Flow Over a Narrow Ridge Covered with a Plant Canopy: A Comparison Between Wind-Tunnel Observations and Linear Theory

We revisit the analytical model for atmospheric boundary-layer flow over a hill covered with a canopy of Finnigan and Belcher (Q J R Meteorol Soc 130:1–29, 2004). Remaining within the overall scope of that analysis we extend in two ways. First we include the impacts of the advection terms within the upper canopy in a simple, but approximate, manner. Second we establish a modification for the associated pressure perturbation. Both extensions allow us to extend the parameter range wherein the analytical framework can be expected to reasonably hold. The within-canopy advection terms act to provide a downstream shift, and decreased magnitude, to the flow perturbations within the canopy as compared to the predictions from the original analysis. Through continuity, similar, but smaller, impacts are seen above the canopy. Together these act to reduce the differences in the streamwise positions of the topographic speed-up seen above and within the canopy. The modified pressure perturbation also acts to decrease the magnitude of the flow perturbations. The predicted topographic influence on the flow is reduced from that given in the original analysis but, importantly, the positions where the topographic influences most strongly affect the flow, and by extension the scalar concentration fields, are also changed. Predictions from the revised analysis are shown to be in good agreement with wind-tunnel data for flow over an isolated narrow ridge covered by a partially dense canopy.     

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.     

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.     

A model of atmospheric boundary-layer flow above an isolated two-dimensional ‘hill’; an example of flow above ‘gentle topography’

A numerical model is developed for two-dimensional turbulent boundary-layer flow above gentle topography — defined as not giving rise to mean flow separation. Although the model is formulated in a framework of mixing length and turbulent energy equation models for the surface layer of the atmospheric boundary layer, it could be modified to include higher-order closure hypotheses and/or extended to model gentle topography for the planetary boundary layer or on the sea bed. Results are presented for flow above a specific shape of hill and the effects of surface roughness and hill height are investigated.     

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.     

Flow Over Partially Forested Ridges

Numerical simulations of flow over hills that are partially covered with a forest canopy are performed. This represents a much more realistic situation than previous studies that have generally concentrated on hills that are fully-forested. The results show that the flow over the hill is sensitive to where on the hill the forest is positioned. In particular, for low slopes flow separation is predominantly located within the forest on the lee slope. This has implications for the transport of scalars in the forest canopy. For large hills the results show more variability in scalar concentrations within the canopy compared to either a fully-forested hill or a patch of forest over flat terrain. These results are likely to have implications for a range of applications including the siting and interpretation of flux measurements over forests in complex terrain, predicting wind damage to trees and wind-farm developments. Calculation of the hill-induced pressure drag and canopy-plus-surface stress shows a strong sensitivity to the position of the forest relative to the hill. Depending on the position of the forest the individual drag terms may be strongly enhanced or reduced and may even change sign. The net impact is generally to reduce the total drag compared to an equivalent fully-forested hill, but the amount of the reduction depends strongly on the position of the forest canopy on the hill. In many cases with large, wide hills there is a clear separation of scales between the adjustment of the canopy to a forest edge (of order 6 ? 8L _c, where L _c is the canopy adjustment length scale) and the width of the hill. This separation means that the hill-induced pressure and flow fields and the forest-edge induced pressure and flow fields can in some sense be considered as acting separately. This provides a means of explaining the combined effects of partial forestation and terrain. It also offers a simple method for modelling the changes in drag over a hill due to partial forest cover by considering the impact of the hill and the partial canopy separately. Scaling arguments based on this idea successfully collapse the modelled drag over a range of different hill widths and heights and for different canopy parameters. This offers scope for a relatively simple parametrization of the effects of partial forest cover on the drag over a hill.     

Large-Eddy Simulation of Coherent Turbulence Structures Associated with Scalar Ramps Over Plant Canopies

Large-eddy simulations were performed of a neutrally-stratified turbulent flow within and above an ideal, horizontally- and vertically-homogeneous plant canopy. Three simulations were performed for shear-driven flows in small and large computational domains, and a pressure-driven flow in a small domain, to enable the nature of canopy turbulence unaffected by external conditions to be captured. The simulations reproduced quite realistic canopy turbulence characteristics, including typical ramp structures appearing in time traces of the scalar concentration near the canopy top. Then, the spatial structure of the organised turbulence that caused the scalar ramps was examined using conditional sampling of three-dimensional instantaneous fields, triggered by the occurrence of ramp structures. A wavelet transform was used for the detection of ramp structures in the time traces. The ensemble-averaged results illustrate that the scalar ramps are associated with the microfrontal structure in the scalar, the ejection-sweep structure in the streamwise and vertical velocities, a laterally divergent flow just around the ramp-detection point, and a positive, vertically-coherent pressure perturbation. These vertical structures were consistent with previous measurements made in fields or wind tunnels. However, the most striking feature is that the horizontal slice of the same structure revealed a streamwise-elongated region of high-speed streamwise velocity impacting on another elongated region of low-speed velocity. These elongated structures resemble the so-called streak structures that are commonly observed in near-wall shear layers. Since elongated structures of essentially similar spatial scales were observed in all of the runs, these streak structures appear to be inherent in near-canopy turbulence. Presumably, strong wind shear formed just above the canopy is involved in their formation. By synthesis of the ensemble-averaged and instantaneous results, the following processes were inferred for the development of scalar microfronts and their associated flow structures: (1) a distinct scalar microfront develops where a coherent downdraft associated with a high-speed streak penetrates into the region of a low-speed streak; (2) a stagnation in flow between two streaks of different velocities builds up a vertically-coherent high-pressure region there; (3) the pressure gradients around the high-pressure region work to reduce the longitudinal variations in streamwise velocity and to enhance the laterally-divergent flow and lifted updrafts downstream of the microfront; (4) as the coherent mother downdraft impinges on the canopy, canopy-scale eddies are formed near the canopy top in a similar manner as observed in conventional mixing-layer turbulence.     

Evidence of pressure-forced turbulent flow in a forest

Lagged cross-correlation analyses between streamwise velocity at several heights within and above a forest, and between streamwise velocity and surface pressure, provide evidence that turbulence in the sub-crown region of the forest is to a large extent driven by pressure perturbations. The analyses support earlier results based on examination of coherent structures observed in the same forest. The phase of the streamwise velocity signal exhibits an increasing delay with decreasing height, indicative of a downwind tilted structure, until the upper region of the forest is reached, at which point the effect is reversed. It is suggested that positive pressure perturbations ahead of advancing microfronts induce streamwise accelerations in the trunk space. This link between the pressure pattern and the wind field explains why velocity spectra in the trunk space are depleted in the higher frequencies, relative to levels above.     

A wind tunnel study of turbulent flow over model hills

Detailed wind tunnel measurements have been made of mean flow and turbulence over a two-dimensional ridge and a circular hill, both having cosine-squared cross-section and maximum slope about 15 °. The measurements were made in an artificially thickened neutrally stratified boundary layer, and have been compared with results from linear models and rapid distortion theory as appropriate.Our study shows that linear theory gives generally good predictions of the mean flow on the upwind side of the hills, and especially of the flow speedup at the hill top, but that the turbulence is less well predicted. In particular, the measurements show a major increase in the vertical component of turbulence and in the shear stress on the upwind slope of both the two- and three-dimensional hills which is not predicted by either equilibrium or isotropic rapid-distortion theories, although this may be partly due to the effect of streamline curvature. Rapid-distortion theory is successful only in describing the streamwise component of turbulence in the outer region of the flow, while in the upper part of the inner region of the flow, the turbulence measurements show disagreement with both the equilibrium and the rapid-distortion theories. Our experiments also confirm that the equilibrium region is a very thin layer close to the surface, while above this region and below the outer region, there is a transitional region where all terms in the stress equation are important.The measurements over the three-dimensional hill suggest that the mean flow and turbulence are broadly similar to those over the two-dimensional ridge, but with reduced perturbation amplitudes. The major differences between the two cases are found on the upwind slope and in the wake where, respectively, horizontal divergence and convergence of the three-dimensional flow are most pronounced.     

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.     

Three-Dimensional Scalar Microfront Systems in a Large-Eddy Simulation of Vegetation Canopy Flow

Large-eddy simulation is used to reproduce neutrallystratified airflow inside and immediately above a vegetation canopy. A passive scalaris released from the canopy and the evolution of scalar concentration above the canopyis studied. The most significant characteristic of the scalar concentration is the repeatedformation and dissipation of scalar microfronts, a phenomenon that has been observedin nature. These scalar microfronts consist of downstream-tilted regions of highscalar concentration gradients. Computer visualization tools and a conditional samplingand compositing technique are utilized to analyze these microfronts. Peaks in positivepressure perturbation exceeding an experimental threshold are found to be effectiveindicators of scalar microfronts. Convergence of the streamwise velocity componentand divergence of the cross-stream velocity component are observed in the immediatevicinity of scalar microfronts, which helps explain their relatively longlifetimes. Many of these three-dimensional features have been observedin previous field studies of canopy flow.     

Wind flow over ridges in simulated atmospheric boundary layers

The flows over four two-dimensional triangular hills and three two-dimensional bell-shaped hills have been investigated in a simulated rural atmospheric boundary layer modelled to a scale of 1:300: Further measurements were made over two of the triangular hills in a simulated rural boundary layer of 1: 3000 scale and in a simulated urban boundary layer modelled to a scale of 1:400. The effect of the model hill surface roughness was also investigated. Flow measurements were restricted to the mean velocity U, RMS velocity fluctuations u and the energy spectra for the streamwise velocity component Measurements were made at a number of longitudinal positions in the approach flow, over the model hills and downstream of the model hills. For each model hill, the crest was the region of largest mean velocity and smallest velocity fluctuations. The largest mean velocities over the model hills occurred for hills of intermediate slope rather than for the steepest hills. A decrease in the scale of the simulated atmospheric boundary layer led to a reduction in the amplification factors at the hill crests, whereas an increase in the surface roughness of the approach flow resulted in increased amplification factors at the hill crests.     

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.     

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.     

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.     

Turbulent Intensities and Velocity Spectra for Bare and Forested Gentle Hills: Flume Experiments

To investigate how velocity variances and spectra are modified by the simultaneous action of topography and canopy, two flume experiments were carried out on a train of gentle cosine hills differing in surface cover. The first experiment was conducted above a bare surface while the second experiment was conducted within and above a densely arrayed rod canopy. The velocity variances and spectra from these two experiments were compared in the middle, inner, and near-surface layers. In the middle layer, and for the canopy surface, longitudinal and vertical velocity variances () were in phase with the hill-induced spatial mean velocity perturbation (Δu) around the so-called background state (taken here as the longitudinal mean at a given height) as predicted by rapid distortion theory (RDT). However, for the bare surface case, and remained out of phase with Δu by about L/2, where L is the hill half-length. In the canopy layer, wake production was a significant source of turbulent energy for , and its action was to re-align velocity variances with Δu in those layers, a mechanism completely absent for the bare surface case. Such a lower ‘boundary condition’ resulted in longitudinal variations of to be nearly in phase with Δu above the canopy surface. In the inner and middle layers, the spectral distortions by the hill remained significant for the background state of the bare surface case but not for the canopy surface case. In particular, in the inner and middle layers of the bare surface case, the effective exponents derived from the locally measured power spectra diverged from their expected  − 5/3 value for inertial subrange scales. These departures spatially correlated with the hill surface. However, for the canopy surface case, the spectral exponents were near  − 5/3 above the canopy though the minor differences from  − 5/3 were also correlated with the hill surface. Inside the canopy, wake production and energy short-circuiting resulted in significant departures from  − 5/3. These departures from  − 5/3 also appeared correlated with the hill surface through the wake production contribution and its alignment with Δu. Moreover, scales commensurate with Von Karman street vorticies well described wake production scales inside the canopy, confirming the important role of the mean flow in producing wakes. The spectra inside the canopy on the lee side of the hill, where a negative mean flow delineated a recirculation zone, suggested that the wake production scales there were ‘broader’ when compared to their counterpart outside the recirculation zone. Inside the recirculation zone, there was significantly more energy at higher frequencies when compared to regions outside the recirculation zone.     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.     

A new large-eddy simulation model for simulating air flow and warm clouds above highly complex terrain. Part I: The dry model

This paper presents the dry version of a new large-eddy simulation (LES) model, which is designed to simulate air flow and clouds above highly complex terrain. The model is three-dimensional and nonhydrostatic, and the governing equations are sound filtered by use of the anelastic approximation. A fractional step method is applied to solve the equations on a staggered Cartesian grid. Arbitrarily steep and complex orography can be accounted for through the method of viscous topography. The dynamical model core is validated by comparing the results for a spreading density current against a benchmark solution. The model accuracy is further assessed through the simulation of turbulent flow across a quasi two-dimensional ridge. The results are compared with wind-tunnel data. The method of viscous topography is not restricted to moderately sloped terrain. Compared to models using curvilinear grids, it allows this model to be applied to a much wider range of flows. This is illustrated through the simulation of an atmospheric boundary-layer flow over a surface mounted cube. The results show that the dry model version is able to accurately represent the complex flow in the vicinity of three-dimensional obstacles. It is concluded that the method of viscous topography was successfully implemented into a micrometeorological LES model. As will be shown in Part II, this allows the detailed study of clouds in highly complex terrain.     

Large-Eddy Simulation of Turbulent Organized Structures within and above Explicitly Resolved Cube Arrays

Large-eddy simulations have been performed for fully developed turbulent flow within and above explicitly resolved simple cube arrays. The results from our model, hereafter LES-CITY, are shown to agree with laboratory experiments. We investigated the systematic influence of cube density on turbulent flow characteristics by performing numerical experiments for cube areal densities from 0 to 44%. The following results were obtained: (1) The dispersive momentum flux was quite large within the canopy layer due to a mean stream re-circulation, whereas it was smaller above the canopy. The spatial variation of temporally averaged momentum in the roughness sub-layer was 20% or less of the total kinematic surface drag. (2) The temporally and spatially-averaged flow structure confirmed the existence of conventionally described canyon flow regimes; isolated, interfacial, and wake. However, the intermittency of the canyon flow for all cube densities was quite large and the stream patterns were never persistent. (3) Turbulent organized structures (TOS) similar to those observed in turbulent surface-layer flows were simulated, which are characterized by longitudinally-elongated low speed streaks and the corresponding shorter streamwise vortices. The streaks in sparse and dense canopy flows were likely to be aligned to the street line and to the roof lines, respectively. Such heterogeneity of TOS partially accounts for the large spatial variation of momentum flux. (4) In contrast to the mixing layer analogy of vegetation flows, the TOS and the resulting turbulent statistics of urban flow above the canopy resembled those in surface layers. The recirculation within the canopy significantly influenced the turbulent statistical properties.