2011/02/15 by Joran Rolland, Paul Manneville
Computer Science · Engineering · Environmental Science · Physics and Astronomy · #Fluid Dynamics and Turbulent Flows #Nonlinear Dynamics and Pattern Formation #Plant Water Relations and Carbon Dynamics #physics.flu-dyn
paper · pdf · doi:10.1140/epjb/e2011-10730-1
published as European Physics Journal B volume 80, pages 529--544 (2011) · 21 pages 21 figures. Accepted for publication in European Physics Journal B
arxiv created 2011/02/15 · openalex publication_date 2011/03/24 · arxiv updated 2011/04/11 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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 [Rg,Rt]. 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 Rt, 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.