Turbulent flow and mixing layer over large two-dimensional square roughness

In this work, we perform large-eddy simulations of the high-Reynolds-number turbulent flows over large two-dimensional transverse bars, aiming to establish the potential relationship between the mixing-layer-like shear flows in the roughness layer and the drag on the turbulent flow above. We systematically change the cavity width while keeping the height of the bars constant, and change the height of the bars with fixed cavity width for a parametric study. The results show that the mixing-layer-like shear flows emerge from the rear edge of the bars due to flow separation and develop along the crest of the cavities. As the cavity width increases, the inflectional mean velocity profile is gradually smoothed, which is related to the increasing roughness function. Meanwhile, the roughness function remains almost unchanged when increasing the height of the bars with fixed cavity width, due to similar momentum transport in the mixing-layer-like shear flows. Analysis based on the Navier-Stokes equations shows that most of the roughness drag is contributed by the Reynolds shear stress in these shear layers. The enhanced Reynolds shear stress leads to increased drag as the cavity width increases, while changing the roughness height has little impact on the mixing layer, resulting in little change in the roughness function. We also found that cavities with a width-to-height ratio equal to 1 have strong vertical motions inside the cavities but smaller drag than expected.