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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.