Abstract
Recent experiments (Weisberg, Kevrekidis & Smits J. Fluid Mechanics 1997)
have demonstrated that the centrifugal instability leading to Taylor vortex
flow can be controlled by harmonic oscillations of the inner cylinder in the
axial direction. Marques & Lopez (J. Fluid Mechanics 1997) used (linear)
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. However, for large
amplitudes of oscillations with small frequencies, the response is
neither axisymmetric nor synchronous, and competition between
different azimuthal and axial modes is important. Here, we present
some further Floquet analysis in the parameter regime where
experimentally the onset is to ``wobbly'' Taylor cells, i.e. the
bifurcated flow is quasiperiodic and not axisymmetric. We also
implement an accurate and efficient spectral-projection scheme for
solving the fully nonlinear axisymmetric Navier-Stokes equations to
examine the effects of endwalls and the breaking of space-time symmetries.
