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| Plumes due to localized buoyancy sources are of wide interest due to
their prevalence in many geophysical 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 sidewall is
maintained at either a fixed uniform temperature or a fixed
temperature which varies linearly up the wall, and there is a
localized heat source on the bottom. For uniform sidewall temperature,
and a moderate heat source, the flow consists of a steady,
axisymmetric purely poloidal plume. On the temperature of the hot
spot, 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 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. With the linearly varying sidewall
temperature, stratification effects come into play and the whole
transition scenario changes. In particular, swirling flows states
spontaneously appear. All of these various transition scenarios can be
tied back to the possible ways that the symmetries of the system can
be broken. |
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