DNS of turbulent plane-Couette flow with surface roughness

Turbulent plane-Couette flow (pCf) between two smooth walls in relative motion is one of the classical problems in fluid mechanics. In practice, however, walls of pCf are never smooth and will have varying degrees of roughness. Barring the lone experimental study of Aydin and Leutheusser (1991), no information on turbulent pCf with surface roughness exists in the literature. In this work, a direct numerical simulation (DNS) of fully-developed turbulent pCf, where the bottom-wall is held stationary and the top-wall moves with a constant velocity U_w in its own plane, is considered to investigate roughness effects. The gap between the two walls is set as 2h. The Reynolds number, based on half the velocity difference between the walls and the channel half-height h, is set to Re = U_wh/2ν = 1300. Two-dimensional rods are periodically arranged with streamwise pitches s = 5r and 10r on the stationary wall and the roughness height is r = 0.2h. The present selection of s = 5r and 10r was made to obtain configurations of d-type and k-type roughness, respectively (Perry et al. 1969). The results have been compared with those of the turbulent pCf with smooth pCf. In each of the rough pCf cases, turbulent statistics collapsed above the channel centerline indicating a localized statistical homogeneity in the streamwise direction. Further, secondary roll cells with streamwise orientation that characterize the core region of smooth pCf are also visible in the current rough pCf cases. Upon roughening a wall, one would anticipate increased turbulence levels only in the near vicinity of the roughness elements. However, in the current rough pCf cases, it has been observed that turbulent kinetic energy (TKE) is increased near both the rough- and the smooth-walls. Further, TKE is higher near the smooth wall than the rough wall. This phenomenon is further elaborated upon using the budget of TKE.