Influence of surface roughness on co-supporting cycle in a turbulent plane Couette-Poiseuille flow

Direct numerical simulations of fully developed turbulent plane Couette-Poiseuille flows (C-P flows) with and without a two-dimensional rod-roughened wall are performed to investigate the influence of the surface roughness on the flows. The Reynolds number based on the centerline laminar velocity and channel half-height is \textit{Re}$=$7200. When the surface roughness is imposed in the C-P flow with the smooth wall, the magnitude of the Reynolds shear stress decreases in the outer layer due to weakened very-large-scale motions (VLSMs) and roll-cell mode near the channel centerline Although the congregation of the near-wall small-scale motions by the roll-cell mode contributes to the formation of the VLSMs and the VLSMs, in turn, generate the roll-cell mode in the smooth-wall C-P flow, the weakened congregation motions of the small-scales by influence of the surface roughness reduces the strength of the VLSMs and roll-cell pattern.