Buoyancy-modified entrainment in plumes: Theoretical predictions

Abstract

A theoretical analysis, based on the self-similar velocity and buoyancy profiles for plumes in the far field region, is conducted to show how buoyancy dually shapes the flow behavior. In particular, it is shown that while buoyancy flux makes a positive contribution to the mean kinetic energy flux, buoyancy also enhances the momentum flux, through which the mean shear is enhanced. This amplifies the loss of mean kinetic energy into turbulent kinetic energy. The ability of buoyancy to increase the range of flow length scales 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 flow, and hence the mean shear, 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, key takeaways from the analysis are juxtaposed with the modern-day view provided by the literature on the entrainment process to propose a mechanistic picture of buoyancy-modified entrainment in plumes.