Reynolds number and roughness effects on turbulent stresses in sandpaper roughness boundary layers

Multicomponent turbulence measurements in rough-wall boundary layers are presented and compared to smooth-wall data over a large friction Reynolds number range (delta(+)). The rough-wall experiments used the same continuous sandpaper sheet as in the study of Squire et al. [J. Fluid Mench. 795, 210 (20:16)]. To the authors' knowledge, the present measurements are unique in that they cover nearly an order of magnitude in Reynolds number (delta(+)similar or equal to 2800-17 400), while spanning the transitionally to fully rough regimes (equivalent sand-grain-roughness range, k(s)(+)similar or equal to 37 - 98), and in doi ng so also maintain very good spatial resolution. Distinct from previous studies, the inner-normalized wall-normal velocity variances, (w) over bar (2), exhibit clear dependencies on both k(s)(+) and delta(+) well into the wake region of the boundary layer, and only for fully rough flows does the outer portion of the profile agree with that in a comparable delta(+) smooth-wall flow. Consistent with the mean dynamical constraints, the inner-normalized Reynolds shear stress profiles in the rough-wall flows are qualitatively similar to their smooth-wall counterparts. Quantitatively, however, at matched Reynolds numbers the peaks in the rough-wall Reynolds shear stress profiles are uniformly located at greater inner-normalized wall-normal positions. The Reynolds stress correlation coefficient, R-uw is also greater in rough-wall flows at a matched Reynolds number. As in smooth-wall flows, R-uw decreases with Reynolds number, but at different rates depending on the roughness condition. Despite the clear variations in the Ruw profiles with roughness, inertial layer u, w cospectra evidence invariance with k(s)(+) when normalized with the distance from the wall. Comparison of the normalized contributions to the Reynolds stress from the second quadrant (Q2) and fourth quadrant (Q4) exhibit noticeable differences between the smooth- and rough-wall flows. The overall time fraction spent in each quadrant is, however, shown to be nearly fixed for all of the flow conditions investigated. The data indicate that at fixed delta(+) both Q2 and Q4 events exhibit a sensitivity to k(s)(+) The present results are discussed relative to the combined influences of roughness and Reynolds number.