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 image and image parameter spaces, dividing stability domains into which either steady or oscillatory convection is preferred, is determined.