### Abstract

A simplified model problem has recently been suggested by Schaeffer (1980) in order to explain the results obtained by Benjamin (1978) in his investigation of Taylor vortices in short cylinders. In particular Schaeffer reproduces the results obtained by Benjamin for cylinders so short that only two-cell or four-cell flows are possible. The model given by Schaeffer has artificial conditions imposed on the fluid velocity field at the end walls. These conditions depend on a parameter α and reduce to the no-slip condition when α = 1. If α = 0 the conditions require that the normal component of the velocity and the normal derivative of the tangential velocity vanish at the ends. In this case the onset of Taylor vortex-like motion occurs as a bifurcation from purely circumferential flow. If α is now taken to be small and positive, there is no bifurcation and the circulatory flow develops smoothly. We shall use perturbations method for the case of small α. The imperfect bifurcation problem which we obtain predicts some results consistent with those of Benjamin.

Original language | English |
---|---|

Pages (from-to) | 575-596 |

Number of pages | 22 |

Journal | Journal of Fluid Mechanics |

Volume | 99 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 Jan 1980 |

Externally published | Yes |

### Cite this

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*Journal of Fluid Mechanics*, vol. 99, no. 3, pp. 575-596. https://doi.org/10.1017/S0022112080000778

**Centrifugal instabilities in finite containers : A periodic model.** / Hall, P.

Research output: Contribution to journal › Article › Research › peer-review

TY - JOUR

T1 - Centrifugal instabilities in finite containers

T2 - A periodic model

AU - Hall, P.

PY - 1980/1/1

Y1 - 1980/1/1

N2 - A simplified model problem has recently been suggested by Schaeffer (1980) in order to explain the results obtained by Benjamin (1978) in his investigation of Taylor vortices in short cylinders. In particular Schaeffer reproduces the results obtained by Benjamin for cylinders so short that only two-cell or four-cell flows are possible. The model given by Schaeffer has artificial conditions imposed on the fluid velocity field at the end walls. These conditions depend on a parameter α and reduce to the no-slip condition when α = 1. If α = 0 the conditions require that the normal component of the velocity and the normal derivative of the tangential velocity vanish at the ends. In this case the onset of Taylor vortex-like motion occurs as a bifurcation from purely circumferential flow. If α is now taken to be small and positive, there is no bifurcation and the circulatory flow develops smoothly. We shall use perturbations method for the case of small α. The imperfect bifurcation problem which we obtain predicts some results consistent with those of Benjamin.

AB - A simplified model problem has recently been suggested by Schaeffer (1980) in order to explain the results obtained by Benjamin (1978) in his investigation of Taylor vortices in short cylinders. In particular Schaeffer reproduces the results obtained by Benjamin for cylinders so short that only two-cell or four-cell flows are possible. The model given by Schaeffer has artificial conditions imposed on the fluid velocity field at the end walls. These conditions depend on a parameter α and reduce to the no-slip condition when α = 1. If α = 0 the conditions require that the normal component of the velocity and the normal derivative of the tangential velocity vanish at the ends. In this case the onset of Taylor vortex-like motion occurs as a bifurcation from purely circumferential flow. If α is now taken to be small and positive, there is no bifurcation and the circulatory flow develops smoothly. We shall use perturbations method for the case of small α. The imperfect bifurcation problem which we obtain predicts some results consistent with those of Benjamin.

UR - http://www.scopus.com/inward/record.url?scp=0019049045&partnerID=8YFLogxK

U2 - 10.1017/S0022112080000778

DO - 10.1017/S0022112080000778

M3 - Article

VL - 99

SP - 575

EP - 596

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

IS - 3

ER -