Hewitt, R.E. and Duck, P.W.
(2009)
*Long's vortex revisited.*
Journal of Fluid Mechanics, 634.
pp. 91-111.

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## Abstract

We reconsider exact solutions to the Navier--Stokes equations that describe a vortex in a viscous, incompressible fluid. This type of solution was first introduced by Long (1958) and is par ameterised by an inverse Reynolds number $\epsilon$. Long's attention (and that of many subsequent investigators) was centred upon the `quasi-cylindrical' (QC) case corresponding to $\epsilon = 0$. We show that the limit $\epsilon \to 0$ is not straightforward, and that it reveals other solutions to this fundamental exact reduction of the Navier--Stokes system (which are not of QC form). Through careful numerical investigation, supported by asymptotic descriptions, we identify new solutions and describe the full parameter space that is spanned by $\epsilon$ and the pressure at the vortex core. Some erroneous results that exist in the literature are corrected.

Item Type: | Article |
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Uncontrolled Keywords: | fluid dynamics, vortex flows, geophysics |

Subjects: | MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanics MSC 2010, the AMS's Mathematics Subject Classification > 86 Geophysics 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: | 29 Jan 2012 |

Last Modified: | 20 Oct 2017 14:13 |

URI: | http://eprints.maths.manchester.ac.uk/id/eprint/1769 |

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