- Wagner, B. A. and Bertozzi, A. L. and Howle, L. E., Positive feedback control of Rayleigh-Benard convection,
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B, vol. 3 no. 4
pp. 619--642 .
(last updated on 2011/07/03)
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.