Positive feedback control of Rayleigh-Bénard convection | Zendy

Barbara Wagner | Zendy; Andrea L. Bertozzi | Zendy; Laurens E. Howle | Zendy

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Positive feedback control of Rayleigh-Bénard convection

Author(s) -

Barbara Wagner,

Andrea L. Bertozzi,

Laurens E. Howle

Publication year - 2003

Publication title -

discrete and continuous dynamical systems - b

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.864

H-Index - 53

eISSN - 1553-524X

pISSN - 1531-3492

DOI - 10.3934/dcdsb.2003.3.619

Subject(s) - convection , rayleigh–bénard convection , galerkin method , feedback control , rayleigh scattering , rayleigh number , dimension (graph theory) , physics , mechanics , control theory (sociology) , statistical physics , negative feedback , control (management) , mathematics , natural convection , computer science , thermodynamics , finite element method , quantum mechanics , engineering , pure mathematics , control engineering , artificial intelligence , voltage

We consider the problem of active feedback control of Rayleigh-Benard convection via shadowgraphic measurement. Our theoretical studies show, that when the feedback control is positive, i.e. is tuned to advance the onset of convection, there is a critical threshold beyond which the system becomes linearly ill-posed so that short-scale disturbances are greatly amplified. Experimental observation suggests that finite size effects become important and we develop a theory to explain these contributions. As an efficient modelling tool for studying the dynamics of such a controlled pattern forming system, we use a Galerkin approximation to derive a dimension reduced model.

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