Surface roughness effects on turbulent Couette flow

Direct numerical simulation of a turbulent Couette flow with two-dimensional (2-D) rod roughness is performed to examine the effects of the surface roughness. The Reynolds number based on the channel centerline laminar velocity ($U_{co})$ and channel half height ($h)$ is \textit{Re}$=$7200. The 2-D rods are periodically arranged with a streamwise pitch of $\lambda =$8$k$ on the bottom wall, and the roughness height is $k=$0.12$h$. It is shown that the wall-normal extent for the logarithmic layer is significantly shortened in the rough-wall turbulent Couette flow, compared to a turbulent Couette flow with smooth wall. Although the Reynolds stresses are increased in a turbulent channel flow with surface roughness in the outer layer due to large-scale ejection motions produced by the 2-D rods, those of the rough-wall Couette flow are decreased. Isosurfaces of the $u$-structures averaged in time suggest that the decrease of the turbulent activity near the centerline is associated with weakened large-scale counter-rotating roll modes by the surface roughness.