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2012.23: Long's vortex revisited

2012.23: R.E. Hewitt and P.W. Duck (2009) Long's vortex revisited. Journal of Fluid Mechanics, 634. pp. 91-111.

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DOI: 10.1017/S0022112009007502

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
Uncontrolled Keywords:fluid dynamics, vortex flows, geophysics
Subjects:MSC 2000 > 76 Fluid mechanics
MSC 2000 > 86 Geophysics
PACS 2003 > 47 Fluid dynamics
MIMS number:2012.23
Deposited By:Dr Richard E. Hewitt
Deposited On:29 January 2012

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