Energetic spanwise modes in the logarithmic layer of a turbulent boundary layer

The influence of large-scale outer-region motions on the properties and processes of the inner layer remains an open issue in wall turbulence research. In the present work, two-dimensional power spectra of the streamwise component are measured in streamwise-spanwise planes throughout the logarithmic region of smooth flat-plate turbulent boundary layers at $Re_\theta\,{=}\,1015$ and 7705. The spectra are based on PIV measurements with a wide spanwise view ($z/\delta\,{>}\, 2.5$), and the spanwise energy distribution is emphasized. The spectra reveal that the mode associated with the spacing of the low-speed streaks near the wall, $\lambda_z^+ \,{\approx}\, 100$, contains surprisingly little energy relative to modes in the range $\lambda_z^+ \,{\approx}\,$200–400 at $y^+ \,{=}\, 21$. This result is consistent with measurements in a channel flow (Liu et al. 1996) at a similar height. Further from the wall, large-scale structures that scale with outer variables organize with spacing $\lambda_z/\delta\,{=}\,$0.75–0.9, and these motions dominate the spanwise distribution of streamwise energy throughout the logarithmic region. The large spanwise modes are associated with the large streamwise modes on average, as the median energetic spanwise mode increases roughly linearly with increasing streamwise mode up to approximately $\lambda_{z,\mathrm{med}}/\delta \,{\approx}\, 0.8$, and then remains roughly constant for larger streamwise modes. The aspect ratio $\lambda_x / \lambda_{z,\mathrm{med}}$ decreases with increasing distance from the wall, suggesting that the most streaky structures remain buried near the wall.