Lazy plumes

We examine the dynamics of turbulent lazy plumes rising from horizontal area sources and from vertically distributed line sources into a quiescent environment of uniform density. First, we consider plumes with internal buoyancy flux gain and, secondly, plumes from horizontal area sources that have significant momentum flux deficits. We re-cast the conservation equations of Morton et al. (1956) for a constant entrainment coefficient (alpha) in terms of three dimensionless parameters: the plume radius; a parameter F characterizing the local balance of momentum, buoyancy and volume fluxes; and a parameter A that characterizes the rate of internal buoyancy flux gain with height. For a plume with a linear internal buoyancy flux gain with height the flow is shown to be a constant-velocity lazy plume. For highly lazy area sources we derive exact solutions for the key plume parameters in terms of F and an approximate solution for the variation of F with height. We show that near the source there is a region of zero entrainment.