The present effort documents the population trends of prograde and retrograde spanwise vortex cores in wall turbulence outside the buffer layer. Large ensembles of instantaneous velocity fields are acquired by particle-image velocimetry in the streamwise-wall-normal plane of both turbulent channel flow at Re τ ≡ u * δ/ν = 570, 1185 and 1760 and a zero-pressure-gradient turbulent boundary layer at Re τ = 1400, 2350 and 3450. Substantial numbers of prograde spanwise vortices are found to populate the inner boundary of the log layer of both flows and most of these vortices have structural signatures consistent with the heads of hairpin vortices. In contrast, retrograde vortices are most prominent at the outer edge of the log layer, often nesting near clusters of prograde vortices. Appropriate Reynolds-number scalings for outer-and inner-scaled population densities of prograde and retrograde vortices are determined. However, the Re τ = 570 channel-flow case deviates from these scalings, indicating that it suffers from low-Re effects. When the population densities are recast in terms of fractions of resolved prograde and retrograde spanwise vortices, similarity is observed for 100 < y + < 0.8δ + in channel flow and in both flows for 100 < y + < 0.3δ + over the Re τ range studied. The fraction of retrograde vortices increases slightly with Re τ beyond the log layer in both flows, suggesting that they may play an increasingly important role at higher Reynolds numbers. Finally, while the overall prograde and retrograde population trends of channel flow and the boundary layer show little difference for y < 0.45δ, the retrograde populations differ considerably beyond this point, highlighting the influence of the opposing wall in channel flow. IntroductionThe results of many recent experimental and computational studies suggest that wall turbulence is populated by hairpin vortices that tend to streamwise-align into larger-scale coherent groups termed vortex packets. The phrase 'hairpin vortex' is used herein to describe both symmetric and asymmetric hairpin-, lambda-and arch-like structures that are composed of either one or two streamwise-oriented legs connected to a spanwise-oriented head whose rotation is of the same sense as the mean shear. (Spanwise vortices with rotation in the same sense as the mean shear, hairpin heads or otherwise, are hereafter referred to as 'prograde' spanwise vortices.) These structures are qualitatively consistent with the horseshoe vortex first proposed by Theodorsen

Particle image velocimetry experiments were performed to study the impact of realistic roughness on the spatial structure of wall turbulence at moderate Reynolds number. This roughness was replicated from an actual turbine blade damaged by deposition of foreign materials and its features are quite distinct from most roughness characterizations previously considered as it is highly irregular and embodies a broad range of topographical scales. The spatial structure of flow over this rough surface near the outer edge of the roughness sublayer is contrasted with that of smooth-wall flow to identify any structural modifications due to roughness. Hairpin vortex packets are observed in the outer layer of the rough-wall flow and are found to contribute heavily to the Reynolds shear stress, consistent with smooth-wall flow. While similar qualitative consistency is observed in comparisons of smooth- and rough-wall two-point correlations, some quantitative differences are also apparent. In particular, a reduction in the streamwise extent of two-point correlations of streamwise velocity is noted which could be indicative of a roughness-induced modification of outer-layer vortex organization. Proper orthogonal decomposition analysis reveals the streamwise coherence of the larger scales to be most sensitive to roughness while the spatial characteristics of the smaller scales appear relatively insensitive to such effects.

High-resolution particle image velocimetry measurements are made in the streamwise-wall-normal plane of a zero-pressure-gradient turbulent boundary layer over smooth and rough walls at Re Ϸ 13000. The roughness considered herein is replicated from a surface scan of a turbine blade damaged by deposition of foreign materials and its topography is highly irregular and contains a broad range of topographical scales. Two physical scalings of the same roughness topography are considered, yielding two different rough surfaces: RF1 with k = 4.2 mm and RF2 with k = 2.1 mm, where k is the average peak-to-valley roughness height. At Re Ϸ 13000, these roughness conditions yield k + ϵ k / y * = 207, ␦ / k = 28, k s + = 115, and ␦ / k s = 48 for RF1 and k + = 91, ␦ / k = 50, k s + = 29, and ␦ / k s = 162 for RF2 ͑where ␦ is the boundary-layer thickness, k s is the equivalent sand-grain height, and y * is the viscous length scale͒. The mean velocity deficits along with the Reynolds normal and shear stress profiles for both roughness conditions collapse on the smooth-wall baseline in the outer layer when appropriately scaled by the friction velocity, u . Probability density functions and quadrant analysis of the instantaneous events contributing to the mean Reynolds shear stress show similar outer-layer consistency between the smooth and rough cases when scaled appropriately with u . In addition, one-dimensional, two-point streamwise, and wall-normal velocity autocorrelation coefficients are also found to collapse in the outer region, indicating a similarity in the spatial structure of the outer-layer turbulence. The observed collapse of the smooth-and rough-wall turbulence statistics in the outer layer supports Townsend's wall similarity hypothesis for flow over the unique surface topography considered herein.

This study established the connection in turbulent boundary layers between the first two dominant proper orthogonal decomposition (POD) modes and the instantaneous large-scale turbulence structures. The velocity fields consistent with the signature velocity fields of the hairpin vortex packets in two-dimensional PIV (particle image velocimetry) measurement planes are observed as the major contributors to the first two POD modes. Another kind of equally important turbulence structure is the large region of Q4 vectors, which may possibly be obtained by slicing the outskirts of the three-dimensional structure of the hairpin vortex packet by PIV planes. The streamwise Reynolds normal stress, Reynolds shear stress, and the length scales of the two-point velocity correlation coefficients ρ uu and ρ uv are noticeably decreased without those large-scale turbulence structures contributing significantly to the first POD mode. Similarity of these results is observed at a higher Reynolds number.

The spatial signatures of retrograde spanwise vortices in wall turbulence are assessed from particle-image velocimetry measurements in the streamwise-wall-normal plane of a zero-pressure-gradient turbulent boundary layer at Re τ ≡ u * δ/ν = 2350. The present results suggest that a proportion of retrograde spanwise vortices have a welldefined spatial relationship with neighbouring prograde vortices. Two-point crosscorrelations and conditionally averaged velocity fields given a retrograde vortex reveal that such structures are typically oriented either upstream of and below or downstream of and above a prograde core. While these pairings are consistent with the typical-eddy patterns reported by Falco and co-workers, we offer an alternative interpretation for a proportion of these retrograde/prograde pairs. In particular, the arrangement of a retrograde spanwise vortex upstream of and below a prograde core is also consistent with the spatial signature revealed if an omega-shaped hairpin structure were sliced through its shoulder region by a fixed streamwise-wall-normal measurement plane.