Outer-layer similarity and coherent structures in turbulent boundary layer over smooth and rough wall

In the paper, we investigate the outer-layer similarity and coherent structures comparing the smooth-wall and rough-wall turbulent boundary layers (TBLs) in the streamwise-wall-normal plane at a low Reynolds number. Global quantities derived from planar velocity fields, measured via two-dimensional particle image velocimetry, are comprehensively assessed under varied surface conditions. The verification of Townsend’s outer-layer similarity is explored based on the comparisons of the mean velocity flow, velocity deficit, Reynolds stress, and diagnostic plots of the second-order statistics, even at these relatively low Reynolds numbers. The analysis of energy spectra and spatial correlation demonstrates that while the energy associated with large-scale motions attenuates and the small-scale fluctuations amplify near the wall, an outer energy peak is still observed, and the coherent structures at higher wall-normal positions are enhanced, retaining the basic spatial topology. Proper orthogonal decomposition, deemed as a global method based on the energy distribution, elucidates similarities in the low-order modes alongside distinct differences in the energy patterns, in agreement with the mechanisms observed in pre-multiplied energy spectra. Furthermore, flow structures associated with the energy transport, particularly ejection (Q2), sweep (Q4) events, and clockwise vortices, are identified by applying conditional average and quadrant analysis to the filtered velocity fields. The Q2/Q4 events, modulated by vortices induced by surface roughness, collectively delineate the footprints of large-scale fluctuations. Additionally, the small-scale flow fields over the rough surface display the wider and stronger upwash and downwash motions, which can be regarded as an imprint of high-speed momentum. These findings offer novel insights into the behavior of TBLs over both smooth and rough surfaces.