Secondary motions and wall-attached structures in a turbulent flow over a random rough surface

Large-eddy simulations (LESs) are performed to explore the effects of roughness on the secondary motions (SMs) and wall-attached structures in a turbulent open-channel flow over a random rough surface at a friction Reynolds number of Re-tau approximate to 1000. Turbulent flow over two groups of rough walls - a homogeneous random arrangement and a clustered arrangement - is considered, and the results are compared with the turbulence over a smooth wall. The results show that the two roughness arrangements exhibit minor differences in the variation of mean streamwise velocity. The rough surfaces of a clustered arrangement can generate large-scale SMs, resulting in spanwise-alternating high-momentum pathways (HMPs) and low-momentum pathways (LMPs) in the time-averaged velocity. Because of SMs, the streamwise turbulence intensity is enhanced in the outer region and a larger-scale spectral peak occurs in the turbulence energy spectra. On the other hand, the outer-layer similarity is still satisfied for the homogeneous random arrangement. The wall-attached structures of streamwise velocity fluctuations in the presence of roughness are extracted through a three-dimensional clustering identification approach. The wall-attached structures retain their geometric self-similarity for both rough surfaces, whereas the length and width of these structures decreases and increases, respectively. The population density scales inversely with the height, reflecting the hierarchical nature of the structures. In addition, when the streamwise velocity fluctuations within the wall-attached structures are conditionally averaged, the profile exhibits logarithmic behavior in the logarithmic region for the homogeneous random arrangement; in the case of the clustered arrangement, the reconstructed profile is affected by the SMs. A new identification approach is applied to decompose the secondary flow structures into wall-detached structures, and the logarithmic behavior of the streamwise turbulence intensity is reconstructed on the basis of the new wall-attached structures. The present results provide evidence of the presence of the wall-attached structures in instantaneous flow fields of rough-wall turbulence, for both homogeneous and heterogeneous roughness arrangements.