Marginally turbulent Couette flow in a spanwise confined passage of square cross section

Abstract

The results of direct numerical simulations to determine the critical conditions for self-sustained turbulence in wall-driven (Couette) square duct flow and its characteristics at relatively low turbulent Reynolds numbers are presented. We focus on the case in which a pair of opposite counter-moving walls translating with the same speed drives the flow. Stabilisation by the side walls is found to play a crucial role in the transition to turbulence, the minimum Reynolds number for maintaining a turbulent state (Rec ≈ 875) being much greater than that in a plane channel. At Reynolds numbers close to the critical, an alternation of the flow field, in time, between two states characterised by a four-vortex secondary flow pattern is observed, one being a mirror reflection of the other, and the flow remains approximately symmetrical about the common bisector of the moving walls. Due to the intermittency, large velocity fluctuations about the long-term mean are observed at different locations in the duct. These findings are consistent with results of previous studies on turbulent pressure-driven (Poiseuille) square duct flow at low Reynolds numbers; hence, the phenomenon is not unique to Poiseuille flows. Instantaneous flow field visualisations reveal the existence of coherent structures which are persistent over the length of the duct, thus indicating that the states are very stable in the streamwise direction. Quadrant analysis of the Reynolds shear stress shows that the secondary motions are closely related to the near-wall ejection and sweeping events.