A Linearized k- ϵ Model of Forest Canopies and Clearings

Antonio Segalini, Tetsuya Nakamura, Koji Fukagata

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


A linearized analysis of the Reynolds-averaged Navier–Stokes (RANS) equations is proposed where the k- ϵ 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 uw¯ 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.

Original languageEnglish
Pages (from-to)439-460
Number of pages22
JournalBoundary-Layer Meteorology
Issue number3
Publication statusPublished - 2016 Dec 1


  • Canopy flows
  • Forest clearings
  • Linearized Reynolds-averaged Navier–Stokes equations

ASJC Scopus subject areas

  • Atmospheric Science


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