Plume rise in a shear layer with neutral stability

Several solutions have been published to predict the rise of buoyant plumes in a shear layer with a power-law velocity profile. Each of these solutions is either a special case or is based on oversimplifying assumptions. In this paper, solutions to the plume-rise equations are given for buoyant and nonbuoyant plumes with initial vertical momentum. Solutions are given for both point sources and sources with a finite initial size under neutral stability. For a constant wind speed, these solutions simplify to the conventional plume-rise equations.