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# Article

## A Linearised k-epsilon Model of Forest Canopies and Clearings

Authors: Segalini, A. S., Nakamura, , Fukagata, K. Article Published 2016

### Abstract

A linearized solution of the Reynolds-averaged Navier-Stokes {(RANS)} equations is proposed where the $k-\epsilon$ turbulence model is used. The flow near the forest is obtained as the superposition of the undisturbed incoming boundary layer plus a velocity perturbation due to the forest presence, similar to the approach proposed by Belcher, Jerram \& Hunt (\textit{J. Fluid Mech.}, \textbf{488}, 369-398). The linearized model has been {compared against several non-linear RANS simulations with many leaf-area index values and} large-eddy simulations using two different values of leaf-area index. {All the simulations have been performed for a homogeneous forest and} for four different clearing configurations. Despite the model approximations, {the mean velocity and the Reynolds stress $\overline{u'w'}$ have been reasonably reproduced by the first-order model}, providing insight about how the clearing perturbs the boundary layer over forested areas. {However, significant departures from the linear predictions are observed in the turbulent kinetic energy and velocity variances. A second-order correction, which partly accounts for some non-linearities, is therefore proposed to improve the estimate of the turbulent kinetic energy and velocity variances.} The results {suggest} that only a region close to the canopy top is significantly affected by the {forest drag and dominated by the non-linearities}, while above three canopy heights from the ground only small effects are visible and both the linearized model and the simulations have the same trends there.