Characteristic Length Scales in Turbulent Flows over Rough Walls

The presence of surface roughness plays a significant role in land-atmosphere exchanges of momentum, heat, and scalars. Recent years have seen extensive applications of the large-eddy simulation technique to investigate this problem. Nevertheless, model domains in existing studies have a limited horizontal span that would not capture the very large scale motions, and the influence of these large-scale turbulent structures is overlooked. This study conducted large-eddy simulations (LES) of atmospheric boundary-layer flow to quantify the length scales of relevance in turbulent flows over different surface roughness under neutral stability conditions, and whether they need to be captured in LES. Two-dimensional street canyons with an aspect ratio of 2 and 0.2 are used to represent d-type and k-type surface roughness, respectively. Their results are then compared to simulations with an equivalent surface roughness of buildings represented using a wall-model. Results show that the mean and variance of the flow velocity are reasonably estimated with a modified roughness length, but the coherent turbulent structures cannot be captured without explicitly modeling the roughness elements. The length scale of relevance in turbulent flows is found to be larger over d-type roughness than over k-type roughness. In large-eddy simulations over the former, a larger horizontal domain is thus required for accurate investigations of turbulent characteristics. The study provides systematic evaluation and guidance on the numerical setup of building-resolved large-eddy simulations over complex urban terrain.