Turbulent Transport of Momentum and Scalars Above an Urban Canopy

Turbulent transport of momentum and scalars over an urban canopy is investigated using the quadrant analysis technique. High-frequency measurements are available at three levels above the urban canopy (47, 140 and 280 m). The characteristics of coherent ejection–sweep motions (flux contributions and time fractions) at the three levels are analyzed, particularly focusing on the difference between ejections and sweeps, the dissimilarity between momentum and scalars, and the dissimilarity between the different scalars (i.e., temperature, water vapour and $\hbox {CO}_{2})$ . It is found that ejections dominate momentum and scalar transfer at all three levels under unstable conditions, while sweeps are the dominant eddy motions for transporting momentum and scalars in the urban roughness sublayer under neutral and stable conditions. The flux contributions and time fractions of ejections and sweeps can be adequately captured by assuming a Gaussian joint probability density function for flow variables. However, the inequality of flux contributions from ejections and sweeps is more accurately reproduced by the third-order cumulant expansion method (CEM). The incomplete cumulant expansion method (ICEM) also works well except for $\hbox {CO}_{2}$ at 47 m where the skewness of $\hbox {CO}_{2}$ fluctuations is significantly larger than that for vertical velocity. The dissimilarity between momentum and scalar transfers is linked to the dissimilarity in the characteristics of ejection–sweep motions and is further quantified by measures of transport efficiencies. Atmospheric stability is the controlling factor for the transport efficiencies of momentum and heat, and fitted functions from the literature describe their behaviour fairly accurately. However, transport efficiencies of water vapour and $\hbox {CO}_{2}$ are less affected by the atmospheric stability. The dissimilarity among the three scalars examined in this study is linked to the active role of temperature and to the surface heterogeneity effect.     

Buoyancy and The Sensible Heat Flux Budget Within Dense Canopies

In contrast to atmospheric surface-layer (ASL) turbulence, a linear relationship between turbulent heat fluxes (F_T) and vertical gradients of mean air temperature within canopies is frustrated by numerous factors, including local variation in heat sources and sinks and large-scale eddy motion whose signature is often linked with the ejection-sweep cycle. Furthermore, how atmospheric stability modifies such a relationship remains poorly understood, especially in stable canopy flows. To date, no explicit model exists for relating F_T to the mean air temperature gradient, buoyancy, and the statistical properties of the ejection-sweep cycle within the canopy volume. Using third-order cumulant expansion methods (CEM) and the heat flux budget equation, a “diagnostic” analytical relationship that links ejections and sweeps and the sensible heat flux for a wide range of atmospheric stability classes is derived. Closure model assumptions that relate scalar dissipation rates with sensible heat flux, and the validity of CEM in linking ejections and sweeps with the triple scalar-velocity correlations, were tested for a mixed hardwood forest in Lavarone, Italy. We showed that when the heat sources (S_T) and F_T have the same sign (i.e. the canopy is heating and sensible heat flux is positive), sweeps dominate the sensible heat flux. Conversely, if S_T and F_T are opposite in sign, standard gradient-diffusion closure model predict that ejections must dominate the sensible heat flux.     

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.     

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.     

Near-Surface Coherent Structures and The Vertical Momentum Flux in a Large-Eddy Simulation of the Neutrally-Stratified Boundary Layer

The near-surface flow of a well-resolved large-eddy simulation of the neutrally-stratified planetary boundary layer is used to explore the relationships between coherent structures and the vertical momentum flux. The near-surface flow is characterized by transient streaks, which are alternating bands of relatively higher and lower speed flow that form parallel to the mean shear direction in the lower part of the boundary layer. Although individual streaks are transient, the overall flow is in a quasi-equilibrium state in which the streaks form, grow, decay and regenerate over lifetimes on the order of tens of minutes. Coupled with the streaky flow is an overturning circulation with alternating bands of updrafts and downdrafts approximately centered on the streaks. The surface stress is dominated by upward ejections of slower moving near-surface air and downward sweeps of higher speed air from higher in the boundary layer. Conditional sampling of the ejection and sweep events shows that they are compact, coherent structures and are intimately related to the streaks: ejections (sweeps) preferentially form in the updrafts (downdrafts) of the three-dimensional streak flow. Hence, consistent with other recent studies, we propose that the streak motion plays an important role in the maintenance of the surface stress by establishing the preferential conditions for the ejections and sweeps that dominate the surface stress. The velocity fluctuation spectra in the model near the surface have a k ⁻¹ spectral slope over an intermediate range of wavenumbers. This behaviour is consistent with recent theoretical predictions that attempt to evaluate the effects of organized flow, such as near-surface streaks, on the variance spectra.     

Shear stress partitioning in large patches of roughness in the atmospheric inertial sublayer

Drag partition measurements were made in the atmospheric inertial sublayer for six roughness configurations made up of solid elements in staggered arrays of different roughness densities. The roughness was in the form of a patch within a large open area and in the shape of an equilateral triangle with 60 m long sides. Measurements were obtained of the total shear stress (τ) acting on the surfaces, the surface shear stress on the ground between the elements (τ_S) and the drag force on the elements for each roughness array. The measurements indicated that τ_S quickly reduced near the leading edge of the roughness compared with τ, and a τ_S minimum occurs at a normalized distance (x/h, where h is element height) of (downwind of the roughness leading edge is negative), then recovers to a relatively stable value. The location of the minimum appears to scale with element height and not roughness density. The force on the elements decreases exponentially with normalized downwind distance and this rate of change scales with the roughness density, with the rate of change increasing as roughness density increases. Average τ_S : τ values for the six roughness surfaces scale predictably as a function of roughness density and in accordance with a shear stress partitioning model. The shear stress partitioning model performed very well in predicting the amount of surface shear stress, given knowledge of the stated input parameters for these patches of roughness. As the shear stress partitioning relationship within the roughness appears to come into equilibrium faster for smaller roughness element sizes it would also appear the shear stress partitioning model can be applied with confidence for smaller patches of smaller roughness elements than those used in this experiment.     

Ejective and Sweeping Motions Above a Peatland and Their Role in Relaxed-Eddy-Accumulation Measurements and Turbulent Transport Modelling

The three turbulent velocity components, water vapour (\(\text {H}_2\text {O}\)), carbon dioxide (\(\text {CO}_{2}\)), and methane (\(\text {CH}_{4}\)) concentration fluctuations are measured above a boreal peatland and analyzed using conditional sampling and quadrant analysis. The overarching question to be addressed is to what degree lower-order cumulant expansion methods describe transport efficiency and the relative importance of ejections and sweeps to momentum, \(\text {CH}_{4}\), \(\text {CO}_{2}\) and \(\text {H}_2\text {O}\) fluxes across a range of atmospheric flow regimes. The patchy peatland surface creates distinctly different source and sink distributions for the three scalars in space and time thereby adding to the uniqueness of the set-up. The measured and modelled fractional contributions to the momentum flux show that sweep events dominate over ejections in agreement with prior studies conducted in the roughness sublayer. For scalar fluxes, ejections dominate the turbulent fluxes over sweeps. While ejective motions persist longer for momentum transport, sweeping events persist longer for all three scalars. Third-order cumulant expansions describe many of the results detailed above, and the results are surprising given the highly non-Gaussian distribution of \(\text {CH}_{4}\) turbulent fluctuations. Connections between the asymmetric contributions of sweeps and ejections and the flux-transport term arising in scalar turbulent-flux-budget closure are derived and shown to agree reasonably well with measurements. The proposed model derived here is much simpler than prior structural models used to describe laboratory experiments. Implications of such asymmetric contributions on, (i) the usage of the now proliferating relaxed-eddy-accumulation method in turbulent flux measurements, (ii) the constant-flux assumption, and (iii) gradient-diffusion closure models are presented.     

Large-Eddy Simulations on the Effects of Surface Geometry of Building Arrays on Turbulent Organized Structures

Turbulent organized structures (TOS) above building arrays were investigated using a large-eddy simulation (LES) model for a city (LES-CITY). Square and staggered building arrays produced contrasting behaviour in terms of turbulence that roughly corresponded to the conventional classification of ‘D-type’ and ‘K-type’ roughness, respectively: (1) The drag coefficients (referred to the building height) for staggered arrays were sensitive to building area density, but those for square arrays were not. (2) The relative contributions of ejections to sweeps (S₂/S₄) at the building height for square arrays were sensitive to building area density and nearly equalled or exceeded 1.0 (ejection dominant), but those for staggered arrays were insensitive to building area density and were mostly below 1.0 (sweep dominant). (3) Streaky patterns of longitudinal low speed regions (i.e., low speed streaks) existed in all flows regardless of array type. Height variations of the buildings in the square array drastically increased the drag coefficient and modified the turbulent flow structures. The mechanism of D-type and K-type urban-like roughness flows and the difference from vegetation flows are discussed. Although urban-like roughness flows exhibited mixed properties of mixing layers and flat-wall boundary layers as far as S₂/S₄ was concerned, the turbulent organized structures of urban-like roughness flows resembled those of flat-wall boundary layers.     

Large-Eddy Simulation of Flow and Pollutant Transports in and Above Two-Dimensional Idealized Street Canyons

A large-eddy simulation (LES) model, using the one-equation subgrid-scale (SGS) parametrization, was developed to study the flow and pollutant transport in and above urban street canyons. Three identical two-dimensional (2D) street canyons of unity aspect ratio, each consisting of a ground-level area source of constant pollutant concentration, are evenly aligned in a cross-flow in the streamwise direction x. The flow falls into the skimming flow regime. A larger computational domain is adopted to accurately resolve the turbulence above roof level and its influence on the flow characteristics in the street canyons. The LES calculated statistics of wind and pollutant transports agree well with other field, laboratory and modelling results available in the literature. The maximum wind velocity standard deviations σ _i in the streamwise (σ _u ), spanwise (σ _v ) and vertical (σ _w ) directions are located near the roof-level windward corners. Moreover, a second σ _w peak is found at z ≈ 1.5h (h is the building height) over the street canyons. Normalizing σ _i by the local friction velocity u _*, it is found that σ _u /u _* ≈ 1.8, σ _v /u _* ≈ 1.3 and σ _w /u _* ≈ 1.25 exhibiting rather uniform values in the urban roughness sublayer. Quadrant analysis of the vertical momentum flux u′′w′′ shows that, while the inward and outward interactions are small, the sweeps and ejections dominate the momentum transport over the street canyons. In the x direction, the two-point correlations of velocity R _v,x and R _w,x drop to zero at a separation larger than h but R _u,x (= 0.2) persists even at a separation of half the domain size. Partitioning the convective transfer coefficient Ω _T of pollutant into its removal and re-entry components, an increasing pollutant re-entrainment from 26.3 to 43.3% in the x direction is revealed, suggesting the impact of background pollutant on the air quality in street canyons.     

Atmospheric Stability Effects on Wind Fields and Scalar Mixing Within and Just Above a Subalpine Forest in Sloping Terrain

Air temperature T _a , specific humidity q, CO₂ mole fraction χ _c , and three-dimensional winds were measured in mountainous terrain from five tall towers within a 1 km region encompassing a wide range of canopy densities. The measurements were sorted by a bulk Richardson number Ri _b . For stable conditions, we found vertical scalar differences developed over a “transition” region between 0.05 < Ri _b < 0.5. For strongly stable conditions (Ri _b > 1), the vertical scalar differences reached a maximum and remained fairly constant with increasing stability. The relationships q and χ _c have with Ri _b are explained by considering their sources and sinks. For winds, the strong momentum absorption in the upper canopy allows the canopy sublayer to be influenced by pressure gradient forces and terrain effects that lead to complex subcanopy flow patterns. At the dense-canopy sites, soil respiration coupled with wind-sheltering resulted in CO₂ near the ground being 5–7 μmol mol⁻¹ larger than aloft, even with strong above-canopy winds (near-neutral conditions). We found Ri _b -binning to be a useful tool for evaluating vertical scalar mixing; however, additional information (e.g., pressure gradients, detailed vegetation/topography, etc.) is needed to fully explain the subcanopy wind patterns. Implications of our results for CO₂ advection over heterogenous, complex terrain are discussed.     

Exploring the Effects of Microscale Structural Heterogeneity of Forest Canopies Using Large-Eddy Simulations

The Regional Atmospheric Modeling System (RAMS)-based Forest Large-Eddy Simulation (RAFLES), developed and evaluated here, is used to explore the effects of three-dimensional canopy heterogeneity, at the individual tree scale, on the statistical properties of turbulence most pertinent to mass and momentum transfer. In RAFLES, the canopy interacts with air by exerting a drag force, by restricting the open volume and apertures available for flow (i.e. finite porosity), and by acting as a heterogeneous source of heat and moisture. The first and second statistical moments of the velocity and flux profiles computed by RAFLES are compared with turbulent velocity and scalar flux measurements collected during spring and winter days. The observations were made at a meteorological tower situated within a southern hardwood canopy at the Duke Forest site, near Durham, North Carolina, U.S.A. Each of the days analyzed is characterized by distinct regimes of atmospheric stability and canopy foliage distribution conditions. RAFLES results agreed with the 30-min averaged flow statistics profiles measured at this single tower. Following this intercomparison, two case studies are numerically considered representing end-members of foliage and midday atmospheric stability conditions: one representing the winter season with strong winds above a sparse canopy and a slightly unstable boundary layer; the other representing the spring season with a dense canopy, calm conditions, and a strongly convective boundary layer. In each case, results from the control canopy, simulating the observed heterogeneous canopy structure at the Duke Forest hardwood stand, are compared with a test case that also includes heterogeneity commensurate in scale to tree-fall gaps. The effects of such tree-scale canopy heterogeneity on the flow are explored at three levels pertinent to biosphere-atmosphere exchange. The first level (zero-dimensional) considers the effects of such heterogeneity on the common representation of the canopy via length scales such as the zero-plane displacement, the aerodynamic roughness length, the surface-layer depth, and the eddy-penetration depth. The second level (one-dimensional) considers the normalized horizontally-averaged profiles of the first and second moments of the flow to assess how tree-scale heterogeneities disturb the entire planar-averaged profiles from their canonical (and well-studied planar-homogeneous) values inside the canopy and in the surface layer. The third level (three-dimensional) considers the effects of such tree-scale heterogeneities on the spatial variability of the ejection-sweep cycle and its propagation to momentum and mass fluxes. From these comparisons, it is shown that such microscale heterogeneity leads to increased spatial correlations between attributes of the ejection-sweep cycle and measures of canopy heterogeneity, resulting in correlated spatial heterogeneity in fluxes. This heterogeneity persisted up to four times the mean height of the canopy (h _c ) for some variables. Interestingly, this estimate is in agreement with the working definition of the thickness of the canopy roughness sublayer (2h _c –5h _c ).     

THE EJECTION-SWEEP CHARACTER OF SCALAR FLUXES IN THE UNSTABLE SURFACE LAYER

In the atmospheric surface layer, it is widely accepted that ejection andsweep eddy motions, typically associated with coherent structures, areresponsible for much of the land-surface evaporation, sensible heat, andmomentum fluxes. The present study analyzes the ejection-sweep propertiesusing velocity and scalar fluctuation measurements over tall natural grassand bare soil surfaces. It is shown that momentum ejections and sweeps occurat equal frequencies (D eject D sweep 0.29) irrespective of surfaceroughness length or atmospheric stability conditions. Also, their magnitudesare comparable to values reported from open channel velocity measurements (Dsweep 0.33; D eject : 0.30). The scalar D eject is constant andsimilar in magnitude to the momentum D eject( 0.29) over both surfacesand for a wide range of atmospheric stability conditions, in contrast to thescalar D sweep. The scalar sweep frequency is shown to depend on the scalarskewness for the dynamic convective and free convective sublayers, but isidentical to D eject for the dynamic sublayer. The threshold scalar skewnessat which the D sweep dependence occurs is 0.25, in agreement with theaccepted temperature skewness value at near-neutral conditions. In contrastto a previous surface-layer experiment, this investigation demonstrates thatthe third-order cumulant expansion method (CEM) reproduces the measuredrelative flux contribution of ejections and sweeps (S0) for momentumand scalars at both sites. Furthermore, a linkage between S0 and thescalar variance budget is derived via the third-order CEM in analogy tomomentum. It is shown that S0 can be related to the flux divergenceterm and that such a relationship can be estimated from surface-layersimilarity theory, and the three sublayer model of Kader and Yaglom andproposed similarity functions.     

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.     

The Effects of Inner- and Outer-Layer Turbulence in a Convective Boundary Layer on the Near-Neutral Inertial Sublayer Over an Urban-Like Surface

A large-eddy simulation of the atmospheric boundary layer, large enough to contain both an urban surface layer and a convective mixed layer, was performed to investigate inner-layer and outer-layer scale motions. The objective was to determine the applicability of Monin–Obukhov similarity theory to inner-layer motions, to investigate the influence of outer-layer motions on surface-layer structure, as well as to assess the interaction of the two scales of motion. The urban surface roughness consisted of square-patterned cubic buildings of dimension H (40 m). A spatial filter was used to decompose the two scales in the inertial sublayer. The horizontal square filter of size 10H was effective in separating the inner-layer (surface-layer height ≈ 2 H) and outer-layer scales (boundary-layer height δ ≈ 30H), where the Reynolds stress contribution of the inner layer dominates in the logarithmic layer (depth 2H). Similarity coefficients for velocity fluctuations were successfully determined for inner-layer motions in the surface layer, proving the robustness of Monin–Obukhov similarity for surface-layer turbulence. The inner-layer structures exhibit streaky structures that have similar streamwise length but narrower spanwise width relative to the streamwise velocity fluctuation field, consistent with observations from an outdoor scale model. The outer-layer motions to some extent influence the location of ejections and sweeps through updraft and downdraft motions, respectively, thus, disturbing the homogeneity and similarity of inner-layer motions. Although the horizontal averages of the variances and covariance of motions reveal that the Reynolds stresses are dominated by inner-layer structures, the localized influence of the interaction of outer-layer horizontal and inner-layer vertical motions on the Reynolds stress is not insignificant.     

Observation of organized structure in turbulent flow within and above a forest canopy

Ramp patterns of temperature and humidity occur coherently at several levels within and above a deciduous forest as shown by data gathered with up to seven triaxial sonic anemometer/thermometers and three Lyman-alpha hygrometers at an experimental site in Ontario, Canada. The ramps appear most clearly in the middle and upper portion of the forest. Time/height cross-sections of scalar contours and velocity vectors, developed from both single events and ensemble averages of several events, portray details of the flow structures associated with the scalar ramps. Near the top of the forest they are composed of a weak ejecting motion transporting warm and/or moist air out of the forest followed by strong sweeps of cool and/or dry air penetrating into the canopy. The sweep is separated from the ejecting air by a sharp scalar microfront. At approximately twice the height of the forest, ejections and sweeps are of about equal strength.In the middle and upper parts of the canopy, sweeps conduct a large proportion of the overall transfer between the forest and the lower atmosphere, with a lesser contribution from ejections. Ejections become equally important aloft. During one 30-min run, identified structures were responsible for more than 75% of the total fluxes of heat and momentum at mid-canopy height. Near the canopy top, the transition from ejection of slow moving fluid to sweep bringing fast moving air from above is very rapid but, at both higher and lower levels, brief periods of upward momentum transfer occur at or immediately before the microfront.     

Experiments on scalar dispersion within a model plant canopy part II: An elevated plane source

This paper describes a wind-tunnel experiment on the dispersion of trace heat from an effectively planar source within a model plant canopy, the source height being h _s = 0.80 h _c , where h _c is the canopy height. A sensor assembly consisting of three coplanar hot wires and one cold wire was used to make simultaneous measurements of the temperature and the streamwise and vertical velocity components. It was found that:

1. The thermal layer consisted of two parts with different length scales, an inner sublayer (scaling with h _s and h _c ) which quickly reached streamwise equilibrium downstream of the leading edge of the source, and an outer sublayer which was self-preserving with a length scale proportional to the depth of the thermal layer.
2. Below 2h _c , the vertical eddy diffusivity for heat from the plane source (K _HP ) was substantially less than the far-field limit of the corresponding diffusivity for heat from a lateral line source at the same height as the plane source. This shows that dispersion from plane or other distributed sources in canopies is influenced, near the canopy, by turbulence ‘memory’ and must be considered as a superposition of both near-field and far-field processes. Hence, one-dimensional models for scalar transport from distributed sources in canopies are wrong in principle, irrespective of the order of closure.
3. In the budgets for temperature variance, and for the vertical and streamwise components of the turbulent heat flux, turbulent transport was a major loss between h _s and h _c and a principal gain mechanism below h _s , as also observed in the budgets for turbulent energy and shear stress.
4. Quadrant analysis of the vertical heat flux showed that sweeps and ejections contributed about equal amounts to the heat flux between h _s and h _c , though among the more intense events, sweeps were dominant. Below h _s , almost all the heat was transported by sweeps.

     

Flux contribution of coherent structures and its implications for the exchange of energy and matter in a tall spruce canopy

The flux contribution of coherent structures to the total exchange of energy and matter is investigated in a spruce canopy of moderate density in heterogeneous, complex terrain. The study deploys two methods of analysis to estimate the coherent exchange: conditional averages in combination with wavelet analysis, and quadrant analysis. The data were obtained by high-frequency single-point measurements using sonic anemometers and gas analysers at five observation heights above and within the canopy and subcanopy, and represent a period of up to 2.5 months. The study mainly addresses the momentum transfer and exchange of sensible heat throughout the roughness sublayer, while results are provided for the exchange of carbon dioxide and water vapour above the canopy. The magnitude of the flux contribution of coherent structures largely depends on the method of analysis, and it is demonstrated that these differences are attributed to differences in the sampling strategy between the two methods. Despite the differences, relational properties such as sweep and ejection ratios and the variation of the flux contribution with height were in agreement for both methods. The sweep phase of coherent structures is the dominant process close to and within the canopy, whereas the ejections gain importance with increasing distance to the canopy. The efficiency of the coherent exchange in transporting scalars exceeds that for momentum by a factor of two. The occurrence of coherent structures results in a flux error less than 4% for the eddy-covariance method. Based on the physical processes identified from the analysis of the ejection and sweep phases along the vertical profile in the roughness sublayer, a classification scheme for the identification of exchange regimes is developed. This scheme allows one to estimate the region of the canopy participating in the exchange of energy and matter with the above-canopy air under varying environmental conditions.     

Coherent eddies and turbulence in vegetation canopies: The mixing-layer analogy

This paper argues that the active turbulence and coherent motions near the top of a vegetation canopy are patterned on a plane mixing layer, because of instabilities associated with the characteristic strong inflection in the mean velocity profile. Mixing-layer turbulence, formed around the inflectional mean velocity profile which develops between two coflowing streams of different velocities, differs in several ways from turbulence in a surface layer. Through these differences, the mixing-layer analogy provides an explanation for many of the observed distinctive features of canopy turbulence. These include: (a) ratios between components of the Reynolds stress tensor; (b) the ratio K _H/K _M of the eddy diffusivities for heat and momentum; (c) the relative roles of ejections and sweeps; (d) the behaviour of the turbulent energy balance, particularly the major role of turbulent transport; and (e) the behaviour of the turbulent length scales of the active coherent motions (the dominant eddies responsible for vertical transfer near the top of the canopy). It is predicted that these length scales are controlled by the shear length scale % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamitamaaBa% aaleaacaWGtbaabeaakiabg2da9iaadwfacaGGOaGaamiAaiaacMca% caGGVaGabmyvayaafaGaaiikaiaadIgacaGGPaaaaa!3FD0!\[L_S = U(h)/U'(h)\] (where h is canopy height, U(z) is mean velocity as a function of height z, and % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyvayaafa% Gaeyypa0JaaeizaiaadwfacaGGVaGaaeizaiaadQhaaaa!3C32!\[U' = {\rm{d}}U/{\rm{d}}z\]). In particular, the streamwise spacing of the dominant canopy eddies is _x = mL _s, with m = 8.1. These predictions are tested against many sets of field and wind-tunnel data. We propose a picture of canopy turbulence in which eddies associated with inflectional instabilities are modulated by larger-scale, inactive turbulence, which is quasi-horizontal on the scale of the canopy.     

Dispersive Stresses at the Canopy Upstream Edge

The derivation of flow and mass transfer models in canopy and porous media environments involves the spatial-averaging of the flow properties and their subscale equations. The averaging of the momentum equation generates the dispersive stress terms that represent the subscale spatial variations of the unresolved velocity field. While previous studies ignored the dispersive stresses in their flow models, recent evidence indicates that the dispersive stresses may be important. Here we focus our attention on the magnitude of the normal dispersive stresses in the entry region of a ‘forest patch’, where the in-canopy velocities are large and the longitudinal derivatives do not cancel out. Highly detailed particle image velocimetry measurements, at a temporal and spatial resolution of 5 Hz and 1.4 mm, are obtained inside and around a 1-m long model canopy which consists of transparent vertical cylinders 6 mm in diameter and 74.3 mm high (h). The cylinders are randomly distributed to form a relatively sparse forest patch with a leaf area density of 7.56 m⁻¹ and a fluid volume fraction (porosity) of 0.965. We present results of the double averaged flow properties at three different regions of the forest patch; the upstream edge (x ≈ 0), the fully-developed interior region (x ≈ 10h) and the downstream edge (x ≈ 13h). We find that the normal dispersive stresses around the entry region of the forest patch are significantly larger than the normal Reynolds stresses. An order of magnitude analysis of the relevant terms in the momentum equation indicates that the longitudinal derivatives of the dispersive stresses are of the same order of magnitude as that of the drag force and similar to that of the horizontal convection term. The longitudinal derivatives of the Reynolds stresses are smaller, though cannot be ignored. Comparing these results with the characteristic profiles measured in the fully-developed region indicates that the dispersive stresses, which are generated at the forest patch entrance, decrease along an adjustment region while maintaining their profile shape. We find that the dispersive stresses influence the rate at which momentum penetrates into the canopy. These observations suggest that under certain flow conditions, dispersive stresses may dominate the momentum balance and therefore must be considered in future canopy and porous media flow models.     

Flux–Profile Relationships Over a Fetch Limited Beech Forest

The influence of an internal boundary layer and a roughness sublayer on flux–profile relationships for momentum and sensible heat have been investigated for a closed beech forest canopy with limited fetch conditions. The influence was quantified by derivation of local scaling functions for sensible heat flux and momentum (_h and _m) and analysed as a function of atmospheric stability and fetch. For heat, the influences of the roughness sublayer and the internal boundary layer were in agreement with previous studies. For momentum, the strong vertical gradient of the flow just above the canopy top for some wind sectors led to an increase in _m, a feature that has not previously been observed. For a fetch of 500 m over the beech forest during neutral atmospheric conditions, there is no height range at the site where profiles can be expected to be logarithmic with respect to the local surface. The different influence of the roughness sublayer on _h and _m is reflected in the aerodynamic resistance for the site. The aerodynamic resistance for sensible heat is considerably smaller than the corresponding value for momentum.