Bifurcation phenomena in a Taylor–Couette flow with asymmetric boundary conditions

Abstract

We present the results of an experimental and numerical study of bifurcation phenomena in the flow between a rotating inner cylinder and a stationary outer one, the so-called Taylor–Couette problem. Novel asymmetric boundary conditions have been used where one end plate is rotated with the inner cylinder while the other is held fixed. The steady cellular flows consist of one or three vortices in the aspect ratio range considered. We have investigated the selection procedure for the preferred steady states experimentally and numerically and good quantitative agreement is found between the two sets of results. The sequence involves a fold in the solution surface which produces a cusp in the bifurcation set. Hopf bifurcations to three-dimensional oscillatory flow are also present and so the full bifurcation structure is revealed using the combined numerical and experimental approach in a complimentary manner.