Centrifugal instabilities of circumferential flows in finite cylinders: linear theory

Abstract

Abstract The linear stability of circular Couette flow in a finite-length cylindrical annulus is investigated. The basic flow is taken to be circumferential, whilst perturbations to the flow are required to vanish at the ends of the annulus, as well as the bounding cylindrical surfaces. Both axisymmetric and non-axisymmetric disturbances are considered, and the governing partial differential system is solved using an eigenfunction expansion technique; the critical Taylor numbers, Tc, for the different modes are then determined as functions of the length of the annulus. It is found that, in a finitelength annulus, Tc is always greater than the critical Taylor number for infinitely long cylinders, though no marked increase in Tc occurs until the length to gap ratio of the annulus is about six. Also, it is found that the finiteness of the container can lead to disturbance flow fields quite different from those of the infinite problem. In particular, it is found that in finite cylinders adjacent vortices can have the same sense of rotation. Streamline patterns illustrating this phenomenon, and showing the arrangement of the Taylor cells in a finite-length container are given for neutrally stable axisymmetric disturbances.