Scale arrangements in the turbulent boundary layer flow over a zigzag riblet surface

The drag-reduction effect and the influence on multi-scale structures arrangements of zigzag riblets surfaces were investigated using particle image velocimetry in fully developed turbulent boundary flows at friction Reynolds numbers in the range of 300-700. The zigzag riblets were designed by introducing spanwise induction of streamwise periodicity on the streamwise riblets. The zigzag riblet surface reaches larger drag reduction rates than that for streamwise riblets. Fluctuating velocities are decomposed into large-scale and small-scale components using proper orthogonal decomposition. In the region of 10-100 viscous units away from the wall, both large-scale and small-scale turbulent components exhibit a reduction in intensity. Within 10 viscous units from the wall, the intensity of large-scale components increases, while that of small-scale components decreases. Spatial forms of multi-scale structures were detected by autocorrelation methods, finding large-scale structures (LCSs) and small-scale structures (SCSs) exhibits a smaller inclination angle and a larger spatial dimension, respectively. The amplitude modulation of LCSs on SCSs, referred by cross-events of LCS and SCS, decreases significantly in near-wall regions, indicating the weakened interactions between LCSs and SCSs. These variations were elucidated by examining the configurations of scale arrangements. The phase relationships between LCSs and SCSs were identified using conditional averaging techniques based on cross-zeros of large-scale streamwise fluctuating velocities from positive to negative. SCSs appear before LCSs over the smooth surface, while the lag of phases between SCSs and LCSs over zigzag riblets is larger than that over the smooth surface. This arrangement may be favorable to drag reduction in turbulent boundary layer flows.