Flow Over Hills Covered by a Plant Canopy: Extension to Generalised Two-Dimensional Topography

An understanding of how topography, including that covered by a plant canopy, influences the flow and turbulence is important in many meteorological and micrometeorological applications. We revisit the framework of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) for neutral flow over sinusoidal two-dimensional topography covered by a canopy and present a minor modification that enables a formal match between the forms for the flow within and above the canopy, including within the deep canopy. The modification then allows the easy extension of the framework to generalised two-dimensional topography. The revised framework affirms the conclusions of Finnigan and Belcher (op.cit.); above the canopy the flow perturbations are maximised near to where the perturbation pressure is a minimum, whereas deep within the canopy the flow perturbations are maximised when the streamwise gradient of the perturbation pressure is largest. However, the extension to general topography strongly illustrates that it is the pressure perturbation, not the hill shape directly, that controls the magnitude and location of the topographic impacts on the flow. For isolated ridges with a plateau, the flow perturbations above the canopy maximise, not at the ridge crest, but where the hill curvature is largest. Multiple recirculation regions can also exist within the canopy, as determined by the streamwise gradient of the pressure perturbation. These results indicate that knowledge of the terrain over a larger area than hither-to-thought is required to assess whether the use of micrometeorological techniques is appropriate at individual sites.     

Dispersion of a Passive Scalar Within and Above an Urban Street Network

The transport of a passive scalar from a continuous point-source release in an urban street network is studied using direct numerical simulation (DNS). Dispersion through the network is characterized by evaluating horizontal fluxes of scalar within and above the urban canopy and vertical exchange fluxes through the canopy top. The relative magnitude and balance of these fluxes are used to distinguish three different regions relative to the source location: a near-field region, a transition region and a far-field region. The partitioning of each of these fluxes into mean and turbulent parts is computed. It is shown that within the canopy the horizontal turbulent flux in the street network is small, whereas above the canopy it comprises a significant fraction of the total flux. Vertical fluxes through the canopy top are predominantly turbulent. The mean and turbulent fluxes are respectively parametrized in terms of an advection velocity and a detrainment velocity and the parametrization incorporated into a simple box-network model. The model treats the coupled dispersion problem within and above the street network in a unified way and predictions of mean concentrations compare well with the DNS data. This demonstrates the usefulness of the box-network approach for process studies and interpretation of results from more detailed numerical simulations.     

Turbulence Structure Within and Above a Canopy of Bluff Elements

Measurements of turbulence structure in a wind-tunnel model canopy of bluff elements show many of the features associated with vegetation canopies and roughness sublayers but also display features more characteristic of the inertial sublayer (ISL). Points of similarity include the existence of an inflexion point in the space-time averaged streamwise velocity at the canopy top, the variation with height of turbulent second moments and the departure of the turbulent kinetic energy budget from local equilibrium in and just above the canopy. Quadrant analysis shows characteristic dominance of sweep over ejection events within the canopy although sweeps are more frequent than usually seen in vegetation canopies. Points of difference are a u′, w′ correlation coefficient that is closer to the ISL value than to most canopy data, and a turbulent Prandtl number midway between canopy and ISL values. Within the canopy there is distinct spatial partitioning into two flow regimes, the wake and non-wake regions. Both time-mean and conditional statistics take different values in these different regions of the canopy flow. We explain many of these features by appealing to a modified version of the mixing-layer hypothesis that links the dominant turbulent eddies to the instability of the inflexion point at canopy top. However, it is evident that these eddies are perturbed by the quasi-coherent wakes of the bluff canopy elements. Based upon an equation for the instantaneous velocity perturbation, we propose a criterion for deciding when the eddies linked to the inflexion point will dominate flow structure and when that structure will be replaced by an array of superimposed element wakes. In particular, we show that the resemblance of some features of the flow to the ISL does not mean that ISL dynamics operate within bluff-body canopies in any sense.     

Scalar Transport over Forested Hills

Numerical simulations of scalar transport in neutral flow over forested ridges are performed using both a 1.5-order mixing-length closure scheme and a large-eddy simulation. Such scalar transport (particularly of CO₂) has been a significant motivation for dynamical studies of forest canopy–atmosphere interactions. Results from the 1.5-order mixing-length simulations show that hills for which there is significant mean flow into and out of the canopy are more efficient at transporting scalars from the canopy to the boundary layer above. For the case with a source in the canopy this leads to lower mean concentrations of tracer within the canopy, although they can be very large horizontal variations over the hill. These variations are closed linked to flow separation and recirculation in the canopy and can lead to maximum concentrations near the separation point that exceed those over flat ground. Simple scaling arguments building on the analytical model of Finnigan and Belcher (Q J Roy Meteorol Soc 130:1–29, 2004) successfully predict the variations in scalar concentration near the canopy top over a range of hills. Interestingly this analysis suggests that variations in the components of the turbulent transport term, rather than advection, give rise to the leading order variations in scalar concentration. The scaling arguments provide a quantitative measure of the role of advection, and suggest that for smaller/steeper hills and deeper/sparser canopies advection will be more important. This agrees well with results from the numerical simulations. A large-eddy simulation is used to support the results from the mixing-length closure model and to allow more detailed investigation of the turbulent transport of scalars within and above the canopy. Scalar concentration profiles are very similar in both models, despite the fact that there are significant differences in the turbulent transport, highlighted by the strong variations in the turbulent Schmidt number both in the vertical and across the hill in the large-eddy simulation that are not represented in the mixing-length model.     

Horizontal and Vertical Co2 Advection In A Sloping Forest

A system measuring the horizontal and vertical advection was devised and installed in a sloping forest at the Vielsalm site, Belgium. The measurements showed that under stable conditions a flow regime established below the canopy: air flowed horizontally along the slope and entrained the air above the canopy vertically. This movement occurs during stable nights characterised by strongly negative net radiation. It creates negative air concentration gradients in both the vertical and horizontal directions. The advection fluxes associated with these movements are opposite and of a similar order of magnitude. This implies that the horizontal advection cannot be ignored in the carbon budget equation at night. Unfortunately, the large variability of, and considerable uncertainty about, advection fluxes does not enable one to produce estimates of the source term from these equations. Advection measurement systems should be improved in order to enable such estimates to be made. Particular attention should be paid to the estimation of the vertical velocity above the canopy and to the vertical profiles of the horizontal velocity and horizontal CO₂ gradient below the canopy.     

The impact of perturbations to ocean-model parameters on climate and climate change in a coupled model

Assessments of the impacts of uncertainties in parameters on mean climate and climate change in complex climate models have, to date, largely focussed on perturbations to parameters in the atmosphere component of the model. Here we expand on a previously published study which found the global impacts of perturbed ocean parameters on the rate of transient climate change to be small compared to perturbed atmosphere parameters. By separating the climate-change-induced ocean vertical heat transport in each perturbed member into components associated with the resolved flow and each parameterisation scheme, we show that variations in global mean heat uptake in different perturbed versions are an order of magnitude smaller than the average heat uptake. The lack of impact of the perturbations is attributed to (1) the relatively small impact of the perturbation on the direct vertical heat transport associated with the perturbed process and (2) a compensation between those direct changes and indirect changes in heat transport from other processes. Interactions between processes and changes appear to combine in complex ways to limit ensemble spread and uncertainty in the rate of warming. We also investigate regional impacts of the perturbations that may be important for climate change predictions. We find variations across the ensemble that are significant when measured against natural variability. In terms of the experimental set-up used here (models without flux adjustments) we conclude that perturbed physics ensembles with ocean parameter perturbations are an important component of any probabilistic estimate of future climate change, despite the low spread in global mean quantities. Hence, careful consideration should be given to assessing uncertainty in ocean processes in future probabilistic assessments of regional climate change.     

The Influence of Hilly Terrain on Canopy-Atmosphere Carbon Dioxide Exchange

Topography influences many aspects of forest-atmosphere carbon exchange; yet only a small number of studies have considered the role of topography on the structure of turbulence within and above vegetation and its effect on canopy photosynthesis and the measurement of net ecosystem exchange of CO₂ (N_ee) using flux towers. Here, we focus on the interplay between radiative transfer, flow dynamics for neutral stratification, and ecophysiological controls on CO₂ sources and sinks within a canopy on a gentle cosine hill. We examine how topography alters the forest-atmosphere CO₂ exchange rate when compared to uniform flat terrain using a newly developed first-order closure model that explicitly accounts for the flow dynamics, radiative transfer, and nonlinear eco physiological processes within a plant canopy. We show that variation in radiation and airflow due to topography causes only a minor departure in horizontally averaged and vertically integrated photosynthesis from their flat terrain values. However, topography perturbs the airflow and concentration fields in and above plant canopies, leading to significant horizontal and vertical advection of CO₂. Advection terms in the conservation equation may be neglected in flow over homogeneous, flat terrain, and then N_ee = F_c, the vertical turbulent flux of CO₂. Model results suggest that vertical and horizontal advection terms are generally of opposite sign and of the same order as the biological sources and sinks. We show that, close to the hilltop, F_c departs by a factor of three compared to its flat terrain counterpart and that the horizontally averaged F_c-at canopy top differs by more than 20% compared to the flat-terrain case.     

Solitary rossby waves over variable relief and their stability. Part II: numerical experiments

The barotropic, quasi-geostrophic vorticity equation describing large scale, rotating flows over zonal relief supports nonlinear permanent form solutions, namely nonlinear topographic Rossby waves. Through an analytical theory, these solutions have been shown to be neutrally stable to infinitesimal perturbations.Numerical algorithms, which necessarily truncate the infinite number of degrees of freedom of any continuum model to a finite number, are capable of reproducing the numerical equivalent of these form-preserving solutions. Moreover, these numerical solutions are shown to preserve their shape throughout the numerical experiment not only in the limit of small amplitude, but also for high amplitude (Rossby number → O(1)).Through numerical simulation, the stability analysis is carried far beyond the analytical limit of infinitesimal perturbations. The solutions maintain their stability in agreement with the analytical theory, up to perturbations having intensities almost of the same order as the solutions themselves. For higher-amplitude perturbations, the solutions break up and typical turbulent behavior ensues. The passage from wave-like to turbulent behavior, upon surpassing a critical perturbation value, can be observed in the sudden loss of phase locking of the permanent solution Fourier modes.     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

A Lagrangian Solution to the Relationship between Source Strength and Concentration Profile Under Conditions of Local Advection

We propose a two-dimensional Lagrangian analytical solution for relating source strength and concentration profiles within and above a plant canopy. The new solution describes passive scalar dispersion under conditions of local advection through a fetch correction function in a one-dimensional Lagrangian analytical dispersion model. The model is capable of predicting absolute concentration profiles of passive scalars for different fetches for situations in which the reference concentration is known or the background concentration is available. Tests of the model showed good agreement with measurements from field and wind-tunnel experiments.     

The Influence of Hilly Terrain on Aerosol-Sized Particle Deposition into Forested Canopies

Virtually all reviews dealing with aerosol-sized particle deposition onto forested ecosystems stress the significance of topographic variations, yet only a handful of studies considered the effects of these variations on the deposition velocity (V _d ). Here, the interplay between the foliage collection mechanisms within a dense canopy for different particle sizes and the flow dynamics for a neutrally stratified boundary layer on a gentle and repeating cosine hill are considered. In particular, how topography alters the spatial structure of V _d and its two constitutive components, particle fluxes and particle mean concentration within and immediately above the canopy, is examined in reference to a uniform flat-terrain case. A two-dimensional and particle-size resolving model based on first-order closure principles that explicitly accounts for (i) the flow dynamics, including the two advective terms, (ii) the spatial variation in turbulent viscosity, and (iii) the three foliage collection mechanisms that include Brownian diffusion, turbo-phoresis, and inertial impaction is developed and used. The model calculations suggest that, individually, the advective terms can be large just above the canopy and comparable to the canopy collection mechanisms in magnitude but tend to be opposite to each other in sign. Moreover, these two advective terms are not precisely out of phase with each other, and hence, do not readily cancel each other upon averaging across the hill wavelength. For the larger aerosol-sized particles, differences between flat-terrain and hill-averaged V _d can be significant, especially in the layers just above the canopy. We also found that the hill-induced variations in turbulent shear stress, which are out-of-phase with the topography in the canopy sublayer, play a significant role in explaining variations in V _d across the hill near the canopy top. Just after the hill summit, the model results suggest that V _d fell to 30% of its flat terrain value for particle sizes in the range of 1–10 μm. This reduction appears consistent with maximum reductions reported in wind-tunnel experiments for similar sized particle deposition on ridges with no canopies.     

Large-eddy Simulation of Turbulent Flow across a Forest Edge. Part II: Momentum and Turbulent Kinetic Energy Budgets

Momentum and turbulent kinetic energy (TKE) budgets across a forest edge have been investigated using large-eddy simulation (LES). Edge effects are observed in the rapid variation of a number of budget terms across this vegetation transition. The enhanced drag force at the forest edge is largely balanced by the pressure gradient force and by streamwise advection of upstream momentum, while vertical turbulent diffusion is relatively insignificant. For variance and TKE budgets, the most important processes at the forest edge are production due to the convergence (or divergence) of the mean flow, streamwise advection, pressure diffusion and enhanced dissipation by canopy drag. Turbulent diffusion, pressure redistribution and vertical shear production, which are characteristic processes in homogeneous canopy flow, are less important at the forest transition. We demonstrate that, in the equilibrated canopy flow, a substantial amount of TKE produced in the streamwise direction by the vertical shear of the mean flow is redistributed in the vertical direction by pressure fluctuations. This redistribution process occurs in the upper canopy layers. Part of the TKE in the vertical velocity component is transferred by turbulent and pressure diffusion to the lower canopy levels, where pressure redistribution takes place again and feeds TKE back to the streamwise direction. In this TKE cycle, the primary source terms are vertical shear production for streamwise velocity variance and pressure redistribution for vertical velocity variance. The evolution of these primary source terms downwind of the forest edge largely controls the adjustment rates of velocity variances.     

GRAPES全球集合预报系统不同随机物理扰动方案影响分析

为了更好地理解不同随机物理扰动方案对全球中期集合预报的影响差异,本研究基于GRAPES全球集合预报系统（GRAPES-GEPS）对比分析了随机物理倾向扰动（Stochastically Perturbed Parameterization Tendencies,SPPT）、随机动能补偿（Stochastic Kinetic Energy Backscatter,SKEB）及联合使用SPPT与SKEB三种模式扰动方案所产生的扰动特征及其对集合预报的影响。为避免初值扰动影响,考察随机物理方案所产生的扰动特征时,不使用初值扰动。通过扰动与误差相关性分析（PECA）发现,不同随机物理扰动方案所产生的扰动对预报误差均具有一定的描述能力,而且联合使用SPPT与SKEB方案时,扰动对误差的描述能力最好。对所有扰动方案来说,扰动总能量最初主要集中在热带地区对流层中高层以及平流层低层。随着预报时效的延长,扰动总能量不断增大,其大值区不断向热带外地区转移。从扰动总能量的谱结构来看,扰动能量均呈现升尺度发展的特征。在基于奇异向量初值扰动的GRAPES-GEPS中,随机物理扰动方案的使用均能够显著增加不同地区等压面要素的集合离散度,并在一定程度上改善集合平均误差。由于集合离散度的增大,预报失误率显著减小。连续分级概率评分也有所减小,尤其是在热带地区,改进更为明显。此外,中国地区不同量级（小雨、中雨、大雨和暴雨）降水概率预报技巧在一定程度上得到改善。上述改进均在联合使用SPPT与SKEB方案时最好,这与扰动总能量、扰动与误差相关分析结果一致。      

Turbulent Statistics of Neutrally Stratified Flow Within and Above a Sparse Forest from Large-Eddy Simulation and Field Observations

Turbulent statistics of neutrally stratified shear-driven flow within and above a sparse forest canopy are presented from a large-eddy simulation (LES) and compared with those from observations within and above a deciduous forest with similar height and foliage density. First- and second-order moments from the LES agree with observations quite well. Third-order moments from the LES have the same sign and similar vertical patterns as those from the observations, but the LES yields smaller magnitudes of such higher-order moments. Turbulent spectra and cospectra from the LES agree well with observations above the forest. However, at the highest frequencies, the LES spectra have steeper slopes than observations. Quadrant and conditional analyses of the LES resolved-scale flow fields also agree with observations. For example, both LES and observation find that sweeps are more important than ejections for the transport of momentum within the forest, while inward and outward interaction contributions are both small, except near the forest floor. The intermittency of the transport of momentum and scalar increases with depth into the forest. Finally, ramp structures in the time series of a passive scalar at multiple levels within and above the forest show similar features to those measured from field towers. Two-dimensional (height-time cross-section) contours of the passive scalar and wind vectors show sweeps and ejections, and the characteristics of the static pressure perturbation near the ground resemble those deduced from field tower-based measurements. In spite of the limited grid resolution (2 m × 2 m × 2 m) and domain size (192 m × 192 m × 60 m) used in this LES, we demonstrate that the LES is capable of resolving the most important characteristics of the turbulent flow within and above a forest canopy.     

Mean Flow Near Edges and Within Cavities Situated Inside Dense Canopies

A streamfunction-vorticity formulation is used to explore the extent to which turbulent and turbulently inviscid solutions to the mean momentum balance explain the mean flow across forest edges and within cavities situated inside dense forested canopies. The turbulent solution is based on the mean momentum balance where first-order closure principles are used to model turbulent stresses. The turbulently inviscid solution retains all the key terms in the mean momentum balance but for the turbulent stress gradients. Both exit and entry versions of the forest edge problem are explored. The turbulent solution is found to describe sufficiently the bulk spatial patterns of the mean flow near the edge including signatures of different length scales reported in canopy transition studies. Next, the ‘clearing inside canopy’ or the so-called ‘cavity’ problem is solved for the inviscid and turbulent solutions and then compared against flume experiments. The inviscid solution describes the bulk flow dynamics in much of the zones within the cavity. In particular, the solution can capture the correct position of the bulk recirculation zone within the cavity, although with a weaker magnitude. The inviscid solution cannot capture the large vertical heterogeneity in the mean velocity above the canopy, as expected. These features are better captured via the first-order closure representation of the turbulent solution. Given the ability of this vorticity formulation to capture the mean pressure variations and the mean advective acceleration terms, it is ideal for exploring the distributions of scalars and roughness-induced flow adjustments on complex topography.     

Characteristics of canopy turbulence over a deciduous forest on complex terrain

Canopy turbulence plays an important role in mass and energy exchanges at the canopy-atmosphere interface. Despite extensive studies on canopy turbulence over a flat terrain, less attention has been given to canopy turbulence in a complex terrain. The purpose of this study is to scrutinize characteristics of canopy turbulence in roughness sublayer over a hilly forest terrain. We investigated basic turbulence statistics, conditionally sampled statistics, and turbulence spectrum in terms of different atmospheric stabilities, wind direction and vertical structures of momentum fluxes. Similarly to canopy turbulence over a homogeneous terrain, turbulence statistics showed coherent structure. Both quadrant and spectrum analysis corroborated the role of intermittent and energetic eddies with length scale of the order of canopy height, regardless of wind direction except for shift of peak in vertical wind spectrum to relatively high frequency in the down-valley wind. However, the magnitude of the momentum correlation coefficient in a neutral condition was smaller than typical value over a flat terrain. Further scrutiny manifested that, in the up-valley flow, temperature skewness was larger and the contribution of ejection to both momentum and heat fluxes was larger compared to the downvalley flow, indicating that thermal instability and weaker wind shear in up-valley flow asymmetrically affect turbulent transport within the canopy.     

Nocturnal Near-Surface Temperature,but not Flow Dynamics,can be Predicted by Microtopography in a Mid-Range Mountain Valley

We investigate nocturnal flow dynamics and temperature behaviour near the surface of a 170-m long gentle slope in a mid-range mountain valley. In contrast to many existing studies focusing on locations with significant topographic variations, gentle slopes cover a greater spatial extent of the Earth’s surface. Air temperatures were measured using the high-resolution distributed-temperature-sensing method within a two-dimensional fibre-optic array in the lowest metre above the surface. The main objectives are to characterize the spatio-temporal patterns in the near-surface temperature and flow dynamics, and quantify their responses to the microtopography and land cover. For the duration of the experiment, including even clear-sky nights with weak winds and strong radiative forcing, the classical cold-air drainage predicted by theory could not be detected. In contrast, we show that the airflow for the two dominant flow modes originates non-locally. The most abundant flow mode is characterized by vertically-decoupled layers featuring a near-surface flow perpendicular to the slope and strong stable stratification, which contradicts the expectation of a gravity-driven downslope flow of locally produced cold air. Differences in microtopography and land cover clearly affect spatio-temporal temperature perturbations. The second most abundant flow mode is characterized by strong mixing, leading to vertical coupling with airflow directed down the local slope. Here variations of microtopography and land cover lead to negligible near-surface temperature perturbations. We conclude that spatio-temporal temperature perturbations, but not flow dynamics, can be predicted by microtopography, which complicates the prediction of advective-heat components and the existence and dynamics of cold-air pools in gently sloped terrain in the absence of observations.     

Study on multi-scale blending initial condition perturbations for a regional ensemble prediction system

An initial conditions (ICs) perturbation method was developed with the aim to improve an operational regional ensemble prediction system (REPS). Three issues were identified and investigated: (2) the impacts of perturbation scale on the ensemble spread and forecast skill of the REPS; (3) the scale characteristic of the IC perturbations of the REPS; and (4) whether the REPS's skill could be improved by adding large-scale information to the IC perturbations. Numerical experiments were conducted to reveal the impact of perturbation scale on the ensemble spread and forecast skill. The scales of IC perturbations from the REPS and an operational global ensemble prediction system (GEPS) were analyzed. A "multi-scale blending" (MSB) IC perturbation scheme was developed, and the main findings can be summarized as follows: The growth rates of the ensemble spread of the REPS are sensitive to the scale of the IC perturbations; the ensemble forecast skills can benefit from large-scale perturbations; the global ensemble IC perturbations exhibit more power at larger scales, while the regional ensemble IC perturbations contain more power at smaller scales; the MSB method can generate IC perturbations by combining the small-scale component from the REPS and the large-scale component from the GEPS; the energy norm growth of the MSB-generated perturbations can be appropriate at all forecast lead times; and the MSB-based REPS shows higher skill than the original system, as determined by ensemble forecast verification.     

Large-Eddy Simulation Comparison of Neutral Flow Over a Canopy: Sensitivities to Physical and Numerical Conditions,and Similarity to Other Representations

The representation of a neutral atmospheric flow over roughness elements simulating a vegetation canopy is compared between two large-eddy simulation models, wind-tunnel data and recently updated empirical flux-gradient relationships. Special attention is devoted to the dynamics in the roughness sublayer above the canopy layer, where turbulence is most intense. By demonstrating that the flow properties are consistent across these different approaches, confidence in the individual independent representations is bolstered. Systematic sensitivity analyses with the Dutch Atmospheric Large-Eddy Simulation model show that the transition in the one-sided plant-area density from the canopy layer to unobstructed air potentially alters the flow in the canopy and roughness sublayer. Anomalously induced fluctuations can be fully suppressed by spreading the transition over four steps. Finer vertical resolutions only serve to reduce the magnitude of these fluctuations, but do not prevent them. To capture the general dynamics of the flow, a resolution of 10 % of the canopy height is found to suffice, while a finer resolution still improves the representation of the turbulent kinetic energy. Finally, quadrant analyses indicate that momentum transport is dominated by the mean velocity components within each quadrant. Consequently, a mass-flux approach can be applied to represent the momentum flux.     

Turbulent Pressure and Velocity Perturbations Induced by Gentle Hills Covered with Sparse and Dense Canopies

How the spatial perturbations of the first and second moments of the velocity and pressure fields differ for flow over a train of gentle hills covered by either sparse or dense vegetation is explored using large-eddy simulation (LES). Two simulations are investigated where the canopy is composed of uniformly arrayed rods each with a height that is comparable to the hill height. In the first simulation, the rod density is chosen so that much of the momentum is absorbed within the canopy volume yet the canopy is not dense enough to induce separation on the lee side of the hill. In the second simulation, the rod density is large enough to induce recirculation inside the canopy on the lee side of the hill. For this separating flow case, zones of intense shear stress originating near the canopy-atmosphere interface persist all the way up to the middle layer, ‘contaminating’ much of the middle and outer layers with shear stress gradients. The implications of these persistent shear-stress gradients on rapid distortion theory and phase relationships between higher order velocity statistics and hill-induced mean velocity perturbations (Δu) are discussed. Within the inner layer, these intense shear zones improve predictions of the spatial perturbation by K-theory, especially for the phase relationships between the shear stress (~ ?Δu/?z) and the velocity variances, where z is the height. For the upper canopy layers, wake production increases with increasing leaf area density resulting in a vertical velocity variance more in phase with Δu than with ?Δu/?z. However, background turbulence and inactive eddies may have dampened this effect for the longitudinal velocity variance. The increase in leaf area density does not significantly affect the phase relationship between mean surface pressure and topography for the two simulations, though the LES results here confirm earlier findings that the minimum mean pressure shifts downstream from the hill crest. The increase in leaf area density and associated flow separation simply stretches this difference further downstream. This shift increases the pressure drag, the dominant term in the overall drag on the hill surface, by some 15%. With regards to the normalized pressure variance, increasing leaf area density increases ${\sigma_p/u_{*}^{2}}$ near the canopy top, where u _* is the longitudinally averaged friction velocity at the canopy top and σ _p is the standard deviation of the pressure fluctuations. This increase is shown to be consistent with a primitive scaling argument on the leading term describing the mean-flow turbulent interaction. This scaling argument also predicts the spatial variations in σ _p above the canopy reasonably well for both simulations, but not inside the canopy.