Direct numerical simulation on the effects of surface slope and skewness on rough-wall turbulence

This paper presents direct numerical simulation results of turbulent flows over systematically varied rough surfaces. Three-dimensional irregular rough surfaces with varying effective slope and skewness factor and fixed roughness height scales were considered in the study. The skewness factor characterizes whether the surface of interest has a peak-dominated or valley-dominated nature, whereas the effective slope measures the wavelength of the surface undulations or solidity of the roughness elements. The influence of these two topological parameters on the friction drag at rough surfaces was investigated. Downward shifts in the inner-scaled mean velocity, which quantify an increase in the friction drag, were found to be larger for surfaces with a positive skewness factor, and this trend was found to be more pronounced as the effective slope increased. In addition, the downward shift value steeply increased with increases in the effective slope, while the dependence weakened when the effective slope was larger than a certain threshold value. The physical mechanism behind the increase in the roughness function was investigated by analyzing the momentum budgets. It was revealed that the viscous drag dominantly contributes to the roughness function when the effective slope value is small, whereas the contribution by the pressure drag progressively increases with the effective slope. We also found that for surfaces with larger effective slope consisting of relatively shorter wavelength undulations, the Reynolds shear stress tends to be reduced because the wall roughness prevents the formation of quasi-streamwise elongated vortices suppressing the turbulent near-wall cycles. This acts as a negative contribution to the roughness function, and the two competing effects (of the increase in pressure drag and decrease in Reynolds shear stress) weaken the dependence of the effective slope value on the roughness function. Further analysis was conducted to better understand how the surface slope and skewness factor values affect the mean flow field, modifying the pressure and viscous drag forces.