Outer-layer similarity from the perspective of uniform momentum zones in turbulent boundary layer over smooth and rough wall

• Outer-layer similarity confirmed in smooth/rough turbulent boundary layers (TBLs) via uniform momentum zone (UMZ) framework. • UMZs arranged hierarchically: thinner near-wall, higher number of UMZ ( N UMZ ), faster modes. • N UMZ -based averaging shows shared and distinct flow/turbulence features. • Sweep–ejection interactions altered in rough-wall quadrant analysis. • Two-point correlations reveal coherent structures across both surfaces. The study investigates outer-layer similarity in turbulent boundary layers (TBLs) over smooth and rough walls through the lens of uniform momentum zones (UMZs), measured via two-dimensional particle image velocimetry (PIV) in the streamwise-wall-normal plane at moderate Reynolds numbers. Preliminary analyses of first-order and second-order statistics confirm the broad consistency of outer-layer dynamics across both wall conditions. The turbulent/non-turbulent interface (TNTI) and associated intermittency were examined in both cases, revealing a region of higher intermittency and a thicker boundary layer in the rough-wall case. Despite these differences, the multiple UMZs observed over both surfaces exhibit comparable structural features, consistent with the expectations of outer-layer similarity. A comparative assessment of UMZ geometrical properties—including modal velocity, interface height, and zone thickness—was conducted under two classification schemes. The observed hierarchical arrangement, where thinner near-wall UMZs evolve into thicker outer-layer zones with higher modal velocities, follows a consistent trend for both surfaces. Further insight was obtained by employing conditional averaging with respect to N UMZ , highlighting both the similarities and deviations in mean velocity, Reynolds stress, dissipation, and production, particularly within the logarithmic region. Quadrant analysis reveals that ejection (Q2) and sweep (Q4) events in rough-wall TBLs exhibit altered scale interactions between small-scale and large-scale motions compared to their smooth-wall counterparts. Two-point conditional correlation analyses stratified by N UMZ further delineate the spatial organization of coherent structures in both near-wall and outer regions, reinforcing the perspective of outer-layer similarity. Our research advances an innovative structural interpretation of the similarity hypothesis, offering a refined framework for examining universality in wall turbulence.