The drag length is key to quantifying tree canopy drag

The effects of trees on urban flows are often determined in computational fluid dynamics simulations using a quadratic drag formulation based on the leaf-area density $a$ and a volumetric drag coefficient $C_d^V$. We develop an analytical model for the flow within a vegetation canopy and identify the drag length ${\ell }_d={\left(a{C}_d^V\right)}^{-1}$ as the key metric to describe the local tree drag, which represents the adjustment lengthscale for the mean velocity inside the canopy due to tree drag. A detailed literature survey suggests that the median ${\ell }_d$ observed in field experiments is 21 m for trees and 0.7 m for low vegetation (crops). Total 168 large-eddy simulations are conducted to obtain a closed form of the analytical model which allows determining $a$ and $C_d^V$ from the wind-tunnel experiments that typically present the drag characteristics in terms of the classical drag coefficient $C_d$ and the aerodynamic porosity α${}_L$. 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 a potential overestimation of vegetative drag.