Taylor vortex instability and annulus length effects

Abstract

THE stability of the flow between rotating cylinders has both fundamental and technological significance. The classical analysis by G. I. Taylor¹ of the stability of the circumferential laminar flow deals with coaxial cylinders for which the length L is infinite and the radial clearance c=R₂−R₁, is small, but subsequent work² has eliminated the need for the small clearance approximation. The flow, once unstable, takes the form of axisymmetric toroidal vortices and these Taylor vortices can in turn become unstable with the onset of non-axisymmetric wavy vortices. Early analysis of this instability³ was again restricted to coaxial cylinders of infinite length and small clearance, but Eagles⁴ has produced a stability analysis avoiding the small clearance approximation and has applied it to a cylinder radius ratio R₁/R₂=0.951. No stability analyses seem to exist for an annulus of finite length and most experimental workers choose to work with long cylinders even though short cylinders are more likely to be encountered in engineering applications. Recently I described some observations⁵ of vortex sizes in short annular clearances and I noticed the apparent absence of wavy vortices in those experiments: now I have more positive evidence of the considerable effect of annulus length on the wavy vortex critical speed.