Ginzburg-Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow

Abstract : Plane Couette flow, the flow between two parallel planes moving in opposite directions, is an example of wall-bounded flow experiencing a transition to turbulence with an ordered coexistence of turbulent and laminar domains in some range of Reynolds numbers [R g, R t] . When the aspect-ratio is sufficiently large, this coexistence occurs in the form of alternately turbulent and laminar oblique bands. As R goes up trough the upper threshold R t, the bands disappear progressively to leave room to a uniform regime of featureless turbulence. This continuous transition is studied here by means of under-resolved numerical simulations understood as a modelling approach adapted to the long time, large aspect-ratio limit. The state of the system is quantitatively characterised using standard observables (turbulent fraction and turbulence intensity inside the bands). A pair of complex order parameters is defined for the pattern which is further analysed within a standard Ginzburg-Landau formalism. Coefficients of the model turn out to be comparable to those experimentally determined for cylindrical Couette flow. © 2011 EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg.
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European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2011, 80 (4), pp.529-544. 〈10.1140/epjb/e2011-10730-1〉
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Soumis le : mercredi 4 juin 2014 - 10:48:26
Dernière modification le : jeudi 10 mai 2018 - 02:02:46

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Joran Rolland, Paul Manneville. Ginzburg-Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow. European Physical Journal B: Condensed Matter and Complex Systems, Springer-Verlag, 2011, 80 (4), pp.529-544. 〈10.1140/epjb/e2011-10730-1〉. 〈hal-00997977〉

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