Comparison of statistical behavior of wall-attached motions in rough and smooth open channel flows

A set of high-resolution, time-resolved particle image velocimetry measurements were conducted in an open channel, with closely arranged glass spheres of 6 mm used to rough the bed, at low to moderate Reynolds numbers (Reτ≈ 600–2000) and intermediate to high relative submergences (h/ks = 6.3–14.7, where h is the flow depth and ks is the equivalent roughness height). Analyses of the wall-attached motions (WAMs) in rough-wall open channel flows (OCFs) are performed using linear coherence spectra at various wall-normal positions, and results of two smooth-wall OCFs are also included for comparison (Reτ≈ 500 and 900). The WAMs in rough-wall OCFs exhibit self-similar properties in the region of 0.2 <y/h< 0.8 (y is the wall-normal position and h is the flow depth), where the critical wavelength of WAMs (denoted as λxWA) increases linearly with y. Furthermore, WAMs in rough OCFs have larger streamwise wavelengths (λxWA≈ 25 y) and inclination angles (θuuWA≈ 18°) compared to their smooth-wall counterparts (λxWA≈ 18.3 y, θuuWA≈ 14°). The strength of WAMs in rough OCFs was lower than that in smooth OCFs, due to the effects of rough wall elements.