Lectures on Air Pollution and Environmental Impact Analyses

Abstract

Methods for predicting plume rise covering a very wide variety of situations have been suggested. All of the predictions are based on a relatively simple, yet versatile, theoretical model. This model is similar to some past models, but they are extended somewhat and the conservation equations are more carefully derived. One consequence is that for bent-over plumes, conservation of vertical momentum involves an effective momentum flux which includes the acceleration of fluid outside the plume, while the buoyancy decay rate in stable fluid is proportional to only the internal momentum flux. The ratio of these two momentum fluxes is estimated to be 2.25. Another consequence for bent-over plumes is that there is no drag force acting on the plume. Adding such a term to the momentum equation leads to results that are inconsistent with observations. To obtain closure, in the self-structured stage of rise the classical assumption that the entrainment velocity is proportional to the shear velocity is employed. The effect of ambient turbulence on plume trajectories is accounted for more simply than in entrainment models, by assuming breakup of the plume and rapid termination of the rise when the internal turbulent energy dissipation rate is matched by the ambient value. (from paper)