Direct numerical simulation of a turbulent Couette-Poiseuille flow with a rod-roughened wall

A direct numerical simulation of a fully developed turbulent Couette-Poiseuille flow with a rod-roughened wall is performed to investigate the impact of the surface roughness on the flow characteristics compared to the influence of the roughness on a turbulent Poiseuille flow. Transverse rods are periodically arranged on the bottom wall with a streamwise pitch of p = 8k. The roughness height is k = 0.12h, where h is the channel half-height. The mean velocity profile shows that the logarithmic layer of a turbulent Couette-Poiseuille flow is significantly shortened by surface roughness, although that of a turbulent Poiseuille flow with surface roughness is increased. In addition, the Reynolds stresses for the Couette-Poiseuille flow with rod roughness are decreased in the outer layer, contrary to the observation of a turbulent Poiseuille flow with rod roughness. The decomposition of the Reynolds stresses into small- and large-scale motions confirms that the large-scale features dominantly contribute to the decrease of the Reynolds stresses in the outer layer. Although a large-scale counter-rotating roll mode is observed through temporally averaged streamwise fluctuating structures, the roll mode for the Couette-Poiseuille flow over a rough wall is significantly inhibited by the surface roughness due to weakened high- and low-streaky patterns near the centerline. The energy spectrum of the streamwise velocity fluctuations shows that the surface roughness contributes mainly to organizing the entire flow field; thus, the large-scale features observed in a turbulent Couette-Poiseuille flow are significantly suppressed with little interaction between the inner and outer layers.