Entrainment in Turbulent Plumes with Time-Varying Source Conditions

Turbulent plumes driven by buoyancy are vital parts of many environmental and engineering problems, from volcanic eruptions and smoke dispersion to ocean mixing. As a plume rises, turbulent motions at the plume edge entrain ambient fluid, causing the plume to expand. Classic self-similar plume models (e.g. Morton et al., 1956, Proc. Roy. Soc. A 234(1196)) parameterise this process using an entrainment coefficient, assumed to be constant, relating the inflow of ambient fluid to the plume rise velocity. We wish to investigate whether this assumption is still valid if we have time-varying source conditions. In this study, we conduct numerical simulations of plumes driven by time-varying axisymmetric sources. We use integrated volume, momentum, and buoyancy fluxes, together with detailed velocity and buoyancy profiles, to quantify the turbulent entrainment in starting, steady, and time-varying plumes.