High-resolution data from the large-eddy simulation of the atmospheric boundary layer (ABL) over a vegetation canopy are used to investigate the interaction between the most energetic large-scale structures from the ABL and the smaller scales from the near-canopy region. First, evidence of amplitude modulation (AM) involving the three velocity components is demonstrated. A multi-scale analysis of the transport equation of both the turbulent kinetic energy (TKE) and Reynolds shear stress (RSS) is then performed using a multi-level filtering procedure. It is found that, on average, in the investigated region, large scales are a source of TKE for the small scales (e.g. forward scatter of TKE) through nonlinear interscale transfer ($T_r^L$) with a maximum at canopy top while they are a sink via turbulent transport ($T_t^L$). Close to the canopy, the small-scale RSS transport behaves the same while, above the roughness sublayer, $T_r^L$ and $T_t^L$ switch roles showing the existence of RSS backscatter. The standard deviation of the transfer terms shows that there are intense instantaneous forward and backscatter of both TKE and RSS via all the transfer terms. It is therefore demonstrated that there is a two-way coupling between the ABL and the near-canopy scales, the well-known top-down mechanism through TKE transfer being complemented by a bottom-up feedback through RSS transfer. This analysis is extended to several stability regimes, confirming the above conclusions and showing the increasing role of the large-scale wall-normal component in AM and TKE or RSS transfers when the flow becomes buoyancy driven.

The deepening of a shear-driven turbulent layer penetrating into a stably stratified quiescent layer is studied using direct numerical simulation (DNS). The simulation design mimics the classical laboratory experiments by Kato & Phillips (J. Fluid Mech., vol. 37, 1969, pp. 643–655) in that it starts with linear stratification and applies a constant shear stress at the lower boundary, but avoids sidewall and rotation effects inherent in the original experiment. It is found that the layers universally deepen as a function of the square root of time, independent of the initial stratification and the Reynolds number of the simulations, provided that the Reynolds number is large enough. Consistent with this finding, the dimensionless entrainment velocity varies with the bulk Richardson number as $R{i}^{- 1/ 2} $ . In addition, it is observed that all cases evolve in a self-similar fashion. A self-similarity analysis of the conservation equations shows that only a square root growth law is consistent with self-similar behaviour.

We compare the turbulence statistics of the canopy/roughness sublayer (RSL) and the inertial sublayer (ISL) above. In the RSL the turbulence is more coherent and more efficient at transporting momentum and scalars and in most ways resembles a turbulent mixing layer rather than a boundary layer. To understand these differences we analyse a large-eddy simulation of the flow above and within a vegetation canopy. The three-dimensional velocity and scalar structure of a characteristic eddy is educed by compositing, using local maxima of static pressure at the canopy top as a trigger. The characteristic eddy consists of an upstream head-down sweep-generating hairpin vortex superimposed on a downstream head-up ejection-generating hairpin. The conjunction of the sweep and ejection produces the pressure maximum between the hairpins, and this is also the location of a coherent scalar microfront. This eddy structure matches that observed in simulations of homogeneous-shear flows and channel flows by several workers and also fits with earlier field and wind-tunnel measurements in canopy flows. It is significantly different from the eddy structure educed over smooth walls by conditional sampling based only on ejections as a trigger. The characteristic eddy was also reconstructed by empirical orthogonal function (EOF) analysis, when only the dominant, sweep-generating head-down hairpin was recovered, prompting a re-evaluation of earlier results based on EOF analysis of wind-tunnel data. A phenomenological model is proposed to explain both the structure of the characteristic eddy and the key differences between turbulence in the canopy/RSL and the ISL above. This model suggests a new scaling length that can be used to collapse turbulence moments over vegetation canopies.