A numerical and experimental study of anomalous modes in the Taylor experiment

Abstract

Anomalous modes are flows in the Taylor experiment that exist only for sufficiently high Reynolds number R and are always distinct from the primary flow produced by gradually increasing R from small values. They are distinguished from all other secondary modes by having a direction of spiralling of one or both of the end cells such that outward flow is found along the stationary endwall. In this paper we present new observations of these flows and compare them with numerical solutions of the Navier–Stokes equations. A numerical technique for calculating anomalous modes is described and stability curves for 2-, 3-, and 4-cell flows are presented. Streamline plots of the numerical solutions are compared with photographs of the observed flows. The agreement between the calculations and experiments is good. The calculations also confirm certain theoretical predictions made by Benjamin (1978), Benjamin & Mullin (1981) and Hall (1982).