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. Neutral curves associated with each instability can be constructed but it has been suggested that these curves do not cross but rather posses 'kinks'. Our work is based in the small gap, large wavenumber limit and considers the simultaneous onset of Taylor and Dean instabilities. The two linear instabilities interact at exponentially small orders and a consistent, matched asymptotic solution is found across the whole annular domain, identifying five regions of interest: two boundary adjustment regions and three internal critical points. We construct necessary conditions for the concurrent onset of the linear Taylor and Dean instabilities and show that neutral curve crossing is possible.
History
Publication title
Journal of Physics: Conference Series
Volume
14
Pagination
101-112
ISSN
1742-6588
Department/School
School of Natural Sciences
Publisher
Institute of Physics Publishing Ltd.
Place of publication
UK
Rights statement
Copyright 2005 IOP Publishing Ltd Licensed under Creative Commons Attribution 3.0 Unported (CC BY 3.0) http://creativecommons.org/licenses/by/3.0/