ArXiv · 2026
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 2.5×10³ ≤ Re_H ≤ 1.2×10⁵, and the analytical model extends predictions to Re_H ∼ 10⁹. Under uniform inflow, the analysis indicates a drag-crisis transition near Re_H ≈ 3×10⁶, with increasing structural complexity smoothing this transition because smaller branches remain subcritical. Introducing inflow turbulence with streamwise intensity Iᵤ ≈ 8%, representative of atmospheric-boundary-layer winds, shifts the apparent onset to Re_H ≈ 1.5×10⁵ 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 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.
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