A Linearized k-ϵ Model of Forest Canopies and Clearings

• A linearized analysis of the Reynolds-averaged Navier–Stokes (RANS) equations is proposed where the (Formula presented.) 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 (Formula presented.) 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.

Ämnesord

TEKNIK OCH TEKNOLOGIER  -- Maskinteknik -- Strömningsmekanik och akustik (hsv//swe)

ENGINEERING AND TECHNOLOGY  -- Mechanical Engineering -- Fluid Mechanics and Acoustics (hsv//eng)

Nyckelord

Canopy flows

Forest clearings

Linearized Reynolds-averaged Navier–Stokes equations

Atmospheric thermodynamics

Boundary layers

Computational fluid dynamics

Drag

Forestry

Kinetic energy

Kinetics

Large eddy simulation

Linearization

Reynolds equation

Reynolds number

Turbulence models

Turbulent flow

Velocity

Linearized analysis

Model approximations

Second-order correction

Stokes equations

Turbulent kinetic energy

Velocity perturbation

Navier Stokes equations

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