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

Second-order closure models for the canopy sublayer (CSL) employ aset of closure schemes developed for `free-air' flow equations andthen add extra terms to account for canopy related processes. Muchof the current research thrust in CSL closure has focused on thesecanopy modifications. Instead of offering new closure formulationshere, we propose a new mixing length model that accounts for basicenergetic modes within the CSL. Detailed flume experiments withcylindrical rods in dense arrays to represent a rigid canopy areconducted to test the closure model. We show that when this lengthscale model is combined with standard second-order closureschemes, first and second moments, triple velocity correlations,the mean turbulent kinetic energy dissipation rate, and the wakeproduction are all well reproduced within the CSL provided thedrag coefficient (C_D) is well parameterized. The maintheoretical novelty here is the analytical linkage betweengradient-diffusion closure schemes for the triple velocitycorrelation and non-local momentum transfer via cumulant expansionmethods. We showed that second-order closure models reproducereasonably well the relative importance of ejections and sweeps onmomentum 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 closureschemes can reproduce key flow statistics without much revision.When all these results are taken together, it appears that thepredictive skills of second-order closure models are not limitedby closure formulations; rather, they are limited by our abilityto independently connect the drag coefficient and the effectivemixing length to the canopy roughness density. With rapidadvancements in laser altimetry, the canopy roughness densitydistribution will become available for many terrestrialecosystems. Quantifying the sheltering effect, the homogeneity andisotropy of the drag coefficient, and more importantly, thecanonical mixing length, for such variable roughness density isstill lacking.     

The ejection-sweep cycle over bare and forested gentle hills: a laboratory experiment

Progress on practical problems such as quantifying gene flow and seed dispersal by wind or turbulent fluxes over nonflat terrain now demands fundamental understanding of how topography modulates the basic properties of turbulence. In particular, the modulation by hilly terrain of the ejection-sweep cycle, which is the main coherent motion responsible for much of the turbulent transport, remains a problem that has received surprisingly little theoretical and experimental attention. Here, we investigate how boundary conditions, including canopy and gentle topography, alter the properties of the ejection-sweep cycle and whether it is possible to quantify their combined impact using simplified models. Towards this goal, we conducted two new flume experiments that explore the higher-order turbulence statistics above a train of gentle hills. The first set of experiments was conducted over a bare surface while the second set of experiments was conducted over a modelled vegetated surface composed of densely arrayed rods. Using these data, the connections between the ejection-sweep cycle and the higher-order turbulence statistics across various positions above the hill surface were investigated. We showed that ejections dominate momentum transfer for both surface covers at the top of the inner layer. However, within the canopy and near the canopy top, sweeps dominate momentum transfer irrespective of the longitudinal position; ejections remain the dominant momentum transfer mode in the whole inner region over the bare surface. These findings were well reproduced using an incomplete cumulant expansion and the measured profiles of the second moments of the flow. This result was possible because the variability in the flux-transport terms, needed in the incomplete cumulant expansion, was shown to be well modelled using “local” gradient-diffusion principles. This result suggests that, in the inner layer, the higher-order turbulence statistics appear to be much more impacted by their relaxation history towards equilibrium rather than the advection-distortion history from the mean flow. Hence, we showed that it is possible to explore how various boundary conditions, including canopy and topography, alter the properties of the ejection-sweep cycle by quantifying their impact on the gradients of the second moments only. Implications for modelling turbulence using Reynolds-averaged Navier Stokes equations and plausible definitions for the canopy sublayer depth are briefly discussed.     

The relative importance of ejections and sweeps to momentum transfer in the atmospheric boundary layer

Using an incomplete third-order cumulant expansion method (ICEM) and standard second-order closure principles, we show that the imbalance in the stress contribution of sweeps and ejections to momentum transfer (ΔS _o ) can be predicted from measured profiles of the Reynolds stress and the longitudinal velocity standard deviation for different boundary-layer regions. The ICEM approximation is independently verified using flume data, atmospheric surface layer measurements above grass and ice-sheet surfaces, and within the canopy sublayer of maturing Loblolly pine and alpine hardwood forests. The model skill for discriminating whether sweeps or ejections dominate momentum transfer (e.g. the sign of ΔS _o ) agrees well with wind-tunnel measurements in the outer and surface layers, and flume measurements within the canopy sublayer for both sparse and dense vegetation. The broader impact of this work is that the “genesis” of the imbalance in ΔS _o is primarily governed by how boundary conditions impact first and second moments.