Low-dimensional dynamics of axisymmetric modes in wavy Taylor vortex flow

Abstract

The dynamics of the ‘very-low-frequency’ (VLF) mode in moderate aspect ratio flow is experimentally investigated. The VLF mode is an axisymmetric, timedependent mode that occurs in wavy Taylor vortex flow at η = 0.5[25]. For normalised aspect ratios Γ/N < 0.89 a ‘universal’ sequence of states from stationary Taylor vortex flow to chaotic VLF mode has recently been discovered for the 10- to 50-vortex flow [26]. We show that a qualitatively different transition to chaos occurs in the 12-vortex flow compared with flow states having 14 and more vortices. A symmetry-breaking bifurcation that appears within this ‘universal’ sequence of states is found to be crucial for this new scenario. The onset of chaos via an intermittency route is accompanied with the restoring of the original Z ₂-symmetry of the system leading to a ‘symmetric’ chaotic attractor for a wide range of aspect ratio. The formation of Shil'nikov-type attractor associated with the unstable symmetric fixed point could be found as well. Further investigations show that a new type of VLF mode appears in the Small-jet regime via a Hopf-bifurcation for slightly larger aspect ratio. We present additionally an examination of the VLF mode in a modulated wavy Taylor vortex flow consisting of Small-jet and axially localised Large-jet mode. The transition to chaos in these two VLF regimes is briefly discussed.