Pattern formation in low Reynolds number plane Couette flow

Abstract

Plane Couette flow is the flow between two counter-sliding plates of velocity U separated by a gap 2h. It has a simple laminar solution with constant shear which is stable for all values of the Reynolds number $Re = \frac{Uh}{v}$ (v is the kinematic viscosity of the fluid). However, transition to turbulence is observed experimentally above a threshold value of Re between 300 and 400. Whereas featureless turbulence is seen for Re ≥ 400, lower-Re experiments have shown a turbulent regime displaying spatio-temporal intermittency effects, notably the appearance of turbulent stripes, inclined with respect to the direction of the base flow, interspersed with quiescent, nearly laminar regions [1], see Figure 1. It is the ‘fspiral turbulence’ regime, so-called because it has also been identified in Taylor-Couette experiments. Similar patterns have also been numerically reproduced in a minimal-like computational domain (of size 10h in length and 40h in width), oriented against the inclination of one stripe [2]. This reduced computational box allows to understand locally the appearance and teh stability of these localised structures.