Advection-Diffusion in the Atmosphere: Equations and Solutions
Pp. 153-173 (21)
Marco T. Vilhena
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.
Advection-diffusion equation, Analytical solutions, Integral
transform, air pollution modeling, atmospheric boundary-layer, atmospheric
dispersion, atmospheric turbulence, air quality management.