Centrifugal instability of a Stokes layer: linear theory

Abstract

The instability of the flow induced by a circular cylinder oscillating in an infinite viscous fluid is investigated. The flow is shown to be unstable to a Taylor vortex mode of instability. A series solution of the partial differential system governing the stability of the flow is obtained. The method used has several advantages over the numerical methods used by different authors for related problems. The instability predicted by the theory leads to a flow with no mean velocity component tangential to the cylinders. The disturbance velocity field decays exponentially at the edge of the Stokes layer. The theoretical results are qualitatively confirmed by an experimental investigation of the problem.