Appropriate Momentum Provision for Numerical Simulations of Horizontally Homogeneous Urban Canopies Using Periodic Boundary Conditions

Abstract Turbulent flow over urban-like roughness has been numerically studied for various purposes, such as the clarification of turbulent characteristics over rough walls, visualization of turbulent structures around block arrays, and evaluation of urban ventilation and pedestrian winds. In such simulations, a portion of the developing boundary layer is extracted as a numerical domain, assuming periodic boundary conditions in the horizontal direction to reproduce laterally homogeneous rough surfaces. However, the conditions required to drive the airflow by an artificial momentum source uniquely determine the turbulent statistics, which are different from those in developing boundary layers. Therefore, this study presents a new approach for driving the airflow over urban-like block arrays. The new method is based on spatially averaged Navier–Stokes equations to prove the necessity of height-dependent momentum provision. The turbulent flow over a cubical-block array is determined using large-eddy simulations driven by four different momentum sources. Regardless of the driving force, the vertical profiles of the streamwise velocity components are identical. In contrast, slight differences in the vertical Reynolds stress, variances in the velocity components, and turbulence kinetic energy are appropriately reproduced in the new approach. In addition, the budget equations of the turbulent statistics reveal that a change in the vertical Reynolds stress affects the energy production and its redistribution into variance components. The proposed method can contribute to the reproduction of a realistic turbulent flow and provide a theoretical understanding of the momentum provision.