On the bimodal nature of a confined buoyant plume. Part I: AÂ topological and analytical insight

The series of bifurcations leading a confined thermal plume from stationary behaviour to deterministic chaos has been recently reported for the case of a horizontal cylindrical heat source within an air-filled, isothermally cooled square cavity. A refined sampling of the bifurcation parameter range revealed that, in the limit of the 2D approximation, transition unfolds through a period doubling cascade; however, a peculiarity of the observed scenario resides in the occurrence of a window of quasiperiodic behaviour at the beginning of the period doubling cascade. In particular, the quasiperiodic range splits the regions of stability of the period-1 and period-2 limit cycles, hinting at the bimodal nature of the subsequent subharmonic cascade. Within this frame, new analyses are presented here, to achieve of a deeper insight on the birth, evolution and disappearance of quasiperiodic flow. Particular attention has been given to the study of the transient dynamics leading to the asymptotic flows, especially in the vicinity of the bifurcation points.