The drag length is key to quantifying tree canopy drag

Abstract: The effects of trees on urban flows are often determined using computational fluid dynamics approaches which typically use a quadratic drag formulation based on the leaf-area density $a$ and a volumetric drag coefficient $C_{d}^V$ to model vegetation. In this paper, we develop an analytical model for the flow within a vegetation canopy and identify that the drag length $\ell_d = (a C_d^V)^{-1}$ is the key metric to describe the local tree drag characteristics. A detailed study of the literature suggests that the median $\ell_d$ observed in field experiments is $21$ m for trees and $0.7$ m for low vegetation (crops). A total of $168$ large-eddy simulations are conducted to obtain a closed form of the analytical model. The model allows determining $a$ and $C_d^V$ from wind-tunnel experiments that typically present the drag characteristics in terms of the classical drag coefficient $C_d$ and the aerodynamic porosity $\alpha_L$. We show that geometric scaling of $\ell_d$ is the appropriate scaling of trees in wind tunnels. Evaluation of $\ell_d$ for numerical simulations and wind-tunnel experiments (assuming geometric scaling $1:100$) in literature shows that the median $\ell_d$ in both these cases is about $5$ m, suggesting possible overestimation of vegetative drag.