Roughness effect in turbulent Couette-Poiseuille flow over a rod-roughened wall*

Direct numerical simulations of fully developed turbulent Couette-Poiseuille flow over a rod-roughened wall is performed to investigate the effects of two-dimensional surface roughness elements at Re=7200, based on the centerline laminar velocity and channel half-height (h). The roughness elements are periodically arranged on the bottom wall with a streamwise pitch of p=8k and the roughness height is k/h=0.12, where k is roughness height. The mean velocity profile shows that the logarithmic layer of a turbulent Couette-Poiseuille flow is shortened by surface roughness, compared to that for the smooth wall.  The Reynolds stresses for the Couette-Poiseuille flow with rod roughness are decreased in the outer layer, contrary to the observation in the turbulent Poiseuille flow with rod roughness, revealed by the decomposition of the Reynolds stresses. The temporally averaged u-structures for the Couette-Poiseuille flow show that the large-scale roll mode dominates the whole domain region but with the significantly weakened roll mode for the flow with rod roughness.