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 ( Re-tau approximate to 600-2000) and intermediate to high relative submergences ( h/k(s) = 6.3-14.7, where h is the flow depth and k(s) 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 ( Re-tau approximate to 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 lambda xWA) increases linearly with y. Furthermore, WAMs in rough OCFs have larger streamwise wavelengths ( lambda(xWA)approximate to 25 y) and inclination angles ( theta(uuWA)approximate to 18 degrees) compared to their smooth-wall counterparts ( lambda(xWA)approximate to 18.3 y, theta(uuWA)approximate to 14 degrees). The strength of WAMs in rough OCFs was lower than that in smooth OCFs, due to the effects of rough wall elements.