### Abstract

We report the results of an experimental study of flow in a Taylor-Couette system where the usual circular outer cylinder is replaced by one with a square cross-section. The objective is to determine the validity of low-dimensional dynamical systems as a descriptive framework for flows in a domain without the special continuous symmetry of the original problem. We focus on a restricted version of the flow, where the steady flow consists of a single cell, thereby minimizing the multiplicity of solutions. The steady-state bifurcation structure is found to be qualitatively unchanged from that of the standard system. A complex but self-consistent bifurcation structure is uncovered for time-dependent flows,culminating in observations of dynamics similar to those of the finite-dimensional Sil'nikov mechanism. Such behaviour has been observed in the standard system with continuous azimuthal symmetry. The present results extend the range of closed-flow problems where there is an apparent connection between the infinite-dimensional Navier-Stokes equations and finite-dimensional dynamical systems.

Original language | English |
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Pages (from-to) | 379-405 |

Number of pages | 27 |

Journal | Journal of Fluid Mechanics |

Volume | 275 |

DOIs | |

Publication status | Published - Sep 1994 |

### Keywords

- CHAOS
- STEADY
- ANOMALOUS MODES

## Cite this

*Journal of Fluid Mechanics*,

*275*, 379-405. https://doi.org/10.1017/S0022112094002405