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

Kalogirou, A.; C�mpeanu, R.; Keaveny, E.�E.; Papageorgiou, D.�T.

Authors

R. C�mpeanu

E.�E. Keaveny

D.�T. Papageorgiou



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(10^3) 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 1/5 of the channel height. Pointwise comparisons of the travelling wave shapes are carried out, and once again the agreement is very good.

Citation

Kalogirou, A., Cîmpeanu, R., Keaveny, E., & Papageorgiou, D. (2016). Capturing nonlinear dynamics of two-fluid Couette flows with asymptotic models. Journal of Fluid Mechanics, 806, R1. https://doi.org/10.1017/jfm.2016.612

Journal Article Type Article
Acceptance Date Sep 8, 2016
Online Publication Date Oct 13, 2016
Publication Date Nov 10, 2016
Deposit Date Jun 4, 2019
Publicly Available Date Mar 29, 2024
Journal Journal of Fluid Mechanics
Print ISSN 0022-1120
Electronic ISSN 1469-7645
Publisher Cambridge University Press
Peer Reviewed Peer Reviewed
Volume 806
Pages R1
DOI https://doi.org/10.1017/jfm.2016.612
Public URL https://nottingham-repository.worktribe.com/output/2138137
Publisher URL https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/capturing-nonlinear-dynamics-of-twofluid-couette-flows-with-asymptotic-models/2C515C2C81DAFF5E4DD859A776E0157B

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