Imperial College London
Alternate

ProfessorDemetriosPapageorgiou

Faculty of Natural Sciences, Department of Mathematics

Chair in Applied Maths and Mathematical Physics
 
 
 
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Contact

 

+44 (0)20 7594 8369d.papageorgiou Website

 
 
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Location

 

750Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Papageorgiou:2017:10.1017/jfm.2017.605,
author = {Papageorgiou, DT and Papaefthymiou, ES},
doi = {10.1017/jfm.2017.605},
journal = {Journal of Fluid Mechanics},
title = {Nonlinear stability in three-layer channel flows},
url = {http://dx.doi.org/10.1017/jfm.2017.605},
volume = {829},
year = {2017}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - The nonlinear stability of viscous, immiscible multilayer flows in plane channelsdriven both by a pressure gradient and gravity is studied. Three fluid phases arepresent with two interfaces. Weakly nonlinear models of coupled evolution equationsfor the interfacial positions are derived and studied for inertialess, stably stratifiedflows in channels at small inclination angles. Interfacial tension is demoted andhigh-wavenumber stabilisation enters due to density stratification through second-orderdissipation terms rather than the fourth-order ones found for strong interfacialtension. An asymptotic analysis is carried out to demonstrate how these models arise.The governing equations are 2 × 2 systems of second-order semi-linear parabolicpartial differential equations (PDEs) that can exhibit inertialess instabilities due tointeraction between the interfaces. Mathematically this takes place due to a transitionof the nonlinear flux function from hyperbolic to elliptic behaviour. The conceptof hyperbolic invariant regions, found in nonlinear parabolic systems, is used toanalyse this inertialess mechanism and to derive a transition criterion to predict thelarge-time nonlinear state of the system. The criterion is shown to predict nonlinearstability or instability of flows that are stable initially, i.e. the initial nonlinear fluxesare hyperbolic. Stability requires the hyperbolicity to persist at large times, whereasinstability sets in when ellipticity is encountered as the system evolves. In the formercase the solution decays asymptotically to its uniform base state, while in the lattercase nonlinear travelling waves can emerge that could not be predicted by a linearstability analysis. The nonlinear analysis predicts threshold initial disturbances abovewhich instability emerges.
AU  - Papageorgiou,DT
AU  - Papaefthymiou,ES
DO  - 10.1017/jfm.2017.605
PY  - 2017///
SN  - 0022-1120
TI  - Nonlinear stability in three-layer channel flows
T2  - Journal of Fluid Mechanics
UR  - http://dx.doi.org/10.1017/jfm.2017.605
UR  - http://hdl.handle.net/10044/1/50422
VL  - 829
ER  -
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