The stability of spiral flow between rotating cylinders

Abstract

The effect of an axial pressure gradient on the stability of viscous flow between rotating cylinders is discussed on the basis of the narrow gap approximation, the assumption of axisymmetric disturbances, and the assumption that the cylinders rotate in the same direction. The onset of instability then depends on both the Taylor number ( T ) and the axial Reynolds number (R). For large values of R, the dominant mechanism of instability is of the Tollmien-Schlichting type and the present theory is based therefore on a generalization of the asymptotic methods of analysis that have been developed for the Orr-Sommerfeld equation. The present results, when combined with previous results for small values of R, give the complete stability boundary in the -plane. Only limited agreement is found with existing experimental data and it is suggested therefore that it may be necessary to consider either non-axisymmetric disturbances or nonlinear effects.