Vertical dispersion of ground-level releases in the surface boundary layer

Abstract

By assuming that the eddy diffusivity of mass is proportional to that of heat, this paper derives simple expressions for the asymptotic behavior of cross-wind integrated ground-level concentrations under neutral, stable, and unstable conditions. We show that: • C∗y ∼ x∗−1 under neutral conditions; • ∼ x∗−13 under stable conditions; • ∼ x∗−2 under unstable conditions; where C∗y = Cyu∗ |L|Q and x∗ = x/|L|, and Cy is the cross-wind integrated concentration, u∗ is the surface friction velocity, L is the Monin-Obukhov length, and Q is the pollutant release rate. We show that simple interpolations between the asymptotic limits provide excellent fits to the Prairie Grass (Barad, 1958, Paper No. 59, Geophysics Research Directorate, MA) diffusion data. Our analysis of surface dispersion in unstable conditions indicates that the concentration decrease with distance is not consistent with that predicted by free convection theory (Yaglom, 1972, Atmos. Ocean Phys.8, 333–340). Under asymptotically unstable conditions, the concentration falls off as x−2 rather than as x−32 predicted by the theory.