Interfacial behaviour in two-fluid taylor-couette flow

The flow of a system of two viscous fluids between two concentric counter-rotating cylinders is discussed. A simple theory is presented that describes the evolution of shape of the interface between the fluids when they have near equal densities and identical viscosities. This suggests that the interface is neutrally stable, but that after sufficient time there are nevertheless points on the profile at which the curvature becomes very large. As a consequence, the interface develops cusp-like portions in its profile. A novel spectral method is developed for this problem in which the interface is represented as a region of finite width and over which the density changes rapidly but smoothly. The results confirm the general predictions of the asymptotic theory for rotation in a horizontal plane but when the rotation occurs vertically additional features develop in the flow.