Similarity criteria for city scale natural convective flow study under calm condition

The launch of the "Beating the Heat: the Sustainable Cooling Handbook for Cities" by the UNEP (UN Environment Programme) Cool Coalition has sparked an unprecedented surge in research on the urban thermal and wind environment. Extreme high temperatures and severe pollution in cities usually occur under stable stratification of the atmosphere. City scale buoyancy-driven flow, often referred to as urban heat dome flow, will dominate city ventilation, pollutants dispersion and heat removal under calm condition. Owing to the advantages of well-controlled boundary conditions compared with field measurements, reduced scale water tank experiments, full scale and reduced scale numerical models are normally used for studying urban heat dome flows. To accurately replicate the structures of prototype urban heat dome flows in both reduced scale water tank experiments and numerical models, establishing an appropriate similarity criterion is crucial. A newly dimensionless number (m_Fr) was proposed for the similarity criterion between full-scale and reduced-scale models in urban heat dome flow studies. As m_Fr increases, the extent of the upper-level outflow branch over square city areas in the lateral direction decreases. m_Fr can be used as an index to evaluate the aspect-ratio and side outflow extent in the lateral direction of square urban heat dome flow. Therefore, m_Fr is a pivotal parameter in the study of urban heat dome flows, which can serve as a basis for the design of reduced scale experiments and numerical simulations. In addition to its relevance to city-scale flow studies, our work is also useful for general applications in natural convection. This study contributes to a deeper understanding of the flow mechanism over a stably stratified square horizontal plate. We believe this study has significant implications on urban climate modeling, ultimately underpining urban planning to mitigate hot spots in vulnerable areas and enhance the well-being of residents.