Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models

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Title: Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models
Author(s): Kalogirou, A
Cîmpeanu, R
Keaveny, EE
Papageorgiou, DT
Item Type: Journal Article
Abstract: The nonlinear stability of two-fluid Couette flows is studied using a novel evolution equation whose dynamics is validated by direct numerical simulation (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. (J. Fluid Mech., vol. 303, 1995, pp. 23–53). 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)O(103) found in the experiments. Direct comparisons are also made with the available experimental results of Barthelet et al. (J. Fluid Mech., vol. 303, 1995, pp. 23–53) when the thin layer occupies 1/51/5 of the channel height. Pointwise comparisons of the travelling wave shapes are carried out, and once again the agreement is very good.
Publication Date: 13-Oct-2016
Date of Acceptance: 17-Sep-2016
URI: http://hdl.handle.net/10044/1/42816
DOI: http://dx.doi.org/10.1017/jfm.2016.612
ISSN: 1469-7645
Publisher: Cambridge University Press
Start Page: R1
End Page: R13
Journal / Book Title: Journal of Fluid Mechanics
Volume: 806
Copyright Statement: © 2016 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press. Journal of Fluid Mechanics https://www.cambridge.org/core/journals/journal-of-fluid-mechanics
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/K041134/1
EP/L020564/1
Keywords: Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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