On the bimodal nature of a confined buoyant plume. Part II: Flow structure echoes in state space

This work represents the second part of a twofold study aiming at a detailed characterisation of the low order dynamics of a buoyant plume arising from an enclosed horizontal cylindrical heat source, for which chaos unfolds through a period doubling cascade preluded by a window of quasiperiodicity. In part I, this behaviour has been found to be related to the inherent bimodal nature of the flow, and an analytical characterisation of the asymptotic flows in the vicinity of the bifurcation points has been carried out.In this second part, the thermo-fluid dynamic origin of this bimodal flow is investigated. A novel approach is proposed based on the observation of the existing correspondences between the recurrent formation of cellular flow structures, and the global structure of the system dynamics, as described by the attractor in an appropriate state space. In particular, the two modes are shown to correspond to the existence of two alternate and distinct sequences of flow patterns, and the locking between them corresponds to the synchronisation of analogous events in the evolution of the flow structures. Moreover, reported results show that, within the same framework, the period doubling cascade generated by the extinction of the quasiperiodic flow can be seen as a consequence of the modulation of the cellular flow structures.In light of the remarkable similarities with experimental evidences of other buoyancy-driven flows, the proposed approach may represent a useful paradigm for the analysis of transitional, confined convection problems. Phenomenological analysis of the bimodal behaviour of a buoyant plume.Identification of the birth and disappearance of different flow structures in the two modes.State-space representation of the two modes and of the time instances relative to different phases in the system evolution.Persistence of the bimodal phenomenology throughout the whole transition to chaos