The Time Evolution of a Constant Mass of Air Pollutant Emitted by a Point Source

Abstract

The transient behaviour of a constant mass (i.e. a blob) of pollutant released from a point source at a height, , above ground level at time is studied. The time dependent atmospheric diffusion equation in the presence of diffusion in both horizontal and vertical directions is used to model the problem. The model is found to be governed by an initial-boundary-value problem for the concentration of the pollutant. The solution is obtained in closed form using integral transform methods. The solution is illustrated graphically using appropriate numerical integrations. As time passes, the pollutant blob moves with a central point of accumulation of pollutant while the blob increases in volume to spread the pollutant around it. The motion of the accumulation point in space and time is strongly influenced by wind and gravity while the spread of the pollutant is governed by diffusion. The time taken by the blob to diffuse into space is estimated as a function of the parameters governing wind, gravity and diffusion.

Keywords

• Initial-boundary value problem, pollutant, diffusion equation, analytic solution, time-dependence, point source.