On the effect of streamwise and spanwise spacing to height ratios of three-dimensional sinusoidal roughness on turbulent boundary layers

A developing zero pressure gradient (ZPG) turbulent boundary layer (TBL) over different three-dimensional (3D) sinewave roughnesses is investigated experimentally using single hot-wire anemometry. Seven different sinewave profiles are fabricated with the same amplitude and with different wavelengths in the streamwise (sx) and spanwise (sz) directions. The effects of varying sx and sz on turbulence statistics and the drag coefficient (Cf) are assessed. The wall-unit normalized streamwise mean velocity profile is shifted downward compared with the smooth wall profile for all roughnesses. The streamwise spacing to height ratio sx=k has a more significant effect on the roughness function DUthorn and Cf compared with the spanwise spacing to height ratio sz=k. However, sz=k has a large impact on the streamwise turbulence intensities in the log and outer layer. An excellent collapse is observed among the mean streamwise velocity profiles plotted in defect form in the outer region. However, a lack of similarity between TBLs over different rough surfaces is observed in the outer region for the turbulence intensities profiles. For isotropic 3D sinusoidal roughness (equal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing spacing to height ratios. For anisotropic 3D sinusoidal roughness (unequal streamwise and spanwise spacing to height ratios), the contours of premultiplied streamwise turbulent energy spectrograms show an increase in energy in the outer layer with increasing sz=sx from half to two in this study.