## Abstract

The three-dimensional flow in a corner of fixed angle α induced by the rotation in its plane of one of the boundaries is considered. A local similarity solution valid in a neighborhood of the centre of rotation is obtained and the streamlines are shown to be closed curves. The effects of inertia are considered and are shown to be significant in a small neighbourhood of the plane of symmetry of the flow. A simple experiment confirms that the streamlines are indeed nearly closed; their projections on planes normal to the line of intersection of the boundaries are precisely the 'Taylor' streamlines of the well-known 'paint-scraper' problem. Three geometrical variants are considered: (i) when the centre of rotation of the lower plate is offset from the contact line; (ii) when both planes rotate with different angular velocities about a vertical axis and Coriolis effects are retained in the analysis; and (iii) when two vertical planes intersecting at an angle 2β are honored by a rotating conical boundary. The last is described by a similarity solution of the first kind (in the terminology of Barenblatt) which incorporates within its structure a similarity solution of the second kind involving corner eddies of a type familiar in two-dimensional corner flows.

Original language | English |
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Pages (from-to) | 119-135 |

Number of pages | 17 |

Journal | Journal of Fluid Mechanics |

Volume | 418 |

DOIs | |

Publication status | Published - 2000 |

Externally published | Yes |

## Keywords

- three-dimensional flow
- rotation
- boundaries
- local similarity solution
- streamlines
- inertia
- plane of symmetry
- experiment
- Taylor streamlines
- paint-scraper problem
- geometrical variants
- angular velocities
- Coriolis effects
- vertical planes
- conical boundary
- similarity solution
- corner eddies
- two-dimensional corner flows