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

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 betwe...

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Bibliographic Details
Published in:Journal of fluid mechanics 2016-11, Vol.806, p.016322-016322, Article R1
Main Authors: Kalogirou, A., Cîmpeanu, R., Keaveny, E. E., Papageorgiou, D. T.
Format: Article
Language:English
Subjects:
Asymmetry
Bistability
Computational fluid dynamics
Couette flow
Direct numerical simulation
Dynamic stability
Dynamics
Evolution
Experiments
Fluid flow
Fluids
Formulas (mathematics)
Inertia
Mathematical analysis
Mathematical models
Nonlinear dynamics
Nonlinear systems
Rapids
Ratios
Reynolds number
Solutions
Surfactants
Thin films
Traveling waves
Viscosity
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Summary: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.
ISSN:0022-1120
1469-7645
DOI:10.1017/jfm.2016.612