Investigation of large-scale coherence in a turbulent boundary layer using two-point correlations

Abstract

Stereoscopic particle image velocimetry (PIV) measurements are made in streamwise–spanwise and inclined cross-stream planes (inclined at $45^\circ$ and $135^\circ$ to the principal flow direction) of a turbulent boundary layer at moderate Reynolds number ($\hbox{\it Re}_\tau\,{\sim} 1100$). Two-point spatial velocity correlations computed using the PIV data reveal results that are consistent with an earlier study in which packets of hairpin vortices were identified by a feature-detection algorithm in the log region, but not in the outer wake region. Both streamwise–streamwise ($R_{\hbox{\scriptsize\it uu}}$) and streamwise–wall-normal ($R_{uw}$) correlations are significant for streamwise displacements of more than 1500 wall units. Zero crossing data for the streamwise fluctuating component $u$ reveal that streamwise strips between zero crossings of 1500 wall units or longer occur more frequently for negative $u$ than positive $u$, suggesting that long streamwise correlations in $R_{\hbox{\scriptsize\it uu}}$ are dominated by slower streamwise structures. Additional analysis of $R_{ww}$ correlations suggests that the long streamwise slow-moving regions contain discrete zones of strong upwash over extended streamwise distances, as might occur within packets of angled hairpin vortices. At a wall-normal location outside of the log region ($z/\delta \,{=}\, 0.5$), the correlations are shorter in the streamwise direction and broader in the spanwise direction. Correlations in the inclined cross-stream plane data reveal good agreement with the streamwise–spanwise plane. $R_{\hbox{\scriptsize\it uu}}$ in the $45^\circ$ plane is more elongated along the in-plane wall-normal direction than in the $135^\circ$ plane, which is consistent with the presence of hairpin packets with a low-speed region lifting away from the wall.