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

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/d. 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-t = 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.

Automated summary

Direct numerical simulations (DNSs) were conducted to investigate the effects of roughness on statistical properties and large-scale coherent structures in turbulent channel flow over three-dimensional sinusoidal rough walls. The study examined the similarities in mean streamwise velocity and Reynolds stresses in the outer layer by varying the roughness Reynolds number and the ratio of roughness height to the half-channel height. Spectral analysis and scale-energy path display were used to explore the energy transfer mechanism of turbulent motions with different sized roughness elements. The results showed that increasing roughness Reynolds number led to a downward shift of the mean velocity profile and decreased intensity of turbulent Reynolds stresses.