Utilizing an optically index-matched facility and high-resolution particle image velocimetry measurements, this paper examines flow structure and turbulence in a rough-wall channel flow for Re in the 3520-5360 range. The scales of pyramidal roughness elements satisfy the well-characterized flow conditions, with h/k 50 and k+ = 60 ~ 100, where h is half height of the channel and k is the roughness height. The near-wall turbulence measurements are sensitive to spatial resolution, and vary with Reynolds number. Spatial variations in the mean flow, Reynolds stresses, as well as the turbulent kinetic energy (TKE) production and dissipation rates are confined to y < 2k. All the Reynolds stress components have local maxima at slightly higher elevations, but the streamwise-normal component increases rapidly at y < k, peaking at the top of the pyramids. The TKE production and dissipation rates along with turbulence transport also peak near the wall. The spatial energy and shear spectra show an increasing contribution of large-scale motions and a diminishing role of small motions with increasing distance from the wall. As the spectra steepen at low wavenumbers, they flatten and develop bumps in wavenumbers corresponding to k 3k, which fall in the dissipation range. Instantaneous realizations show that roughness-scale eddies are generated near the wall, and lifted up rapidly by large-scale structures that populate the outer layer. A linear stochastic estimation-based analysis shows that the latter share common features with hairpin packets. This process floods the outer layer with roughness-scale eddies, in addition to those generated by the energy-cascading process. Consequently, although the imprints of roughness diminish in the outer-layer Reynolds stresses, consistent with the wall similarity hypothesis, the small-scale turbulence contains a clear roughness signature across the entire channel.
Bibliographical noteFunding Information:
This research has been funded by the Office of Naval Research under grant N00014-06-1-0650. The programme officer is Ronald Joslin. Construction of the optically index-matched facility has been funded by ONR, in part under grant N00014-06-1-0160, and in part by DURIP grant N00014-06-1-0556. The programme officer is Ki Han Kim. The authors would like to thank Yury Ronzhes for designing the new facility, as well as Siddharth Talapatra, Joshi Pranav and Huixuan Wu for their help during the experiments.
- boundary layer structure
- boundary layers
- turbulent boundary layers