HYDRODYNAMIC INSTABILITY OF A FLUID LAYER FLOWING DOWN A ROTATING CYLINDER

Abstract

In this paper the linear stability of a fluid layer flowing down the inside and outside of a rotating vertical cylinder is investigated. To this end, two approximations are made: the small wave number approximation and the small Reynolds number approximation. In the former, only the radial destabilizing effect of surface tension is important and may be counteracted by the centrifugal force at a critical value. In the latter, the analysis integrates the azimuthal modes different from m=0. It is shown that for flow outside the cylinder, the magnitude of centrifugal force and wave number may change the dominant mode of instability. For flow inside the cylinder, only the mode m=0 may be unstable. These results generalize those of Boudourides and Davis [Z. Angew. Math. Phys. 37, 597 (1986)] for swirling viscous flows.