# Long's vortex revisited

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 fluid dynamics, vortex flows, geophysics MSC 2010, the AMS's Mathematics Subject Classification > 76 Fluid mechanicsMSC 2010, the AMS's Mathematics Subject Classification > 86 GeophysicsPACS 2010, the AIP's Physics and Astronomy Classification Scheme > 40 ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID MECHANICS > 47 Fluid dynamics Dr Richard E. Hewitt 29 Jan 2012 20 Oct 2017 14:13 http://eprints.maths.manchester.ac.uk/id/eprint/1769

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