Turbulent Flow Over Large Roughness Elements: Effect of Frontal and Plan Solidity on Turbulence Statistics and...

Wind-tunnel experiments were carried out on fully-rough boundary layers with large roughness ( $\delta /h\approx 10$ , where h is the height of the roughness elements and $\delta$ is the boundary-layer thickness). Twelve different surface conditions were created by using LEGO™ bricks of uniform height. Six cases are tested for a fixed plan solidity ( ${\lambda }_P$ ) with variations in frontal density ( ${\lambda }_F$ ), while the other six cases have varying ${\lambda }_P$ for fixed ${\lambda }_F$ . Particle image velocimetry and floating-element drag-balance measurements were performed. The current results complement those contained in Placidi and Ganapathisubramani (J Fluid Mech 782:541-566, 2015), extending the previous analysis to the turbulence statistics and spatial structure. Results indicate that mean velocity profiles in defect form agree with Townsend's similarity hypothesis with varying ${\lambda }_F$ , however, the agreement is worse for cases with varying ${\lambda }_P$ . The streamwise and wall-normal turbulent stresses, as well as the Reynolds shear stresses, show a lack of similarity across most examined cases. This suggests that the critical height of the roughness for which outer-layer similarity holds depends not only on the height of the roughness, but also on the local wall morphology. A new criterion based on shelter solidity, defined as the sheltered plan area per unit wall-parallel area, which is similar to the 'effective shelter area' in Raupach and Shaw (Boundary-Layer Meteorol 22:79-90, 1982), is found to capture the departure of the turbulence statistics from outer-layer similarity. Despite this lack of similarity reported in the turbulence statistics, proper orthogonal decomposition analysis, as well as two-point spatial correlations, show that some form of universal flow structure is present, as all cases exhibit virtually identical proper orthogonal decomposition mode shapes and correlation fields. Finally, reduced models based on proper orthogonal decomposition reveal that the small scales of the turbulence play a significant role in assessing outer-layer similarity.