Application of an analytical solution for unsteady, advective-diffusion to dispersion in the atmosphere

Application of an analytical solution for unsteady, advective-diffusion to dispersion in the atmosphere—I

I—theory

Nunge, Richard J.

Abstract The theory of an exact analytical procedure for solving the unsteady, advective-diffusion equation is developed for an empirical eddy diffusivity model of dispersion in the atmosphere. The main advantage of the technique is that it allows the prediction of the point concentration in time and space, and thus may be used to investigate pollutant cloud movement and ground level concentrations. Since analytical solutions are obtained, the method is useful for testing numerical integration schemes, for rapid estimations of dispersion under different conditions, and for approximations to more complex situations wherein the heat, mass and momentum transport processes in the atmosphere cannot be uncoupled. The method is developed for a three dimensional initial value problem with the downwind coordinate oriented in the direction of the mean wind so that the crosswind velocity component may be ignored. Later, generalizations to include the cross-wind component, first-order chemical reactions, and continuous, time-dependent, distributed sources are discussed. Particular solutions of the dispersion problem are obtained for a linear time-independent wind in three dimensions and for a time-dependent, periodic wind in a two-dimensional model. In Part II, these particular solutions are used to predict point concentration distributions for various physical situations.