Stabilization of Steady and Oscillatory Marangoni Instability in Rotating Fluid Layer by Feedback Control Strategy

Abstract

The effect of feedback control on the onset of steady and oscillatory surface tension-driven (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. Some cases in which increasing the controller gain parameter can be ineffective are also presented. The thresholds and codimension-2 points for the onset of steady and oscillatory convection are determined. We show how the Pr–Ta parameter space is divided into regions in which steady or oscillatory convection is preferred.

This work was supported by the Malaysian Ministry of Science, Technology & Innovation under Grant 06-01-02-SF0115, UKM RU Grant for the Engineering Mathematics Research Group UKMGUP- BTT-07-25-173, and the University of Malaya. The referees' comments which led to an improvement to the article are acknowledged.