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Rendering a subcritical Hopf bifurcation supercritical

Published online by Cambridge University Press:  26 April 2006

Po Ki Yuen  and
Haim H. Bau
Po Ki Yuen
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104-6315, USA
Haim H. Bau
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA, 19104-6315, USA
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Abstract

It is demonstrated experimentally and theoretically that through the use of a nonlinear feedback controller, one can render a subcritical Hopf bifurcation supercritical and thus dramatically modify the nature of the flow in a thermal convection loop heated from below and cooled from above. In particular, we show that the controller can replace the naturally occurring chaotic motion with a stable, periodic limit cycle. The control strategy consists of sensing the deviation of fluid temperatures from desired values at a number of locations inside the loop and then altering the wall heating to counteract such deviations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 317 , 25 June 1996 , pp. 91 - 109
Copyright
© 1996 Cambridge University Press

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