentration for cases where the source is not too near the ground. The predictions for ground-level concentration are validated against experimental data for the particular case of a line source in the recirculating wake behind a two-dimensional backward-facing step. The extension of the analysis to the case of a point source is also discussed.