Endwall effects in a periodically forced centrifugally unstable flow

Recent experiments of Weisberg et al. (1997. J. Fluid Mech. 348, 141-151) h ave demonstrated that the onset of the centrifugal instability leading to T aylor vortex flow can be delayed by harmonic oscillations of the inner cyli nder in the axial direction. Marques and Lopez (1997. J. Fluid Mech. 348, 1 53-175) used Floquet analysis to describe the observed control of the insta bility over a wide range of frequencies and amplitudes of this oscillation; the dynamics remained axisymmetric and the response to the applied periodi c 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-tim e symmetries. By varying a single parameter we have detected a route to cha os. As the parameter is increased the system undergoes a quasiperiodic Naim ark-Sacker bifurcation, goes through a 1:9 resonance horn (Arnold's tongue) , and then chaos. (C) 2000 The Japan Society of Fluid Mechanics and Elsevie r Science B.V. All rights reserved.