Research Report 1: Experiments on the Hydrodynamic Stability of the Flow between Eccentric Rotating Cylinders

Abstract

Since THE Early Work of Taylor (I)^†, it has become well known that the Couette flow between an inner, rotating circular cylinder and a concentric, stationary outer cylinder becomes unstable at sufficiently high rotational speeds. The initial instability leads to the formation of a series of toroidal vortices, commonly referred to as Taylor vortices. The vortices occupy approximately square cells, and adjacent pairs are contra-rotating. When the gap d between the cylinders is small compared with the inner cylinder radius R₁, the criterion for the onset on the instability is the Taylor number T = Ω₁R₁d³ / v² where Ω₁ is the rotational speed and v the kinematic viscosity of the fluid. A widely accepted critical value is T_c = 1708. Recently Coles (2) has shown the existence of a second instability consisting of travelling circumferential waves superimposed on the Taylor vortices.