Density - Velocity Relationships in Explosive Volcanic Plumes

Positively buoyant volcanic plumes rise until the bulk density of the plume is equal to the density of the ambient atmosphere. As ambient air mixes with the plume, it lowers the plume bulk density; thus, the plume is diluted enough to reach neutral density in a naturally stratified atmospheric environment. We produced scaled plumes in analogue laboratory experiments by injecting a saline solution with a tracer dye into distilled water, using a high-pressure injection system. We recorded each eruption with a CASIO HD digital camera and used ImageJ's FeatureJ Edge toolbox to identify individual eddies. We used an optical flow software based off the ImageJ toolbox FlowJ to determine the velocities along the edge of each eddy. Eddy densities were calculated by mapping the dye concentration to the RGB digital color value. We overlaid the eddy velocities over the densities in order to track the behavioral relationship between the two variables with regard to plume motion. As an eddy's bulk density decreases, the vertical velocity decreases; this is a result of decreased mass, and therefore momentum, in the eddy. Furthermore as the density rate of change increases, the eddy deceleration increases. Eddies are most dense at their top and least dense at their bottom. The less dense sections of the eddies have lower vertical velocities than the sections of the eddies with the higher densities, relating to the expanding radial size of an eddy as it rises and the preferential ingestion of ambient air at the base of eddies. Thus the mixing rate in volcanic plumes fluctuates not only as a function of height as described by the classic 1D entrainment hypothesis, but also as a function of position in an eddy itself.