Effects of rotation and feedback control on Bénard–Marangoni convection

The effect of a feedback control on the onset of steady and oscillatory Bénard–Marangoni instability in a rotating horizontal fluid layer is considered theoretically using linear stability theory. It is demonstrated that generally the critical Marangoni number for transition from the no-motion (conduction) to the motion state can be drastically increased by the combined effects of feedback control and rotation. The role of the controller gain parameter on the Pr-Ta and Pr-R/R_c parameter spaces, dividing stability domains into which either steady or oscillatory convection is preferred, is determined.