Taylor vortices between almost cylindrical boundaries

Summary We consider a modified Taylor problem, with the fluid flowing between a rotating inner circular cylinder and an outer stationary surface whose radius is a constant plus a small and slowly varying function of the axial co-ordinate z. This variation is chosen in such a way that the flow is locally more unstable near z=0 than near z=±, so that Taylor vortices appear more readily near z=0. The theory is developed to show how vortices of strength varying with z develop as the speed of rotation is increased through a critical value which is a perturbation of the classical value. Wave number changes in the axial direction are also calculated.