Modulating the near-wall velocity fields in wall-bounded turbulence via discrete surface roughness

The present work investigates the effect of discrete surface roughness, which falls in the transitionally rough regime, on the near-wall velocity fields of a smooth-wall turbulent boundary layer with zero pressure gradient. A spanwise array of cylindrical elements, whose diameters were d = 4 mmand heights were k = 5 mm, were attached onto the wall with spanwise spacing of Δz/d = 4. Three roughness Reynolds numbers Rek = 450, 1000, and 1500 were studied, and the ratio between the roughness height and the boundary-layer thickness was k/δ = 0.06 ~ 0.08. Two-dimensional velocity fields in multiple wall-parallel planes at y/k = 0.4 ~ 1.8 were measured by twodimensional particle image velocimetry. For each Rek case, it is found that roughness elements always introduce Δ-shaped low-speed regions in the near-wall mean velocity fields by direct wake interaction, in the downstream of which a phase shift occurs to form one high-speed mean streak with reduced streamwise velocity fluctuation intensity behind each roughness element, marking the onset of the modulation effect on the mean velocity fields. Further analysis on the swirling strength fields suggests that such a modulation effect can be attributed to the roughnessintroduced streamwise vortex pairs, which compete with hairpin vortices shedding from the top of the roughness elements and promote the phase shift in a bottom-up way.