The modulation of the turbulent structures in channel flow with porous and rough wall

Flows over porous walls at friction Reynolds number Reτ≈198 are investigated using the lattice Boltzmann method, where the rough and porous walls are treated as spherical arrays. Compared with the smooth wall, the wall roughness significantly enhances the Reynolds shear stress in the near-wall region due to the stronger upwash and downwash motions, and the downwash motion is stronger in the permeable-wall case. As the turbulent fluctuation is closely related to the near-wall coherent structures, the characteristic structures are investigated. In both cases, the near-wall turbulent structures and the relatively large-scale spanwise rollers are identified. Through the clustering method, the spatial distributions of the coherent structures with different wall-normal scales (ly+) are analyzed, and it is found that the near-wall vortical structures with ly+) < d (d is the roughness height) dominate below the logarithmic region (y≲0.1H, where H represents the distance from the crest of the sphere to the upper wall), while the relatively large-scale spanwise rollers with ly+≳d are distributed within the logarithmic region. Furthermore, turbulent fluctuations contributed from different scales of vortical structures are analyzed. It is observed that the fluctuation of the coherent structures is reduced in the permeable-wall case compared with the rough-wall case, and the reduction of the near-wall vortical structures is stronger. Finally, the conditional averaged flow reveals the similarity of the spatial distribution of low/high-speed structures in the rough and permeable wall, but the normal size of the high-speed fluid structure is decreased in the permeable wall, indicating the downward motion.