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The transition route and bifurcations of the buoyant flow developing on aheated circular horizontal surface are elaborated using direct numericalsimulations and direct stability analysis. A series of bifurcations, as afunction of Rayleigh numbers (Ra) ranging from $10^1$ to $6\times10^7$, arefound on the route to the chaos of the flow at $Pr=7$. When $Ra<1.0\times10^3$,the buoyant flow above the heated horizontal surface is dominated byconduction, because of which distinct thermal boundary layer and plume are notpresent. At $Ra=1.1\times10^6$, a Hopf bifurcation occurs, resulting in theflow transition from a steady state to a periodic puffing state. As Raincreases further, the flow enters a periodic rotating state at$Ra=1.9\times10^6$, which is a unique state that was rarely discussed in theliterature. These critical transitions, leaving from a steady state andsubsequently entering a series of periodic states (puffing, rotating, flappingand doubling) and finally leading to chaos, are diagnosed using spectralanalysis and two-dimensional Fourier Transform (2DFT). Moreover, directstability analysis is conducted by introducing random numerical perturbationsinto the boundary condition of the surface heating. We find that when the stateof a flow is in the vicinity of bifurcation points (e.g., $Ra=2.0\times10^6$),the flow is conditionally unstable to perturbations, and it can bifurcate fromthe rotating state to the flapping state in advance. However, for relativelystable flow states, such as at $Ra=1.5\times10^6$, the flow remains itsperiodic puffing state even though it is being perturbed.

Critical transitions on route to chaos of natural convection on a heated horizontal circular surface