The drag length is key to quantifying tree canopy drag

TL;DR

This paper introduces an analytical model emphasizing the drag length as a key metric for quantifying tree canopy drag, supported by simulations and literature data, to improve urban flow modeling.

Contribution

It develops an analytical model linking drag length to vegetation drag characteristics and demonstrates how to derive key parameters from wind-tunnel data.

Findings

Median drag length for trees is 21 m in field experiments.

Numerical and wind-tunnel simulations show a median drag length of about 5 m.

Overestimation of vegetative drag in existing models is suggested.

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.