Linear stability analysis of controlled Rayleigh-Benard convection using shadowgraphic measurement

We conduct a linear stability analysis of Rayleigh-Benard convection in an infinite horizontal layer with active control of the lower boundary heat flux. A simple linear proportional control loop uses a shadowgraph of the convection pattern to actively distribute the constant-mean lower boundary heat flux while the upper boundary is kept at a constant temperature. We find it possible to shift the convection threshold by a factor of approximately 3. This is a companion paper to our recent experimental work. (C) 1997 American Institute of Physics.