Stability of a Liguid Layer down the Surface of a Vertical Rotating Cylinder

Abstract

The hydrodynamic stability of a liquid layer down the inner and outer surfaces of a vertical circular cylinder rotating about its axis is investigated taking exactly the curvature of a cylinder into account. In the case of long waves, the stability characteristics of this flow is clarified from the neutral stability curves and the phase velocity. The rotation of a cylinder stabilizes the flow of a liquid layer down the inner wall of a cylinder, while the curvature of a cylinder destabilizes it. For the flow down the inner wall of a cylinder, there exists a critical Reynolds number corresponding to an angular velocity of a cylinder. In the case of small Reynolds numbers, the neutral stability curves do not depend on the rotation of a cylinder but depend on its curvature.