Impact of spanwise effective slope upon rough-wall turbulent channel flow. (25th November 2022) - Jelly, T.O.; Ramani, A.; Nugroho, B.; Hutchins, N.; Busse, A.
Abstract: Abstract : Whereas streamwise effective slope ( ES_x ) is accepted as a key topographical parameter in the context of rough-wall turbulent flows, the significance of its spanwise counterpart ( ES_y ) remains largely unexplored. Here, the response of turbulent channel flow over irregular, three-dimensional rough walls with systematically varied values of ES_y 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 ES_y for three different values of ES_x . 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 ES_y, since roughness amplitude, skewness and ES_x 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 ES_y can strongly affect the roughness drag penalty – particularly for low- ES_x surfaces. A secondary observation is that particular low- ES_y 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.