Reynolds number effects on turbulent flow over pyramid roughness with varied solidity

Direct numerical simulations (DNS) of turbulent channel flow over pyramid roughness are performed over a range of friction Reynolds numbers. The rough surfaces are inspired by the experimental work of Schultz and Flack (Phys. Fluids, 21:015104, 2009) and are composed of square pyramids in regular arrangements. Pyramids, unlike uniformly sized cubic roughness elements, allow for independent variation of frontal and plan solidity. Nine different rough surfaces are investigated. The height of the roughness elements is kept constant in all cases, while frontal and plan solidities of the roughness are systematically varied focussing on the 'waviness' regime, i.e., the low frontal solidity range. The results show that the roughness function increases with increase in frontal solidity and decrease in plan solidity. For most surfaces, the mean velocity profiles collapse onto the smooth wall data when plotted in defect form. However, for several cases a clear departure from the outer layer similarity is present, and this departure becomes more prominent at higher Reynolds number. In these cases, the spanwise peak-to-peak distance between pyramid elements is comparable to the channel half-height inducing significant levels of the dispersive stresses well above the roughness canopy.