Modelling the flow within forests: The canopy-related terms in the Reynolds-averaged formulation

Abstract

The canopy-related terms in the transport equations for momentum, Reynolds stresses, turbulent kinetic energy and its dissipation rate were described by a perturbative expansion around a velocity scale based on the mean total kinetic energy. The quality of the series and the relative magnitude of the first orders were analysed through comparison with the results of large-eddy simulation of three canopy flows representative of real-life applications. The flows in question were those over a horizontally homogeneous forest, a sequence of forest stands and clearings, and a forested hill. The analysis gave both the highest order required for an accurate evaluation of the canopy effects and a mathematical formulation for the canopy-related terms in a Reynolds-averaged Navier-Stokes formulation. This offers a sounder basis and assured consistency for the turbulence modelling of canopy flows between Reynolds-averaged Navier-Stokes and large-eddy simulation frameworks.