Accounting for wind shear in Gaussian dispersion models

A mathematical solution to the steady-state advection-diffusion equation for point sources of pollution emitted into an environment containing turbulence and wind shear perpendicular to the mean flow is derived. It is found that shearing motions perpendicular to the mean downwind plume motion significantly enhance horizontal plume dispersion in a manner consistent with observations. Current-generation Gaussian plume models only indirectly and empirically account for the influence of shear on plume dispersion, and here a mathematically rigorous formulation for calculating concentrations downwind of point sources in sheared flows is presented. According to the ideal mathematical derivation, shearing effects lead to plume dispersions (?) increasing with powers of downwind distance (x) ranging from ? ~ x^0.5 to ? ~ x^1.5, depending on the distance from the release location, and the relative magnitudes of turbulence and shear in the flow. With plume vertical dispersion limited by the surface and the depth of the planetary boundary layer, it is found using an Eulerian advection-diffusion model that plume dispersion transitions from turbulence-dominated dispersion close to a source (?~x^0.5), to a shear-dominated regime at intermediate distances (?~x^1.5), followed by a shear-enhanced “effective diffusion” regime again at far distances where dispersion grows with the square root of downwind distance (?~x^0.5). Observations of shear in the planetary boundary layer derived from high time-resolution wind profilers are presented showing typical magnitudes of shear perpendicular and parallel to the mean wind for a continental location in the eastern U. S.