WIAS Preprint No. 780, (2002)

Positive feedback control of Rayleigh-Bénard convection


  • Wagner, Barbara
  • Bertozzi, Andrea
  • Howle, Laurens

2010 Mathematics Subject Classification

  • 37L65 93A30 76E15


  • Hydrodynamic stability, Galerkin method, Mathematical modeling




We consider the problem of active feedback control of rbc 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.

Appeared in

  • Discrete Contin. Dyn. Syst. Ser. B, 3 (2003), pp. 619--642.

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