A First Order Pertubative Analysis of the Advection-Diffusion Equation for Pollutant Dispersion in the Atmospheric Boundary Layer

Abstract

The present discussion focuses on the dispersion of pollution plu mes in the at mospheric boundary layer. Fro m a comparison between first order perturbation theory with equivalent findings from a spectral theory approach we identify significant contributions under certain conditions filtered out by perturbation technique. To this end we make use of the Intermediate Variable Technique and simp lify the three-dimensional advection-diffusion equation according to the findings of the former. Results, where certain characteristics (diffusion, advection, turbulence) are either amp lified or suppressed are compared with the co mplete GILTT solution. Dispersion of pollution plu mes in the at mospheric boundary layer (A BL) has undergone a considerable evolution fro m its early classification scheme according to stability to more advanced models that are based on the Monin-Obukhov similarity theory. However, the complexity mo re or less turbulent of the phenomenon is still man ifest in parameterizat ions that hide physical details in phenomenological coefficients and it would be desirable to shade further light on at least some of their p roperties. In this sense the current discussion is an attempt to identify significant contributions fro m first order perturbation theory with equivalent findings fro m a spectral theory approach. Studies of pollutant dispersion, and in particular of its governing advection-diffusion equation (ADE), have a long tradition of being treated analytically. In fact analytical solutions are of fundamental importance in understanding and describing physical phenomena. Analytical solutions explicit ly take into account all the parameters of a problem, so that their influence can reliab ly be investigated. It is also easy to obtain the asymptotic behaviour of the solution, which is usually mo re tedious to generate numerically. Moreover, in the same spirit as the Gaussian solution (the first solution of the ADE with the wind and eddy diffusivity coefficients set constant in space), the former suggest the