Population trends of spanwise vortices in wall turbulence

Abstract

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.