Influence of the surface roughness on inner–outer interactions in a turbulent Couette–Poiseuille flow

Abstract

When rod surface roughness is introduced in a turbulent Couette–Poiseuille flow (CP-flow), it is known that the Reynolds stresses near the centerline decrease due to weakened very-large-scale motions (VLSMs) and roll-cell motions [Lee, Y. M. et al., “Direct numerical simulation of a turbulent Couette–Poiseuille flow with a rod-roughened wall,” Phys. Fluids 30, 105101 (2018)]. In the present study, we examine the origin of the weakened turbulent structures near the centerline in a CP-flow with roughness (CPR-flow) using a dataset from direct numerical simulation. The top–down and bottom–up interactions to organize a CP-flow are very similar to those found in earlier studies in turbulent channel/pipe and boundary layer flows. The circulation of roll-cells in the outer region induces the spanwise congregation of negative streamwise velocity fluctuating structures (u) near the wall, leading to a large-scale ejection into the outer region. This large-scale ejection contributes to the formation of a negative VLSM when two adjacent negative large-scale motions merge, and the VLSM induces the circulation of roll-cell motion due to the pure kinematics. A similar process for the inner–outer interactions is found for a CPR-flow. However, because the impact of the surface roughness suppresses the collective motion of negative u-structures near the surface roughness, strong congregation by roll-cells is observed to occur far from the wall, indicating that relatively few negative u-structures with low strength contribute to the formation of a large-scale ejection for the CPR-flow. The weakened large-scale ejection decreases the strength of the VLSM, resulting in weakened roll-cell motion.