Direct numerical simulation of turbulent flow over irregular rough surfaces

Direct numerical simulations of turbulent channel flow at a shear Reynolds number of Re*=360 in smooth and rough channels have been performed. Made of irregular undulations, surface roughness was such that the ratio of the channel half-height to the root mean square roughness height is equal to 48, and the root mean square and the maximum crest and trough heights are equal to 7.5 and 23 wall units, respectively. The simulation results confirm that turbulence in the outer layer is not directly affected by the rough surface. The roughness effects on the turbulent stresses, the mean momentum balance, and the budget of turbulence kinetic energy are confined to the layer between 0 and 25 wall units; beyond which the profiles collapse with those for smooth channels. In the roughness sublayer, the peak value of the streamwise normal stress is reduced, while the spanwise and wall-normal components are increased. The largest increase is for the Reynolds shear stress, resulting in a significant increase in the turbulence production near the wall, even though the velocity gradient is decreased. The kinetic energy budget shows that turbulence production dominates the mean viscous diffusion of turbulence kinetic energy, and both mechanisms are balanced by turbulent dissipation. The friction factor using the Colebrook–White correlation calculated by specifying the sand–grain roughness equal to the root mean square of the roughness height predicts the friction velocity and the bulk velocity accurately. The streaky structures that exist near smooth walls were observed to be broken by the roughness elements, leading to a denser population of coherent structures near the wall, which increases the velocity fluctuations. The coherent structures developed in the roughness layer do not seem to penetrate into the outer layer.