Instability of plumes driven by localized heating

Abstract

AbstractPlumes due to localized buoyancy sources are of wide interest owing to their prevalence in many situations. This study investigates the transition from laminar to turbulent dynamics. Several experiments have reported that this transition is sensitive to external perturbations. As such, a well-controlled set-up has been chosen for our numerical study, consisting of a localized heat source at the bottom of an enclosed cylinder whose walls are all maintained at a fixed uniform temperature, except for the localized heat source. At moderate Rayleigh numbers $\mathit{Ra}$, the flow consists of a steady, axisymmetric purely poloidal plume. On increasing $\mathit{Ra}$, the flow undergoes a supercritical Hopf bifurcation to an axisymmetric ‘puffing’ plume, where a vortex ring is periodically emitted from the localized heater. At higher $\mathit{Ra}$, this state becomes unstable to a sequence of symmetry-breaking bifurcations, going through a quasi-periodic ‘fluttering’ stage where the axisymmetric rings are tilted, and other states in which the sequence of tilted rings interact with each other. The sequence of symmetry-breaking bifurcations in the transition to turbulence culminates in a torus breakup event in which all the spatial and spatio-temporal symmetries of the system are broken.