The dynamics and mixing of turbulent plumes in a turbulently convecting environment

Abstract

The turbulent motion of buoyant plumes released into turbulently convecting environments is studied. By assuming that the turbulent environment removes fluid from the plume at a rate proportional to a characteristic environmental velocity scale, we derive a model describing the fluid behaviour. For the example of pure buoyancy plumes, entrainment dominates near the source and the plume radius increases with distance, while further from the source removal, or extrainment, of plume material dominates, and the plume radius decreases to zero. Theoretical predictions are consistent with laboratory experiments, a major feature of which is the natural variability of the convection. We extend the study to include the evolution of a finite confined environment, the end-member regimes of which are a well-mixed environment at all times (high convective velocities), and a ‘filling-box’ model similar to that of Baines & Turner (1969) (low convective velocities). These regimes, and the motion of the interface in a ‘filling-box’ experiment, match experimental observations. We find that the convecting filling box is not stable indefinitely, but that the density stratification will eventually be overcome by thermal convection. The model presented here has important applications in volcanology, ventilation studies and environmental science.