The stability of spiral flow between rotating cylinders

Abstract

The stability of viscous flow under an axial pressure gradient between two co-axial cylinders rotating in the same direction is considered. The critical Taylor number (T c) for the onset of instability is then a function of the Reynolds number (R) of the mean axial flow. A perturbation theory valid in the limit P-> 0 is developed and the formula T_c(B) = T_c(0) + 26.5P² (R-> 0) is established.