Hewitt, R.E. and Duck, P.W.
(2000)
*Non-axisymmetric rotating-disk flows: nonlinear travelling-wave states.*
Journal of Fluid Mechanics, 413.
pp. 287-316.
ISSN 1469-7645

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## Abstract

We consider the classical problem of the laminar flow of an incompressible rotating fluid above a rotating, impermeable, infinite disk. There is a well-known class of solutions to this configuration in the form of an exact axisymmetric solution to the Navierâ��Stokes equations. However, the radial self-similarity that leads to the â��rotating- disk equationsâ�� can also be used to obtain solutions that are non-axisymmetric in nature, although (in general) this requires a boundary-layer approximation. In this manner, we locate several new solution branches, which are non-axisymmetric travelling-wave states that satisfy axisymmetric boundary conditions at infinity and at the disk. These states are shown to appear as symmetry-breaking bifurcations of the well-known axisymmetric solution branches of the rotating-disk equations. Numerical results are presented, which suggest that an infinity of such travelling states exist in some parameter regimes. The numerical results are also presented in a manner that allows their application to the analogous flow in a conical geometry. Two of the many states described are of particular interest. The first is an exact, nonlinear, non-axisymmetric, stationary state for a rotating disk in a counter-rotating fluid; this solution was first presented by Hewitt, Duck & Foster (1999) and here we provide further details. The second state corresponds to a new boundary-layer-type approximation to the Navierâ��Stokes equations in the form of azimuthally propagating waves in a rotating fluid above a stationary disk. This second state is a new non- axisymmetric alternative to the classical axisymmetric Bodewadt solution.

Item Type: | Article |
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Additional Information: | Â© 2000 Cambridge University Press |

Uncontrolled Keywords: | Exact Navier-Stokes solutions self-similar non-axisymmetric rotating disk nonlinear |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics PACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics |

Depositing User: | Dr Richard E. Hewitt |

Date Deposited: | 14 Nov 2013 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | https://eprints.maths.manchester.ac.uk/id/eprint/2051 |

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