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

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.

21 pages 21 figures. Accepted for publication in European Physics Journal B

References in corpus (2)

• Computational Study of Turbulent-Laminar Patterns in Couette Flow
• Pattern fluctuations in transitional plane Couette flow

Cited by in corpus (8)

• On the transition to turbulence of wall-bounded flows in general, and plane Couette flow in particular
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• Decay of streaks and rolls in plane Couette-Poiseuille flow
• Pattern fluctuations in transitional plane Couette flow
• Patterns in transitional shear turbulence. Part 2: Emergence and optimal wavelength
• Patterns in transitional shear turbulence. Part 1. Energy transfer and mean-flow interaction
• Mechanical and statistical study of the laminar hole formation in transitional plane Couette flow
• Formation of spanwise vorticy in oblique turbulent bands of transitional plane Couette flow, part 1: Numerical experiments