DNS of plane Couette flow with surface roughness

Abstract

Direct numerical simulation of fully developed turbulent plane Couette flow (pCf) has been performed to investigate the effect of surface roughness. Flow characteristics in a statistically stationary field are then compared with the smooth pCf data. The present study considers a case, where the bottom wall is fixed, while the top wall is moving with a constant velocity $$U_{\mathrm{w}}$$ in the flow direction. For roughening, square ribs are placed on the stationary wall with a streamwise pitch $$\lambda = 5k$$, where $$k = 0.2h$$ is the roughness height and h is half the height between the walls. In the present study, we examined the flow and pressure fields around the ribs. For the pitch $$\lambda = 5k$$, a single recirculation zone is observed in the cavity between any two consecutive ribs. In addition, the profiles of the mean data in the channel core region at different streamwise locations are shown to collapse with each other, indicating that the flow is quasi-homogeneous in the streamwise direction. Further, counter-rotating secondary roll cells or Taylor–Gortler-like vortices, which evolve temporally and oriented along the flow direction, are also observed in the rough pCf. In addition, the large-scale turbulent structures are distorted into fine-scale motion around the ribs. Furthermore, the skin friction coefficient and the mean pressure fields are qualitatively similar to a rough Poiseuille flow (with ribs only on one wall).