Direct numerical simulations in turbulent boundary layers over cube-roughened walls with varying spanwise spacing

Direct numerical simulations of turbulent boundary layers over three-dimensional cube-roughened walls were performed to investigate the effects of the spanwise spacing ($p_{z}/k)$ on the turbulent statistics. The spanwise extent between the cubes was varied $p_{z}/k$=2, 3, 4 and 6 at the fixed streamwise extent ($p_{x}/k$=3), where $k$ is the roughness height. Lee \textit{et al}. (2012) examined by varying the streamwise extent (2$\le p_{x}/k\le $10) that the roughness function has the maximum contribution at $p_{x}/k$=4 and the outer value of the Reynolds stresses at \textit{y/$\delta $}$\approx $0.4 increases with increasing the streamwise pitch ($p_{x}/k)$. The roughness function has the local maximum at $p_{z}/k$=3 and the value of the Reynolds stresses at the same outer location increases linearly with increasing the spanwise pitch ($p_{z}/k)$. This implies that the wall friction is closely correlated with the roughness density because the roughness function has the maximum at the similar roughness density and there is also a strong interaction between the inner and outer regions at large spacing values of $p_{z}/k$. Furthermore, we can understand the roughness effects on the turbulence structures.