Impact of spanwise effective slope upon rough-wall turbulent channel flow

Whereas streamwise effective slope ( ESₓ ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( ESy ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of ESy is studied using direct numerical simulation. All simulations were performed at a fixed friction Reynolds number 395, corresponding to a viscous-scaled roughness height k⁺≈ 65.8 (where k is the mean peak-to-valley height). A surface generation algorithm is used to synthesise a set of ten irregular surfaces with specified ESy for three different values of ESₓ . All surfaces share a common mean peak-to-valley height and are near-Gaussian, which allows this study to focus on the impact of varying ESy , since roughness amplitude, skewness and ESₓ can be eliminated simultaneously as parameters. Based on an analysis of first- and second-order velocity statistics, as well as turbulence co-spectra and the fractional contribution of pressure and viscous drag, the study shows that ESy can strongly affect the roughness drag penalty – particularly for low- ESₓ surfaces. A secondary observation is that particular low- ESy surfaces in this study can lead to diminished levels of outer-layer similarity in both mean flow and turbulence statistics, which is attributed to insufficient scale separation between the outer length scale and the in-plane spanwise roughness wavelength.