Mechanisms of Buoyancy-Modified Entrainment in Plumes: Theoretical Analysis

We present a theoretical analysis, based on the self-similar velocity and buoyancy profiles for plumes in the far field region, to show how buoyancy dually shapes the flow behavior. In particular, we show that while buoyancy flux makes a positive contribution to mean kinetic energy flux, buoyancy also enhances the mean velocity gradients so that the loss of mean kinetic energy to turbulent kinetic energy is amplified. The ability of buoyancy to increase the separation between the large and small length scales of the flow is discussed in terms of its impact on the evolutionary dynamics of the flow structures. It is also shown, as a result of the scaling laws that follow from the analysis, that the ability of buoyancy to strengthen the eddy vorticity in plumes is primarily through its leading order effect of enhancing the mean velocity gradients, and less so through its lower order contributions to the baroclinic component of torque. We then provide a perspective on how the small-scale nibbling contribution to the entrainment process is affected by such buoyancy-induced modifications to the mean flow. Finally, we juxtapose key takeaways from the analysis with the contemporary view provided by the literature on the entrainment process to propose a mechanistic picture of buoyancy-modified entrainment in plumes.