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

Published online by Cambridge University Press:  04 August 2023

Guo-Zhen Ma ,
Chun-Xiao Xu Open the ORCID record for Chun-Xiao Xu [Opens in a new window] ,
Hyung Jin Sung Open the ORCID record for Hyung Jin Sung [Opens in a new window]  and
Wei-Xi Huang Open the ORCID record for Wei-Xi Huang [Opens in a new window]
Guo-Zhen Ma
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Chun-Xiao Xu
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
Hyung Jin Sung
Affiliation:
Department of Mechanical Engineering, KAIST, Daejeon 34141, Korea
Wei-Xi Huang*
Affiliation:
AML, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, PR China
*
†Email address for correspondence: hwx@tsinghua.edu.cn
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Abstract

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.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulent boundary layers
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 968 , 10 August 2023 , A18
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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