Kalogirou, A orcid.org/0000-0002-4668-7747, Cimpeanu, R, Keaveny, EE et al. (1 more author) (2016) Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models. Journal of Fluid Mechanics, 806. ISSN 0022-1120
Abstract
The nonlinear stability of two-fluid Couette flows is studied using a novel evolution equation whose dynamics are validated by direct numerical simulations (DNS). The evolution equation incorporates inertial effects at arbitrary Reynolds numbers through a non-local term arising from the coupling between the two fluid regions, and is valid when one of the layers is thin. The equation predicts asymmetric solutions and exhibits bistability, features that are essential observations in the experiments of Barthelet et al. (1995). Related low-inertia models have been used in qualitative predictions rather than the direct comparisons carried out here, and ad hoc modifications appear to be necessary in order to predict asymmetry and bistability. Comparisons between model solutions and DNS show excellent agreement at Reynolds numbers of O(10³) found in the experiments. Direct comparisons are also made with the available experimental results of Barthelet et al. (1995) when the thin layer occupies 1/5 of the channel height. Pointwise comparisons of the travelling wave shapes are carried out and once again the agreement is very good.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | This article has been published in a revised form in Journal of Fluid Mechanics, http://dx.doi.org/10.1017/jfm.2016.612. This version is free to view and download for private research and study only. Not for re-distribution, re-sale or use in derivative works. © 2016, Cambridge University Press. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 15 Sep 2016 09:22 |
Last Modified: | 14 Apr 2017 03:31 |
Published Version: | http://dx.doi.org/10.1017/jfm.2016.612 |
Status: | Published |
Publisher: | Cambridge University Press |
Identification Number: | 10.1017/jfm.2016.612 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:104553 |