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Control of chaos and intermittent periodic motions in Rayleigh-Bénard convection using a feedback controller

Abstract:

Control of regular convective motion, chaos and periodic motion in the Rayleigh-Bénard system is studied by considering a feedback control mechanism that considers the dependence of the heating (cooling) of the two boundary plates on one another. This set up ensures that the different flow regimes (convective, chaotic and periodic) in the system have no mechanical interference and the control remains an external mechanism. The rheostatic influence of feedback control on these flows is demonstrated by investigating in detail the critical Rayleigh number in the case of regular convective motion and the Hopf-Rayleigh number in the case of chaotic motion. For mild coupling between lower and upper boundary temperatures, periodic motions are intermittently observed in an otherwise chaotic regime at times when the system arrives at a situation (fuelling zone) wherein it needs to conserve energy in order to sustain chaos at subsequent times. For strong coupling between the boundary temperatures, an interesting situation arises wherein chaos makes a delayed and brief appearance and gives way to a prolonged spell of periodic motion. Features of the classical Rayleigh-Bénard system are retained but each regime makes a delayed appearance.