A solution of the time-dependent advection-diffusion equation

Abstract

We present an analytical solution that considers time dependence in the wind profile and the eddy diffusivity. The solution accepts any profiles of wind and eddy coefficient diffusions in a limited planetary boundary layer. The solution is based on the idea of a decomposition method upon expanding the pollutant concentration in a truncated series. This produces a set of recursive equations whose solutions are known. Each equation of this set is solved by the generalised integral Laplace transform technique (GILTT) method. The solution's ability to represent real situations was checked, comparing model predictions with the over-land along-wind dispersion (OLAD) experimental dataset.