A Three-Dimensional Analytical Solution for the Study of Air Pollutant Dispersion in a Finite Layer

Abstract

We present a closed-form analytical solution for the advection–diffusion equation, where the planetary boundary layer is divided into subdomains, where in each subdomain averaged values of eddy diffusivity and wind speed are assumed. The solution procedure combines an appropriate auxiliary eigenvalue problem with mathematical induction. A transcendental equation giving the eigenvalues for any numbers of subdomains is also developed. Convergence of the solution is numerically verified. The solution is used to evaluate the model against the Copenhagen experiment and computed results are in agreement with experimental ones.