Journal of Fluid Mechanics

The effect of boundary properties on controlled Rayleigh–Bénard convection

a1 Department of Mechanical Engineering and Materials Science, and Center for Nonlinear and Complex Systems, Duke University, Durham, NC 27708-0300, USA


We investigate the effect of the finite horizontal boundary properties on the critical Rayleigh and wave numbers for controlled Rayleigh–Bénard convection in an infinite horizontal domain. Specifically, we examine boundary thickness, thermal diffusivity and thermal conductivity. Our control method is through perturbation of the lower-boundary heat flux. A linear proportional-differential control method uses the local amplitude of a shadowgraph to actively redistribute the lower-boundary heat flux. Realistic boundary conditions for laboratory experiments are selected. Through linear stability analysis we examine, in turn, the important boundary properties and make predictions of the properties necessary for successful control experiments. A surprising finding of this work is that for certain realistic parameter ranges, one may find an isola to time-dependent convection as the primary bifurcation.

(Received February 15 1999)
(Revised December 20 1999)