Momentum Transfer and Turbulent Kinetic Energy Budgets within a Dense Model Canopy

Second-order closure models for the canopy sublayer (CSL) employ a set of closure schemes developed for ‘free-air’ flow equations and then add extra terms to account for canopy related processes. Much of the current research thrust in CSL closure has focused on these canopy modifications. Instead of offering new closure formulations here, we propose a new mixing length model that accounts for basic energetic modes within the CSL. Detailed flume experiments with cylindrical rods in dense arrays to represent a rigid canopy are conducted to test the closure model. We show that when this length scale model is combined with standard second-order closure schemes, first and second moments, triple velocity correlations, the mean turbulent kinetic energy dissipation rate, and the wake production are all well reproduced within the CSL provided the drag coefficient (CD) is well parameterized. The main theoretical novelty here is the analytical linkage between gradientdiffusion closure schemes for the triple velocity correlation and non-local momentum transfer via cumulant expansion methods. We showed that second-order closure models reproduce reasonably well the relative importance of ejections and sweeps on momentum transfer despite their local closure approximations. Hence, it is demonstrated that for simple canopy morphology (e.g., cylindrical rods) with well-defined length scales, standard closure schemes can reproduce key flow statistics without much revision. When all these results are taken together, it appears that the predictive skills of secondorder closure models are not limited by closure formulations; rather, they are limited by our ability to independently connect the drag coefficient and the effective mixing length to the canopy roughness density. With rapid advancements in laser altimetry, the canopy roughness density distribution will become available for many terrestrial ecosystems. Quantifying the sheltering effect, the homogeneity and isotropy of the drag coefficient, and more importantly, the canonical mixing length, for such variable roughness density is still lacking.