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

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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.

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Authors and Affiliations

  1. Laboratoire d’hydrodynamique de l’École Polytechnique, 91128, Palaiseau, France

    J. Rolland & P. Manneville

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  1. J. Rolland
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  2. P. Manneville
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Correspondence to J. Rolland.

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Rolland, J., Manneville, P. Ginzburg–Landau description of laminar-turbulent oblique band formation in transitional plane Couette flow. Eur. Phys. J. B 80, 529–544 (2011). https://doi.org/10.1140/epjb/e2011-10730-1

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  • DOI: https://doi.org/10.1140/epjb/e2011-10730-1

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