Drag Crisis in Fractal Trees Revealed by Simulation and Theory

TL;DR

This study combines simulations and theory to analyze the drag crisis in fractal trees, revealing how structural complexity and turbulence influence aerodynamic drag at high Reynolds numbers.

Contribution

It introduces a combined simulation-theoretical framework to characterize the drag crisis in fractal trees across a wide range of Reynolds numbers.

Findings

Drag crisis occurs near Re_H ≈ 3×10^6 under uniform flow.

Turbulence shifts the apparent drag crisis to lower Re_H.

More complex trees experience a smoother transition and altered drag behavior.

Abstract

Trees are key roughness elements in urban environments, shaping airflow, microclimates, and pollutant dispersion. Yet the aerodynamic drag of complex tree-like structures at high Reynolds numbers remains poorly characterized compared with the well-studied drag crisis of simple bluff bodies. We combine large-scale lattice Boltzmann simulations with an analytical branch-wise drag model to examine fractal trees over a wide range of height-based Reynolds numbers, $Re_H$. Direct numerical simulations using a cumulant lattice Boltzmann method with adaptive mesh refinement cover $2.5\times10^3 \le Re_H \le 1.2\times10^5$, and the analytical model extends predictions to $Re_H \sim 10^9$. Under uniform inflow, the analysis indicates a drag-crisis transition near $Re_H \approx 3\times10^6$, with increasing structural complexity smoothing this transition because smaller branches remain subcritical. Introducing inflow turbulence with streamwise intensity $I_u \approx 8\%$, representative of atmospheric-boundary-layer winds, shifts the apparent onset to $Re_H \approx 1.5\times10^5$ and further moderates the drag reduction. Interpreted at full scale, this suggests that urban trees of order $10$--$30$ m exposed to winds of $1$--$10~\mathrm{m/s}$ generally operate in the crisis or post-crisis regime. In both uniform and turbulent inflow, the framework predicts a reversal in drag-coefficient ordering across geometries: simplified trees show lower drag in the subcritical regime but may exhibit higher drag in the supercritical regime, whereas more complex trees undergo a smoother, moderated crisis. These results challenge the common assumption that pruning always reduces aerodynamic loading and highlight the need to reassess vegetation-drag parameterizations and pruning strategies in high-$Re_H$ conditions.