| Rough-wall turbulence arises in many applications. Besides, most walls should often be considered to be rough in the high Reynolds number limit. Our objective has been to understand turbulence modifications for their relevance to statistical closure models on the rough-wall boundary layer via Direct Numerical Simulations (DNS). In this study, we performed the simulations of turbulent flow over rectangular-rib roughness, provided on one side of a plane in a channel, with the other side being smooth. The separation between ribs is large enough to reproduce k-type, or sand-grain roughness. The Reynolds number Retau of our representative DNS case is 460 based on the smooth-wall friction velocity and the channel half width. The roughness height h is estimated as 110 in wall units based on the rough-wall friction velocity.; Our study consists of two main parts. First, a numerical issue due to mesh stretch is discussed. It was found that statistical data were noticeably affected by the numerical mesh highly stretched in both the streamwise and wall-normal directions. Truncation error analysis shows that the energy conserving scheme produces anti-diffusion error if mesh is stretched, or positive diffusion if narrowed. However, high frequencies in turbulent flow cause further adverse effect on statistics, if solely the lowest-order error is removed. An appropriate form of convection scheme that minimizes the mesh-stretch error is proposed and evaluated through numerical analyses.; In the second part, the simulation results of the asymmetric channel flow are presented. The velocity profile and kinetic energy budget verify the presence of an equilibrium, logarithmic layer at y ≳ 2h. In the roughness sublayer, however, a significant turbulent energy flux was observed. Visualizations of vortical streaks, disrupted in all the three directions in the roughness sublayer, indicate that the three-dimensional flow structure of sand-grain roughness is replicated by the two-dimensional roughness, and that this vortical structure is responsible for high energy production. The difference in turbulence structure between smooth- and rough-wall layers can also be seen in other flow properties, such as anisotropy and turbulence length scales. |
