Endwall effects in a periodically forced centrifugally unstable flow

Recent experiments of Weisberg et al. (1997. J. Fluid Mech. 348, 141-151) have demonstrated that the onset of the centrifugal instability leading to Taylor vortex flow can be delayed by harmonic oscillations of the inner cylinder in the axial direction. Marques and Lopez (1997. J. Fluid Mech. 348, 153-175) used Floquet analysis to describe the observed control of the instability over a wide range of frequencies and amplitudes of this oscillation; the dynamics remained axisymmetric and the response to the applied periodic control mechanism was synchronous over an extensive range of parameters. Here we implement an accurate and efficient spectral-projection scheme for solving the fully nonlinear axisymmetric Navier-Stokes equations to examine the effects of endwalls on the flow dynamics and the breaking of space-time symmetries. By varying a single parameter we have detected a route to chaos. As the parameter is increased the system undergoes a quasiperiodic Naimark-Sacker bifurcation, goes through a 1:9 resonance horn (Arnold's tongue), and then chaos. (C) 2000 The Japan Society of Fluid Mechanics and Elsevier Science B.V. All rights reserved.