Influence of irregular three-dimensional rough surfaces on the roughness function

The influence of irregular three-dimensional rough surfaces on the displacement of the logarithmic velocity profile relative to that of a smooth wall in turbulent flow, known as the roughness function, is studied using direct numerical simulations. Five different surface power spectral density (PSD) shapes were considered, and for each, several rough Gaussian surfaces were generated by varying the root mean square (krms ) of the surface heights. It is shown that the roughness function (Delta U+) depends on both the PSD and krms . For a given krms , Delta U+ increases as the wavenumbers of the PSD expand to large values, but at a rate that decreases with the magnitude of the wavenumbers. Although Delta U+ generally does not scale with either krms or the effective slope ES when these variables are considered singularly, for PSDs with low wavenumbers, Delta U+ tends to scale with ES, whereas as wavenumbers increase, Delta U+ tends to scale with krms . An equivalent Nikuradse sand roughness of about eight times krms is found, which is similar to that observed in previous studies for a regular three-dimensional roughness. Finally, it is shown that krms and the effective slope are sufficient to describe the roughness function in the transitional rough regime.