Plume rise, entrainment and dispersion in turbulent winds

Abstract

This paper describes a new analytical model which combines within one theoretical framework several aspects of the phenomena of plume rise, dispersion, thermal stratification and ambient turbulence. The model is based in part on knowledge gained from recent investigations of flow within free shear layers. The observations suggest a simple model for the turbulent mixing process, which accounts for the known entrainment of air into smoke plumes by plume-generated turbulence. More importantly, the model also predicts a path by which ambient turbulence causes reverse entrainment of plume material into the surrounding fluids. This gives rise to a new ‘extrainment’ term in each of the plume momentum and buoyancy equations. These equations are solved for a turbulent atmosphere of arbitrary thermal stability, and yield plume trajectories which gradually level off at final rise heights that depend on the degree of thermal stratification and on the scale and intensity of ambient turbulence. A link between plume rise and dispersion is identified by means of the concentration species equation, which is solved to show that the plume acts along its length as a distributed source of passively dispersing material. The new theory, specialized for an adiabatic atmosphere, plus the familiar x 2/3 law and a semi-empirical final rise theory from the literature, are all compared against full-scale data on plume rise in turbulent winds. The new theory significantly improves the accuracy of estimates of plume trajectory and final plume height. The price for this improved predictive ability is the need to evaluate the air temperature and its gradient at plume level, and the corresponding intensity and scale of turbulent air movement. This is no longer a technical obstacle since recently developed SODAR and RASS remote sensors have this capability.