Eur. Phys. J. B 80, 529-544 (2011)
https://doi.org/10.1140/epjb/e2011-10730-1

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

Laboratoire d'hydrodynamique de l'École Polytechnique, 91128 Palaiseau, France

Corresponding author: ^a joran.rolland@ladhyx.polytechnique.fr

Received: 22 September 2010
Revised: 6 January 2011
Published online: 24 March 2011

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.