An application of generalized similarity analysis to atmospheric diffusion

The generalized type of dimensional analysis, for well-posed boundary value problems, can frequently provide more informative results than those obtained by the ordinary dimensional analysis. The present paper applies the ordinary and the generalized dimensional analysis to two well-known problems of turbulent atmospheric diffusion. The three-dimensional problem of a continuous ground level point source and the two-dimensional problem of a continuous crosswind ground level line source are considered. It is shown that for the point-source problem the generalized dimensional analysis leads to a universal relationship between only three combinations of the problem parameters instead of the five combinations required by the ordinary dimensional analysis. For the line source problem the generalized dimensional analysis gives a relationship between only two dimensionless combinations, while the ordinary analysis result requires three dimensionless quantities.