Direct numerical simulation study in turbulent boundary layers with the cube-roughened walls

Direct numerical simulations of turbulent boundary layers over the cube-roughened walls were performed to investigate the effects of the streamwise ($p_{x}/k)$ and spanwise ($p_{z}/k)$ extents between the cubes on the properties in the outer-layer statistics. The streamwise extent of the cubes was varied from $p_{x}/k$=2, 3, 4, 6, 8, and 10 at fixed $p_{z}/k$=2 and, the spanwise extent of the cubes was varied from $p_{z}/k$=2, 3, 4 6 including aligned configuration at fixed $p_{x}/k$=3, where $k$ is the roughness height. The results showed that the outer peak values of the Reynolds stresses are increased with increasing streamwise spacing, indicating the strong inner and outer-layer interaction at large $p_{x}/k$ and the profiles of the Reynolds stresses with varying spanwise spacing show the similar trends in the outer region except $p_{z}/k$=4. In addition, we found that there is no difference between staggered and aligned cube geometries.