Global and local aspects of entrainment in temporal plumes

Abstract

To date, the understanding of the role buoyancy plays in the entrainment process in unstable configurations such as turbulent plumes remains incomplete. Towards addressing this question, we set up a flow in which a plume evolves in time instead of space. We demonstrate that the temporal problem is equivalent to a spatial plume in a strong coflow and address in detail how the temporal plume can be realized via direct numerical simulation. Using numerical data of plume simulations up to $Re_{\unicode[STIX]{x1D706}}\approx 100$, we show that the entrainment coefficient can be determined consistently using a global entrainment analysis in an integral framework as well as via a local approach. The latter is based on a study of the local propagation of the turbulent/non-turbulent interface relative to the fluid. Locally, this process is dominated by small-scale diffusion which is amplified by interface convolutions such that the total entrained flux is independent of viscosity. Further, we identify a direct buoyancy contribution to entrainment by baroclinic torque, which accounts for 8 %–12 % of the entrained flux locally, comparable to the 15 % buoyancy contribution at the integral level. It appears that the baroclinic torque is a mechanism that might explain higher values of the entrainment coefficient in spatial plumes compared with jets.