Document Type
Article
Rights
This item is available under a Creative Commons License for non-commercial use only
Disciplines
Applied mathematics
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.
DOI
https://doi.org/10.21427/gzdh-4595
Recommended Citation
Hills, C.P. & Bassom, A.P. (2006). The asymptotics of neutral curve crossing in Taylor–Dean flow, Zamp:Zeitschrift für Angewandte Mathematik und Physik (ZAMP). vol 57, no 1, pg. 76-93. doi:10.21427/gzdh-4595
Publication Details
Zeitschrift fur angewandte Mathematik und Physik ZAMP, 2006, Volume 57, Issue 1,pp. 76-93. Available from http://www.springerlink.com/content/f3658t318j4257h5/?p=286acb6bde1548b7a03c6f7d54f9ef58π=5