Diagnosing tracer transport in convective penetration of a stably stratified layer

We use large-eddy simulations to consider the penetration of a buoyant plume carrying a passive tracer into a stably stratified layer with constant buoyancy frequency. Using a buoyancy-tracer volume distribution, we develop a method of objectively partitioning buoyancy-tracer space into three regions, each of which corresponds to a coherent region in physical space. Specifically, we identify a source region where undiluted plume fluid enters the stratified layer, a transport region where much of the transition from undiluted to mixed fluid occurs in the plume cap, and an accumulation region corresponding to the radially spreading intrusion. This method enables quantification of different measures of turbulence and mixing within each of the three regions, including potential energy and turbulent kinetic energy dissipation rates, an activity parameter, and the instantaneous mixing efficiency. We find that the most intense buoyancy gradients are found in a thin layer at the cap of the penetrating plume, which forms the primary mixing stage and exhibits the most efficient mixing. Newly generated mixtures of environmental and plume fluid joining the intrusion are subjected to relatively weak turbulence and buoyancy gradients weaken as subsiding fluid is homogenised. As the intrusion spreads radially, environmental fluid at the bottom of the stratified layer is efficiently mixed into the intrusion which dominates the total entrainment into the plume.