Buoyant Plume Rise in Nonuniform Wind Conditions

Abstract

The conservation equations governing buoyant plume rise are solved for the case of non-uniform wind conditions. A power law is selected to represent the actual wind profile. Analytical solutions are presented both for uniformly stable and neutral atmospheric conditions. These solutions are shown to be of the same form as those obtained in the simpler uniform case but with the plume rise now depending explicitly on the wind speed shear. A sensitivity analysis of the effects on plume rise of typical variation in wind shear and entrainment reveals that the two quantities have an almost equal effect therefore justifying the use of the present model. To simplify computations a “uniform wind” is introduced such that when used in conjunction with Briggs' equations the results become consistent with those of the present theory.