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

J. Rolland () and P. Manneville

The European Physical Journal B: Condensed Matter and Complex Systems, 2011, vol. 80, issue 4, 529-544

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. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Date: 2011
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DOI: 10.1140/epjb/e2011-10730-1

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