Wall roughness produces a downward shift of the mean streamwise velocity profile in the log region, known as the roughness function. The dependence of the roughness function on the height and arrangement of roughness elements has been confirmed in several studies where regular rough walls were analysed; less attention has been paid to non-regular rough walls. Here, a numerical analysis of turbulent flows over irregularly shaped rough walls is performed, clearly identifying the importance of a parameter, called the effective slope (ES) of the wall corrugations, in characterizing the geometry of non-smooth irregular walls. The effective slope proves to be one of the fundamental geometric parameters for scaling the roughness function. Specifically, for a moderate range of roughness heights, both in the transitionally and in the fully rough regime, ES appears to scale the roughness function for a wide range of irregular rough geometric configurations. The effective slope determines the relative importance of friction drag and pressure drag. For ES ~ 0.15 we find that the friction contribution to the total wall stress is nearly in balance with the pressure-drag contribution. This value separates the region where the roughness function ΔU+ = f(ES) is linear from that where a smooth nonlinear behaviour is observed. In the cases investigated, value ES ~ 0.15 also separates the transitionally rough regime from the fully rough regime.
