The structure of velocity in the outer region of turbulent channel flow (y⁺ [gsim ] 100) is examined statistically to determine the average flow field associated with spanwise vortical motions. Particle image velocimetry measurements of the streamwise and wall-normal velocity components are correlated with a vortex marker (swirling strength) in the streamwise–wall-normal plane, and linear stochastic estimation is used to estimate the conditional average of the two-dimensional velocity field associated with a swirling motion. The mean structure consists of a series of swirling motions located along a line inclined at 12°–13° from the wall. The pattern is consistent with the observations of outer-layer wall turbulence in which groups of hairpin vortices occur aligned in the streamwise direction. While the observational evidence for the aforementioned model was based upon both experimental and computational visualization of instantaneous structures, the present results show that, on average, the instantaneous structures occur with sufficient frequency, strength, and order to leave an imprint on the statistics of the flow as well. Results at Re_τ = 547 and 1734 are presented.

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 $\hbox{\it Re}_\tau\equiv u_*\delta/\nu=570$, 1185 and 1760 and a zero-pressure-gradient turbulent boundary layer at $\hbox{\it Re}_\tau=1400$, 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$_\tau=570$ 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 $100\,{<}\,y^+\,{<}\,0.8\delta^+$ in channel flow and in both flows for $100\,{<}\,y^+\,{<}\,0.3\delta^+$ over the Re$_\tau$ range studied. The fraction of retrograde vortices increases slightly with $Re_\tau$ 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 $y\,{<}\,0.45\delta$, the retrograde populations differ considerably beyond this point, highlighting the influence of the opposing wall in channel flow.

We study the dynamics of turbulent boundary layer flow over a heterogeneous topography composed of roughness patches exhibiting relatively high and low correlation in the streamwise and spanwise directions, respectively (i.e. the roughness appears as streamwise-aligned ‘strips’). It has been reported that such roughness induces a spanwise-wall normal mean secondary flow in the form of mean streamwise vorticity associated with counter-rotating boundary-layer-scale circulations. Here, we demonstrate that this mean secondary flow is Prandtl’s secondary flow of the second kind, both driven and sustained by spatial gradients in the Reynolds-stress components, which cause a subsequent imbalance between production and dissipation of turbulent kinetic energy that necessitates secondary advective velocities. In reaching this conclusion, we study (i) secondary circulations due to spatial gradients of turbulent kinetic energy, and (ii) the production budgets of mean streamwise vorticity by gradients of the Reynolds stresses. We attribute the secondary flow phenomena to extreme peaks of surface stress on the relatively high-roughness regions and associated elevated turbulence production in the fluid immediately above. An optimized state is attained by entrainment of fluid exhibiting the lowest turbulent stresses – from above – and subsequent lateral ejection in order to preserve conservation of mass.

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.