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The simultaneous onset and interaction of Taylor and Dean instabilities in a Couette geometry

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posted on 2023-05-18, 17:49 authored by Hills, CP, Andrew BassomAndrew Bassom
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/

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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