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Large-scale circulations around a city are co-modulated by the urban heat island and by regional wind patterns. Depending on these variables, the circulations fall into different regimes ranging from advection-dominated (plume regime) to convection-driven (bubble regime). Using dimensional analysis and large-eddy simulations, this study investigates how these different circulations scale with urban and rural heat fluxes, as well as upstream wind speed. Two dimensionless parameters are shown to control the dynamics of the flow: (1) the ratio of rural to urban thermal convective velocities that contrasts their respective buoyancy fluxes and (2) the ratio of bulk inflow velocity to the convection velocity in the rural area. Finally, the vertical flow velocities transecting the rural to urban transitions are used to develop a criterion for categorizing different large-scale circulations into plume, bubble or transitional regimes. The findings have implications for city ventilation since bubble regimes are expected to trap pollutants, as well as for scaling analysis in canonical mixed-convection flows.

Large Eddy Simulations (LES) of neutral flow over regular arrays of cuboids are conducted to explore connections between momentum (z 0m ) and scalar (z 0s ) roughness lengths in urban environments, and how they are influenced by surface geometry. As LES resolves the obstacles but not the micro‐scale boundary layers attached to them, the aforementioned roughness lengths are analyzed at two distinct spatial scales. At the micro‐scale (roughness of individual facets, e.g. roofs), it is assumed that both momentum and scalar transfer are governed by accepted arguments for smooth walls that form the basis for the LES wall model. At the macro‐scale, the roughness lengths are representative of the aggregate effects of momentum and scalar transfer over the resolved roughness elements of the whole surface, and hence they are directly computed from the LES. The results indicate that morphologically‐based parameterizations for macro‐scale z 0m are adequate overall. The relation between the momentum and scalar macro‐roughness values, as conventionally represented by log(z 0m /z 0s ) and assumed to scale with urn:x-wiley:00359009:media:qj3839:qj3839-math-0001 (where Re * is a roughness Reynolds number), is then interpreted using surface renewal theory (SRT). SRT predicts n = 1/4 when only Kolmogorov‐scale eddies dominate the scalarmore »exchange, whereas n = 1/2 is predicted when large eddies limit the renewal dynamics. The latter is found to better capture the LES results. However, both scaling relations indicate that z 0s decreases when z 0m increases for typical urban geometries and scales. This is opposite to how their relation is usually modeled for urban canopies (i.e. z 0s /z 0m is a fixed value smaller than unity).« less