Abstract
The stability of flow in an annulus capped at both ends and bounded by a fixed outer cylinder and a spiraling inner rod is determined in the context of linear theory. For infinite aspect ratio and constant fluid properties the problem is governed by a Taylor number Ta, an axial Reynolds number Re, and the radius ratio η. Linear stability is tested with respect to both axisymmetric (n=0) and nonaxisymmetric (n≠0) disturbances for η=0.2, 0.4, 0.6, 0.8 over the range 0≤Re≤2000. The evolution of axial wave number, axial phase speed, and spiral inclination angle with increasing Re at each η through all mode transitions to an asymptotic state n=N is reported. It is found that N=2, 4, 7, 19 for η=0.2, 0.4, 0.6, 0.8, respectively, and that the asymptotic state is reached at Re≂2000 for all radius ratios. The asymptotic state is characterized by critical Taylor numbers and frequencies that approach constant values while critical wave numbers fall off as Re−1. In this same limit the counter‐rotating vortex pairs align themselves axially within the annulus. A conjecture is made on the influence of η on stability in the high Reynolds number limit.