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

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  • J. Rolland
  • P. Manneville

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

Suggested Citation

  • J. Rolland & P. Manneville, 2011. "Ginzburg–Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 80(4), pages 529-544, April.
    • Handle: RePEc:spr:eurphb:v:80:y:2011:i:4:p:529-544
    DOI: 10.1140/epjb/e2011-10730-1
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    Cited by:

    1. Faranda, Davide & Lucarini, Valerio & Manneville, Paul & Wouters, Jeroen, 2014. "On using extreme values to detect global stability thresholds in multi-stable systems: The case of transitional plane Couette flow," Chaos, Solitons & Fractals, Elsevier, vol. 64(C), pages 26-35.

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