STABILIZATION OF THE NO-MOTION STATE IN THE RAYLEIGH-BENARD PROBLEM

Using linear stability theory and numerical simulations, we demonstrate that the critical Rayleigh number for bifurcation from the,no-motion (conduction) state to the motion state in the Rayleigh-Benard problem of an infinite fluid layer heated from below and cooled from above can be significantly increased through the use of a feedback controller effectuating small perturbations in the boundary data. The controller consists of sensors which detect deviations in the fluid's temperature from the motionless, conductive values and then direct actuators to respond to these deviations in such a way as to suppress the naturally occurring flow instabilities. Actuators which modify the boundary's temperature or velocity are considered. The feedback controller can also be used to control flow patterns and generate complex dynamic behaviour at relatively low Rayleigh numbers.