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The asymptotics of neutral curve crossing in Taylor-Dean flow

Citation

Hills, CP and Bassom, AP, The asymptotics of neutral curve crossing in Taylor-Dean flow, Zeitschrift Fuer Angewandte Mathematik Und Physik, 57, (1) pp. 76-93. ISSN 0044-2275 (2005) [Refereed Article]

Copyright Statement

copyright 2006 Birkhauser Verlag

DOI: doi:10.1007/s00033-005-0006-9

Abstract

The fluid flow between a pair of coaxial circular cylinders generated by the uniform rotation of the inner cylinder and an azimuthal pressure gradient is susceptible to both Taylor and Dean type instabilities. The flow can be characterised by two parameters: a measure of the relative magnitude of the rotation and pressure effects and a non-dimensional Taylor number. This work considers the small gap, large wavenumber limit for linear perturbations when the onset of the Taylor and Dean instabilities is concurrent. A consistent, matched asymptotic solution is found across the whole annular domain and identifies five regions of interest: two boundary adjustment regions and three internal critical points. Necessary conditions for the Taylor number and wavenumber are found and interpreted with reference to the suggestion of neutral curve kinks occurring at moderate wavelengths.

Item Details

Item Type:Refereed Article
Keywords:Concentric cylinder flow; Matched asymptotics; Mode-crossing; Stability; Vortices
Research Division:Mathematical Sciences
Research Group:Applied Mathematics
Research Field:Theoretical and Applied Mechanics
Objective Division:Expanding Knowledge
Objective Group:Expanding Knowledge
Objective Field:Expanding Knowledge in the Mathematical Sciences
Author:Bassom, AP (Professor Andrew Bassom)
ID Code:107377
Year Published:2005
Web of Science® Times Cited:1
Deposited By:Mathematics and Physics
Deposited On:2016-03-11
Last Modified:2016-09-06
Downloads:0

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