Effects of the Upstream-Flow Regime and Canyon Aspect Ratio on Non-linear Interactions Between a Street-Canyon Flow and the Overlying Boundary Layer

Abstract

Large-scale structures within a rough-wall boundary layer generated over a cube array have recently been linked to small-scale fluctuations close to the roughness through a dynamical mechanism similar to amplitude modulation. Demonstrating the existence of this mechanism for different roughness types is a crucial step towards the development of a generic model for wind fluctuations in the urban canopy. Here the influence of the upstream roughness geometry (two-dimensional (2D) and three-dimensional (3D)) and planform packing density ( $$ \lambda_{p} $$ ) and street-canyon aspect ratio on the non-linear interactions between large-scale momentum regions and the small scales induced by the presence of the roughness is studied within a wind tunnel using combined particle-image velocimetry and hot-wire anemometry. A multi-time delay linear stochastic estimation is used to decompose the flow into large scales that participate in modulation and the remaining small scales. Using three different upstream roughness configurations composed of either 3D cubes or 2D rectangular blocks it is shown that the upstream roughness configuration has an influence on the non-linear interactions in the rough-wall boundary layer. Analysis of the turbulence skewness decomposition shows a change in the location of the maximum of the term $$ \overline{{u_{L}^{\prime} u_{S}^{\prime 2}}} $$ , which represents the influence of the large-scale momentum regions on the small scales, whilst the temporal correlation shows a modification of the interaction located closer to the roughness with a change from 3D to 2D roughness. Furthermore, a two-point spatio–temporal correlation demonstrates that the non-linear relationship is significantly modified in the wake-interference-flow regime compared to the skimming-flow regime. Through skewness decomposition and temporal correlations the canyon aspect ratio is shown to have no influence on the non-linear interactions, indicating that the mechanism depends only on the flow developing upstream. Finally, although the upstream roughness configuration is shown to influence the non-linear interactions, the nature of the mechanism remains the same in all configurations.