Impact of nonuniform ambient stratification on thermal plume dynamics

Thermal plumes arising from localized buoyancy sources are very common in nature and industrial settings. They have been extensively studied experimentally, theoretically, and numerically, mostly focusing on entrainment and mixing processes in fully developed turbulent regimes. Here, we focus on the primary instabilities of laminar plumes and their transitions as the strength of the buoyancy source (quantified by a Rayleigh number) is increased. Numerous prior studies in this transitional regime have reported a myriad of disparate spatiotemporal plume characteristics. We show that this wide variety of behavior is tied to the various ways an O(2) axisymmetric system can undergo symmetry breaking. Our equivariant dynamical systems theory analyzing the breaking of O(2) symmetry accounts for the spatiotemporal characteristics of the plumes we compute solving the Navier-Stokes-Boussinesq equations. We find that the nature of the ambient stratification plays an important role in determining how O(2) symmetry is broken with increasing Rayleigh number, and this in turn determines the details of the plume spatiotemporal characteristics.