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The skewness of the roughness height distribution is one of the key topographical parameters that govern roughness effects on wall-bounded turbulence. In this paper mathematical bounds for realisable values of skewness and kurtosis are discussed in the context of irregular multi-scale rough surfaces, which are representative of typical forms of engineering roughness. The properties of a set of irregular rough surfaces fully covered by roughness features with very high positive and negative skewness and high kurtosis are investigated using direct numerical simulations of turbulent channel flow at. While an increase of the roughness function is observed at moderate skewness values in line with empirical predictions and previous results for moderately skewed surfaces, the roughness function saturates at extreme values of skewness. Overall, the roughness effect is found to be more sensitive to skewness over the negative skewness range compared to the positive skewness range. Surface pressure statistics show that for surfaces with extreme skewness fully covered by roughness features extreme pits or peaks do not dominate the roughness effect and that surrounding roughness features (‘background’ roughness) retain a significant influence. This is because, while extreme roughness features emerge as skewness approaches high positive or negative values, they tend to be sparse decreasing their overall impact on the wall-bounded flow.

Effect of high skewness and kurtosis on turbulent channel flow over irregular rough walls