Scale- and order-dependent roughness effects on multiscale organization in turbulent boundary layers

It remains unclear whether roughness-induced differences across statistical orders merely reflect a redistribution of local statistical weight or instead indicate a reorganization of the underlying multiscale hierarchy of turbulence. Here, particle image velocimetry measurements of smooth- and rough-wall turbulent boundary layers at low-to-moderate Reynolds numbers are used to compare velocity structure functions across different flow conditions. Extended self-similarity, multifractal analysis, and characterization of the large-scale spatial organization are further employed to examine roughness effects across three complementary levels: scale, statistical order, and spatial structure. The results show that the lower-order structure functions exhibit strong similarity between the two wall conditions over a broad range of scales, whereas the smooth-rough differences become progressively more pronounced with increasing statistical order and emerge preferentially over scales that are more sensitive to intense velocity-increment events. Nevertheless, the relative-scaling relationships of the higher-order structure functions remain in close agreement between the two wall conditions, and the multifractal characteristics indicate similar cascade hierarchies. This suggests that roughness-induced modifications of the absolute velocity-increment statistics do not necessarily imply a corresponding reorganization of the underlying scale-cascade dynamics. Further analysis reveals that wall-attached large-scale motions over smooth and rough walls retain similar geometric scaling and spatial-coherence characteristics. In conclusion, these results indicate that roughness primarily modifies local statistics through the selective modulation of higher-order, strongly intermittent events over specific scales, while the relative cascade organization and large-scale spatial structure indicate substantially greater robustness to wall condition.