File(s) under permanent embargo
The asymptotics of neutral curve crossing in Taylor-Dean flow
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.
History
Publication title
Zeitschrift Fuer Angewandte Mathematik Und PhysikVolume
57Pagination
76-93ISSN
0044-2275Department/School
School of Natural SciencesPublisher
Birkhauser Verlag AgPlace of publication
Viadukstrasse 40-44, Po Box 133, Basel, Switzerland, Ch-4010Rights statement
copyright 2006 Birkhauser VerlagRepository Status
- Restricted