Modelling flows within forested areas using the k—ɛ RaNS model

A new canopy model for the Reynolds-averaged Navier-Stokes (RaNS) method with the k—ɛ turbulence model was developed. To derive the effect of vegetation on the transport of turbulent quantities, it uses a Taylor series expansion of the velocity magnitude, which is part of the definition of the canopy drag force, and assumes that the turbulent kinetic energy is much smaller than the kinetic energy of the mean flow. The resultant model is composed by a sum of velocity moments of increasing order. Initially, it was expected that truncating the sum at low-order, including only terms that can be expressed using quantities available within the k—ɛ RaNS model, would provide better accuracy than traditional models, based mainly on dimensional arguments. However, the results obtained with this approach mimic those obtained with a model based on dimensional arguments and calibrated using results of large-eddy simulations, proving the validity of both approaches and showing that the accuracy in the modelling of the flows over vegetation is limited by the k—ɛ model itself and not by the modelling of vegetation effects on turbulence.