Routes to chaos in confined thermal convectionarising from a cylindrical heat source

Natural convection ows arising from a horizontal cylinder centred ina square-sectioned enclosure are studied numerically. The sequence of bifurcations marking the transition of base fixed-point solutions to unsteady, chaotic ows is followed for increasing values of the Rayleigh number, and for two values of the enclosure aspect ratio, A. It is observed that, for the lower A-value, the route to chaosis triggered by a supercritical Hopf bifurcation, followed by a sequence of period- doublings, while, for the higher A-value, the symmetry of the system is broken by a pitchfork bifurcation, with periodic orbits originating from both branches, and eventually approaching chaos, exhibiting features typical of blue-sky catastrophes.