Turbulent dispersion of pollutant over complex terrain

A two-dimensional turbulent diffusion equation is derived in a streamline coordinate system, defined for rotational flow over complex terrain and limited aloft by an elevated, impenetrable inversion. In the first instance, the steady-state equation is solved for an inner region of the boundary layer, in which the effect of curvature is negligible and, for simplicity, it is assumed that vorticity has a power-law dependence upon stream function. A variational method of solution is also discussed, in which vorticity may have a more general representation. A numerical calculation is performed for a special case of symmetrical flow over an isolated hill. The dependence of pollutant concentration upon the flow field, downwind distance and source is examined and the effect of wind acceleration in the neighbourhood of the top of the hill is discussed. It is pointed out that the diffusion model can be applied to any realistic flow field, provided that the streamlines are specified.