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Abstract: Trees play an important role in the wind and thermal microclimate of urban environments. The effect of trees on urban flows is often determined using computational fluid dynamics (CFD) which typically models trees using a quadratic drag formulation that depends on the leaf-area density (LAD) and a volumetric drag coefficient (CdV). In the present work, we develop an analytical model for the flow within a finite-length vegetation canopy. We identify the drag length – inverse of (LAD times CdV), a metric that fully defines the local drag characteristics of a tree canopy. A detailed study of the literature suggests that the median value of drag length observed in field experiments is 21 m for trees and 0.7 m for low vegetation (e.g., crops). For both the tree canopy and low vegetation, there is a substantial spread in the data. A systematic large-eddy simulation (LES) investigation for a total 168 canopy configurations and drag lengths is used to obtain a closed form of the analytical model. The analytical model allows determining of LAD and CdV from wind-tunnel experiments that typically present the drag characteristics in terms of the classical drag coefficient (Cd, which is different from CdV) based on the frontal area and the aerodynamic porosity. The present work provides insight into the appropriate scaling of trees in wind-tunnel experiments: the drag length must be scaled geometrically. Evaluation of the drag length for numerical simulations and wind-tunnel experiments (assuming geometric scaling 1:100) in literature shows that the median drag length in both these cases is about 5 m, substantially lower than the 21 m found in field experiments. This suggests that the effect of vegetative drag might be overestimated in these studies.

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