Drag Crisis in Fractal Trees Revealed by Simulation and Theory
arXiv:2603.27954
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, . Direct numerical simulations using a cumulant lattice Boltzmann method with adaptive mesh refinement cover , and the analytical model extends predictions to . Under uniform inflow, the analysis indicates a drag-crisis transition near , with increasing structural complexity smoothing this transition because smaller branches remain subcritical. Introducing inflow turbulence with streamwise intensity , representative of atmospheric-boundary-layer winds, shifts the apparent onset to and further moderates the drag reduction. Interpreted at full scale, this suggests that urban trees of order -- m exposed to winds of -- 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- conditions.
The abstract provided here is a tightened version to ensure it remains under the 1920-character limit. This paper is currently under review at the peer-reviewed journal "Urban Forestry and Urban Greening"