Modes of instability in spiral flow between rotating cylinders

Abstract

A study of the stability of flow between concentric cylinders, with the inner one rotating, distinguished three kinds of instabilities: the familiar axisymmetric mode, an azimuthal mode with the predicted exp i(θ—ωt) angular dependence, and a completely non-symmetric instability which apparently arises from the interaction of the other two. The effect of small axial flow upon all of these modes was to give an approximately parabolic dependence of the critical Taylor number on the axial flow rate. In the case of the axisymmetric mode, agreement with the theory of Krueger & Di Prima (1964) was found to be excellent.