Outer-layer similarity and energy transfer in a rough-wall turbulent channel flow

• Published in: Journal of fluid mechanics 2023-08, Vol.968, Article A18
• Main Authors: Ma, Guo-Zhen, Xu, Chun-Xiao, Sung, Hyung Jin, Huang, Wei-Xi
• Format: Article
• Language: English
• Subjects: Channel flow; Direct numerical simulation; Energy; Energy transfer; Fluid dynamics; Fluid flow; Height; Hypotheses; JFM Papers; Reynolds number; Reynolds stresses; Roughness; Similarity; Spectral analysis; Spectrum analysis; Stresses; Structures; Three dimensional flow; Transport; Transport equations; Turbulence; Turbulent flow; Velocity; Velocity distribution; Velocity profiles
• ISSN: 0022-1120; 1469-7645
• DOI: 10.1017/jfm.2023.425

Direct numerical simulations (DNSs) are performed to investigate the roughness effects on the statistical properties and the large-scale coherent structures in the turbulent channel flow over three-dimensional sinusoidal rough walls. The outer-layer similarities of mean streamwise velocity and Reynolds stresses are examined by systematically varying the roughness Reynolds number $k^{+}$ and the ratio of the roughness height to the half-channel height $k / \delta$. The energy transfer mechanism of turbulent motions in the presence of roughness elements with different sizes is explored through spectral analysis of the transport equation of the two-point velocity correlation and the scale-energy path display of the generalized Kolmogorov equation. The results show that, with increasing $k^+$, the downward shift of the mean streamwise velocity profile in the logarithmic region increases and the peak intensities of turbulent Reynolds stresses decrease. At an intermediate Reynolds number ($Re_{\tau }= 1080$), the length scale and intensity of the large-scale coherent structures increase for a small roughness ($k^{+}=10$), which leads to failure of the outer-layer similarity in rough-wall turbulence, and decrease for a large roughness ($k^{+}=60$), as compared with the smooth-wall case. The existence of the small roughness ($k^{+}=10$) enhances the mechanism of inverse energy cascade from the inner-layer small-scale structures to the outer-layer large-scale structures. Correspondingly, the self-sustaining processes of the outer-layer large-scale coherent structures, including turbulent production, interscale transport, pressure transport and spatial turbulent transport, are all enhanced, whereas the large roughness ($k^{+}=60$) weakens the energy transfer between the inner and outer regions.