On the evolution of the plume function and entrainment in the near-source region of lazy plumes

Abstract

Plumes occur in many natural and industrial settings, such as chimney smoke, volcanic eruptions and deep water oil spills. A plume function, $\unicode[STIX]{x1D6E4}$, is used to characterize plumes and jets. The far-field behaviour of these flows has been studied in great detail while the near-field behaviour has not quite received the same attention. We examine near-field phenomena such as radial constriction, termed necking, and vortex structure formations with new high resolution direct numerical simulations. Four lazy plumes with increasing values of the source plume parameter, $\unicode[STIX]{x1D6E4}_{0}$, are simulated. We study the evolution of entrainment and the plume function. The original assumptions, that Reynolds stresses dominate viscous shear stresses, do not hold for lazy plumes in the near field. Due to this, a deviation from self-similarity occurs initially and is corrected by a large entrainment coefficient caused by vortex stretching and compression. After correcting for the virtual origin, comparison between theory and simulations shows a monotonic decay of $\unicode[STIX]{x1D6E4}$ towards pure plume behaviour. The entrainment coefficient asymptotes to a widely accepted constant value for plumes.