Advection-Diffusion in the Atmosphere: Equations and Solutions

Analytical solutions of equations are of fundamental importance in understanding and describing physical phenomena. We provide a short review of the analytical solutions of the advection-diffusion equation. Two new solutions are presented, adopting novel analytical approaches named Generalized Integral Laplace Transform Technique (GILTT) and Advection Diffusion Multilayer Model (ADMM). The GILTT method is an analytical series solution of the advection-diffusion equation including the solution of an associate Sturn-Liouville problem, expansion of the pollutant concentration in a series in terms of the attained eigefunction, replacement of this expansion in the advection-diffusion equation and, finally, taking moments. This procedure leads to a set of differential ordinary equations that is solved analytically by Laplace transform technique. The ADMM method is an analytical integral solution of the advection-diffusion equation based on a discretization of the PBL in N sub-layers; in each sub-layers the advection-diffusion equation is solved by the Laplace transform technique, considering an average value for eddy diffusivity and the wind speed.

Keywords: Advection-diffusion equation, Analytical solutions, Integral transform, air pollution modeling, atmospheric boundary-layer, atmospheric dispersion, atmospheric turbulence, air quality management.