Direct numerical simulation of flow in a turbulent channel with a random rough bottom wall is performed at friction Reynolds number and. The rough surface corresponds to the experiments of Flack et al. (Flow Turbul. Combust., vol. 104, 2020, pp. 317-329). The computed skin-friction coefficients and the roughness functions show good agreement with experimental results. The double-averaging methodology is used to investigate mean velocity, Reynolds stresses, dispersive flux and mean momentum balance. The roll-up of the shear layer on the roughness crests is identified as a primary contributor to the wall-normal momentum transfer. The mean-square pressure fluctuations increase in the roughness layer and collapse onto their smooth-wall levels away from the wall. The dominant source terms in the pressure Poisson equation are examined. The rapid term shows that high pressure fluctuations observed in front of and above the roughness elements are mainly due to the attached shear layer formed upstream of the protrusions. The contribution of the slow term is smaller. The slow term is primarily increased in the troughs and in front of the roughness elements, corresponding to the occurrence of quasi-streamwise vortices and secondary vortical structures. The mean wall shear on the rough surface is highly correlated with the roughness height, and depends on the local roughness topography. The probability distribution function of wall shear stress fluctuations is consistent with higher velocities at roughness crests and reverse flow in the valley regions. Extreme events are more probable due to the roughness. Events with comparable magnitudes of the streamwise and spanwise wall shear stress occur more frequently, corresponding to a more isotropic vorticity field in the roughness layer.
Bibliographical noteFunding Information:
This work was supported by the United States Office of Naval Research (ONR) Grant N00014-17-1-2308 managed by Drs J. Gorski, T. Fu and P. Chang. Computing resources were provided by the Minnesota Supercomputing Institute (MSI). We are grateful to Professor K. Flack at the United States Naval Academy for providing us with the scanned surface data used in the present work. The authors would like to thank Mr S. Anantharamu, Dr P. Kumar and Dr Y. Li for their helpful discussions and suggestions.
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- Key words turbulence simulation
- turbulent boundary layers