Impact of the Numerical Domain on Turbulent Flow Statistics: Scalings and Considerations for Canopy Flows

Motivated by the need to better predict weather and dispersion processes, the past decades have seen substantial efforts devoted to the study of turbulence within and above urban canopies. Vast majority of studies have relied on the open channel flow over arrays of surface mounted cuboids setup, which is a convenient surrogate of the urban boundary layer. However, as these simulations are an approximation of reality, special care is often required in the setup of the computational model. Many-a-times, findings are not in agreement with well established theories, experimental results, and with results from related numerical investigations. This is often the result of a poorly designed computational domain. This work examines the impact of domain size on selected flow statistics and turbulent flow structures, and discusses scaling relations that should be taken into account at the simulation-design stage. We will present an approach based on Buckingham Pi theorem to analyze the effect of scale separation in flow over surface-mounted cuboids, and elucidate fundamental mechanisms controlling the scaling of flow statistics in both densely and sparsely packed cuboid configurations. We will show how flow statistics scale differently for densely and sparsely packed cases, and why two different sets of pi groups are required to accurately isolate the impact of scale separation. Ultimately, this research offers valuable recommendations to help researchers tailor the domain size for their specific applications.