A note on k-ε modelling of vegetation canopy air-flows

The k-epsilon turbulence model is a standard of computational software packages for engineering, yet its application to canopy turbulence has not received comparable attention. This is probably due to the additional source (and/or sink) terms, whose parameterization remained uncertain. This model must include source terms for both turbulent kinetic energy (k) and the viscous dissipation rate (epsilon), to account for vegetation wake turbulence budget. In this note, we show how Kolmogorov's relation allows for an analytical solution to be calculated within the portion of a dense and homogeneous canopy where the mixing length does not vary. By substitution within model equations, this solution allows for a set of constraints on source term model coefficients to be derived. Those constraints should meet both Reynolds averaged Navier-Stokes equations and large-eddy simulation sub-grid scale turbulence modelling requirements. Although originating from within a limited portion of the canopy, the predicted coefficients values must be valid elsewhere in order to make the model capable of predicting the whole canopy-layer flow with a single set of constants.