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The nonlinear dynamics of a buoyant air flow in the gap formed by a horizontal cylindrical heat source and a concentric isothermally cooled square enclosure have been recently studied, in the limits of a two-dimensional approximation, for different values of the system aspect ratio, defined as the ratio between the cavity side length and the minimum gap width. Accurate analyses have revealed that, for low values of the aspect ratio, the dominant pattern is the swaying motion of a buoyant plume, which undergoes a period-doubling cascade for increasing values of the Rayleigh number. On the other hand, a substantially different behaviour has been preliminarily observed for higher values of the aspect ratio, since, in a thinner gap, the flow exhibits Rayleigh-Bénard-like cellular patterns above the cylinder. The aim of this communication is to describe the peculiar route to chaos which has been detected for this second type of geometry. The scenario consists in the progressive winding of a periodic limit cycle on an attractor whose topology resembles that of a French horn, which is a typical signature of the codimension-2 Shilnikov bifurcation from periodic dynamics to chaos. A similar feature, known as the blue-sky catastrophe, has never been reported so far for confined convection of pure fluids. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Abstract: The sequence of bifurcations leading to the onset of chaotic flow is determined numerically, for the case of a buoyant plume arising from a horizontal cylinder, centred in a square-sectioned, air-filled enclosure. In the frame of the 2D assumption, a specifically-developed high resolution simulation procedure is adopted, with the aim of achieving a detailed description of the transitional dynamics occurring within the system. A large number of simulations are performed, allowing for an accurate estimate of the critical values of the main system parameter, the Rayleigh number Ra, at which bifurcations occur. A single value of the geometric aspect ratio A of the system is considered, for which transition is found to be characterized by an imperfect period-doubling cascade, an uncommon behaviour in thermofluid systems. Peculiarities of the route to chaos are highlighted, such as the existence of a window of quasiperiodic flow, and the detection of high-order period orbits. [Copyright &y& Elsevier]

Abstract: The competition of buoyancy with electromagnetic body forces is examined numerically in terms of flow structure transitions by means of a two-dimensional unsteady, finite volume model. In the present numerical study, we consider a low-Prandtl liquid metal heated by Joule effect in a rectangular cavity with an aspect ratio of 2. The direct current provides heat to the process medium by a pair of plate electrodes, located at the cavity sidewalls. The simulations have been carried out for fixed values of the Prandtl number, Pr = 0.01, and of the Rayleigh number, Ra = 1.5 × 104, while the Hartmann number, Ha, varies from 0 to 104. The variation of Ha is found to have considerable effects on flow patterns and heat transfer inside the cavity. Several hitherto unknown flow structures are revealed, increasing in complexity with increasing Ha. Amongst the oscillatory flows predicted, intermittency and chaos are detected. The effect of Ha on the overall heat transfer performance of the system is also assessed. [Copyright &y& Elsevier]

The transition mechanisms of natural convection flows ensuing in a fluid layer between two differentially heated vertical plates at Prandtl number Pr = 0.71 are investigated by means of Direct Numerical Simulations. In accordance with several previous studies, results show a first bifurcation from the so-called laminar conduction regime to steady convection at Rayleigh number Ra = 5708. On the other hand, the subsequent transition to turbulence appears to be accompanied by a great sensitivity to some fundamental numerical choices such as domain size, accuracy, resolution and amplitude of the imposed perturbations. Results reveal the occurrence of a bifurcation branch which leads the system to chaos via a second bifurcation to a steady-state, a Hopf bifurcation and, seemingly, a period-doubling cascade. Although the described scenario compares well with previous findings, some doubts persist upon the possible pitfalls in the use of numerical simulation for the study of transition in this kind of systems. Indeed, several numerical aspects are found to become of crucial importance for the prediction of the dynamical behaviour and heat transfer rate of the system. [ABSTRACT FROM AUTHOR]