Abstract
A linearized analysis 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 et al. (J Fluid Mech 488:369–398, 2003). 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.
Highlights
The study of the atmospheric boundary layer over forested areas has numerous applications in micrometeorology and wind energy but, despite much effort, there are still numerous open questions, especially regarding complex terrain and how complex forest configurations modify the flow field above and in the wake of forests
The velocity statistics obtained for the full-forest configuration are shown in Fig. 7 where the proposed model is compared with the large-eddy simulations (LES) data for leaf-area index (L AI) values of 2 and 5 that, on, are studied in the present section
Some discrepancy is instead observed in the turbulent kinetic energy (TKE), which is significantly underestimated by the first-order model by almost a factor of two over the canopy, while the disagreement decreases in the wake of the forest
Summary
The study of the atmospheric boundary layer over forested areas has numerous applications in micrometeorology and wind energy but, despite much effort, there are still numerous. Intensive research efforts have focussed on describing the flow field over a homogeneous forest canopy (Stacey et al 1994; Irvine et al 1997; Harman and Finnigan 2007; Segalini et al 2013; Arnqvist et al 2015), where it is assumed that the streamwise extension of the canopy is at least one order of magnitude larger than the local boundary-layer thickness, δ. In order to validate the model, LES was performed with different clearing configurations and different forest densities, as discussed in Sect.
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