Aerodynamic admittance and dynamics of an open-grown tree

Enhancing our understanding of the structural response of trees exposed to wind loading is important, since the knowledge of their aerodynamic behaviour is necessary for a realistic risk assessment of tree damage during extreme wind conditions. Here, we first present an analytical model of the aerodynamic admittance function that relates the turbulence fluctuations of the wind at a single point to their spatial average over the crown’s frontal area. The latter is responsible for the wind-induced bending moments at the base of a tree’s stem. We employ the aerodynamic admittance function to model the dynamic structural response of an open-grown oak tree. The analysis is performed along two axes to express both the longitudinal and transverse response with respect to the mean wind direction. The resulting predictions are compared with strain gauge observations taken at the lower part of the stem. The presented framework shows that the spatial averaging over the crown’s frontal area has a stronger effect on the tree’s movements in the streamwise wind direction compared to the spanwise direction. Further, the aerodynamic damping is also stronger in the streamwise direction and generally correlates positively with the inflow wind speed.