Characteristics of air flow above and within soybean canopies

Air flow was observed above and within canopies of a number of kinds of soybeans. The Clark cultivar and two isolines of the Harosoy cultivar were studied in 1979 and 1980, respectively. Wind speed above the canopy was measured with cup anemometers. Heated thermistor anemometers were used to measure air flow within the canopy. Above-canopy air flow was characterized in terms of the zero-plane displacement (d), roughness parameter (z _o) and drag coefficient (C _d). d and z _o were dependent on canopy height but were independent of friction velocity in the range 0.55 to 0.75 m s^?1 · C _d for the various canopies ranged from 0.027 to 0.035. Greater C _d values were measured over an erectophile canopy than over a planophile canopy. C _d was not measurably affected by differences in leaf pubescence. Within-canopy wind profiles were measured at two locations: within and between rows. The wind profile was characterized by a region of great wind shear in the upper canopy and by a region of relatively weak wind shear in the middle canopy. Considerable spatial variability in wind speed was evident, however. This result has significant implications for canopy flow modeling efforts aimed at evaluating transport in the canopy. In the lower canopy, wind speed within a row increased with depth whereas wind speed between two rows decreased with depth. The wind speeds at the two locations tended to converge to a common value at a height near 0.10 m. The attenuation of within-canopy air flow was stronger in canopies with greater foliage density. Canopy flow attenuation seemed to decrease with increasing wind speed, suggesting that high winds distorted the shape of the canopy in such a manner that the penetration of wind into the canopy increased.     

Equations for the Drag Force and Aerodynamic Roughness Length of Urban Areas with Random Building Heights

We use a conceptual model to investigate how randomly varying building heights within a city affect the atmospheric drag forces and the aerodynamic roughness length of the city. The model is based on the assumptions regarding wake spreading and mutual sheltering effects proposed by Raupach (Boundary-Layer Meteorol 60:375?C395, 1992). It is applied both to canopies having uniform building heights and to those having the same building density and mean height, but with variability about the mean. For each simulated urban area, a correction is determined, due to height variability, to the shear stress predicted for the uniform building height case. It is found that u _*/u _*R , where u _* is the friction velocity and u _*R is the friction velocity from the uniform building height case, is expressed well as an algebraic function of ?? and ?? _h /h _m , where ?? is the frontal area index, ?? _h is the standard deviation of the building height, and h _m is the mean building height. The simulations also resulted in a simple algebraic relation for z ₀/z _0R as a function of ?? and ?? _h /h _m , where z ₀ is the aerodynamic roughness length and z _0R is z ₀ found from the original Raupach formulation for a uniform canopy. Model results are in keeping with those of several previous studies.     

Mean Flow and Turbulence Characteristics in an Urban Roughness Sublayer

In this study, a detailed model of an urban landscape has been re-constructed inthe wind tunnel and the flow structure inside and above the urban canopy has beeninvestigated. Vertical profiles of all three velocity components have been measuredwith a Laser-Doppler velocimeter, and an extensive analysis of the measured meanflow and turbulence profiles carried out. With respect to the flow structure inside thecanopy, two types of velocity profiles can be distinguished. Within street canyons,the mean wind velocities are almost zero or negative below roof level, while closeto intersections or open squares, significantly higher mean velocities are observed.In the latter case, the turbulent velocities inside the canopy also tend to be higherthan at street-canyon locations. For both types, turbulence kinetic energy and shearstress profiles show pronounced maxima in the flow region immediately above rooflevel.Based on the experimental data, a shear-stress parameterization is proposed, inwhich the velocity scale, u_s, and length scale, z_s, are based on the level and magnitude of the shear stress peak value. In order to account for a flow region inside the canopy with negligible momentum transport, a shear stress displacement height, d_s, is introduced. The proposed scaling and parameterization perform well for the measured profiles and shear-stress data published in the literature.The length scales derived from the shear-stress parameterization also allowdetermination of appropriate scales for the mean wind profile. The roughnesslength, z₀, and displacement height, d₀, can both be described as fractions of the distance, z_s - d_s, between the level of the shear-stress peak and the shear-stress displacement height. This result can be interpreted in such a way that the flow only feels the zone of depth z_s - d_s as the roughness layer. With respect to the lower part of the canopy (z < d_s) the flow behaves as a skimming flow. Correlations between the length scales z_s and d_s and morphometric parameters are discussed.The mean wind profiles above the urban structure follow a logarithmic windlaw. A combination of morphometric estimation methods for d₀ and z₀ with wind velocity measurements at a reference height, which allow calculation of the shear-stress velocity, u_*, appears to be the most reliable and easiest procedure to determine mean wind profile parameters. Inside the roughnesssublayer, a local scaling approach results in good agreement between measuredand predicted mean wind profiles.     

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.     

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.     

Heat and Mass Transfer to and from Surfaces with Dense Vegetation or Similar Permeable Roughness

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO₂, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z ₀/ z _oc ) (where z ₀ is the momentum roughness and Z _oc the scalar roughness) for permeable roughness elements is relatively insensitive to u _* and practically independent of z ₀.     

Influence of non-flat terrain and wind direction shear on canopy turbulence

We have analyzed eddy covariance data collected within open canopy to investigate the influence of non-flat terrain and wind direction shear on the canopy turbulence. The study site is located on non-flat terrain with slopes in both south-north and east-west directions. The surface elevation change is smaller than the height of roughness element such as building and tree at this site. A variety of turbulent statistics were examined as a function of wind direction in near-neutral conditions. Heterogeneous surface characteristics results in significant differences in measured turbulent statistics. Upwind trees on the flat and up-sloping terrains yield typical features of canopy turbulence while upwind elevated surface with trees yields significant wind direction shear, reduced u and w skewness, and negligible correlation between u and w. The directional dependence of turbulence statistics is due that strong wind blows more horizontally rather than following terrain, and hence combination of slope related momentum flux and canopy eddy motion decreases the magnitude of Sk _w and r _uw for the downslope flow while it enhances them for the upslope flow. Significant v skewness to the west indicates intermittent downdraft of northerly wind, possibly due to lateral shear of wind in the presence of significant wind direction shear. The effects of wind direction shear on turbulent statistics were also examined. The results showed that correlation coefficient between lateral velocities and vertical velocity show significant dependence on wind direction shear through change of lateral wind shear. Quadrant analysis shows increased outward interaction and reduced role of sweep motion for longitudinal momentum flux for the downslope flow. Multi-resolution analysis indicates that uw correlation shows peak at larger averaging time for the upslope flow than for the downslope flow, indicating that large eddy plays an active role in momentum transfer for the upslope flow. On the other hand, downslope flow shows larger velocity variances than other flows despite similar wind speed. These results suggest that non-flatness of terrain significantly influences on canopy-atmosphere exchange.     

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.     

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.     

A Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.     

Large-eddy Simulations of Flow Over Forested Ridges

Large-eddy simulations (LES) of flow over a series of small forested ridges are performed, and compared with numerical simulations using a one-and-a-half order mixing length closure scheme. The qualitative and quantitative similarity between these results provides some confidence in the results of recent analytical and numerical studies of flow over forested hills using first-order mixing length schemes. Time series of model velocities at various locations within the canopy allow the application of various experimental techniques to study the turbulence in the LES. The application of conditional analysis shows that the structure of the turbulence over a forested hill is broadly similar to that over flat ground, with sweeps and ejections dominating. Differences are seen across the hill, particularly associated with regions of mean flow separation and recirculation near the summit and in the lee of the hill. Detailed comparison of derived mixing lengths from the LES with the assumed values used in mixing-length closure schemes show that the mixing length varies with location across the hill and with height in the canopy. This is consistent with previous wind-tunnel measurements, and demonstrates that a constant mixing-length assumption is not strictly valid within the canopy. Despite this, the first-order mixing-length schemes do give similar results both for the mean flow and the turbulence in such situations.     

Calculation of velocity skewness in real and artificial plant canopies

Wind velocities within a plant canopy are much more strongly skewed than those of the air flow above. We have examined the governing Eulerian equations for the velocity products u _i, u _j u_k using data from a wind tunnel study with an artificial canopy consisting of an array of 5 cm lengths of monofilament fishing line, and from measurements in corn (Zea mays L).Simple parameterizations for pressure-velocity correlations, and for the quadruple velocity products allowed reasonably accurate calculations of the third moments using measured profiles of the mean velocity, variance and covariance fields. Comparisons of individual terms in the rate equations for ovu _i, u _j u _krevealed that diffusion (from above) and mean shear were most important in creating large skewness in the canopy. A drag term also contributed but was of lesser importance. These terms were balanced by return-to-isotropy and a turbulence interaction term. A quasi-Gaussian approximation considerably underestimated the magnitude of the fourth moments within the canopy.     

Influence of foliar density and thermal stability on profiles of Reynolds stress and turbulence intensity in a deciduous forest

Observations were made of turbulence in an extensive deciduous forest on level terrain using a vertical array of seven three-dimensional sonic anemometer/thermometers within and above the canopy. Data were collected through the period of leaf fall and over a range of thermal stabilities. A bulk canopy drag coefficient was nearly independent of the density of the forest but decreased greatly with the onset of nocturnal stability. The depth of penetration of momentum into the forest increased with leaf fall but, again, was greatly curtailed by stable conditions. Turbulent velocities decreased with increasing depth in the forest but relative turbulence intensities increased to mid-canopy levels. Leaf density influenced turbulence levels but not as strongly as did thermal stability. Thermal effects were adequately described by the single parameter h/L, where h is the canopy height and L is the Monin-Obukhov length. The longitudinal and vertical velocity correlation coefficient was larger in magnitude than expected in the upper layers of the forest but decreased to a small value in the lowest layers where the Reynolds stress was small. The ratio _w /u ^*, where u ^* is the local friction velocity, reflected changes in the uw correlation, becoming smaller than usual in the upper canopy layers. It is believed that these effects result from the intermittent, spatially coherent structures that are responsible for a large fraction of the momentum flux to the forest.     

Heat and mass transfer to and from surfaces with dense vegetation or similar permeable roughness

A differential equation is obtained to describe the concentration of passive admixtures (water vapor, sensible heat, pollutants, CO₂, etc.) of turbulent flow inside a dense and uniform vegetational canopy. The profiles of eddy diffusivity, wind speed and shear stress are assumed to be exponential decay functions of depth below the top of the canopy. This equation is solved for the case of a vegetation with constant concentration of the admixture at the foliage surfaces. The solution is used to formulate bulk mass or heat transfer coefficients, which can be applied to practical problems involving surfaces covered with a vegetation or with similar porous or fibrous roughness elements. The results are shown to be consistent with experimental data presented by Chamberlain (1966), Garratt and Hicks (1973) and Garratt (1978). Calculations with the model illustrate that, as compared to its behavior over surfaces with bluff roughness elements, ln(z ₀/z _0c ) (wherez ₀ is the momentum roughness andz _0c , the scalar roughness) for permeable roughness elements is relatively insensitive tou _* and practically independent ofz ₀.     

Intermittent wind close to the ground within a grass canopy

Wind speed was measured at a height of 1 cm above the ground and at several other heights in and above a canopy of tall fescue grass (Festuca arundinacea) using single hot-wire and triple hot-film anemometers. The plant area density in the canopy was concentrated close to the ground, with 75% of the plant area standing belowz=15 cm, wherez is height above the ground. The frequency distributions of horizontal wind speeds,s, were sharply skewed towards positive values at all measurement heights, but were most highly skewed near the ground where the coefficient of skewness ranged from 1.6 to 2.9. Above mid-canopy height, the frequency distribution ofs was described reasonably well by a Gumbel extreme value distribution. Average wind speed,S, decreased exponentially with depth into the canopy with an exponential scale length of abouth/2.8, whereh is the height of the canopy. Atz=1 cm, the value ofS was about 11% of the surface-layeru _*. The standard deviation of the fluctuations of the vertical and horizontal components of the wind speed also decreased exponentially with depth inside the canopy with a scale length of abouth/2.5.Inside the canopy, the Eulerian integral time scales for the vertical ( _w ) and horizontal ( _u ) components of wind speed were about 0.1 s and 1.0 s, respectively, and were approximately constant with height. Above the canopy, these time scales increased sharply and, atz=2.25h, _w and _u were approximately 1.0 and 3.0s, respectively. Turbulence length scales in the vertical and downwind directions, _u and _w ·U, respectively, were approximately 1 cm for heights between 1 to 10 cm above the ground inside the canopy, while atz=2.25h, they were about 55 cm and 277 cm. Relatively quiescent periods (lulls) in the air close to the ground were interrupted frequently by gusts. The frequency of occurrence of gusts appears to be correlated with the value of the local shear near the top of the canopy.     

Dispersion in sheared Gaussian homogeneous turbulence

By integrating the Fokker-Planck equation corresponding to a Lagrangian stochastic trajectory model, which is consitent with the selection criterion of Thomson (1987), an analytical solution is given for the joint probability density functionp(x_i, u_i, t) for the position (x _i) and velocity (u _i) at timet of a neutral particle released into linearly-sheared, homogeneous turbulence. The solution is compared with dispersion experiments conforming to the restrictions of the model and with a shortrange experiment performed in highly inhomogeneous turbulence within and above a model crop canopy. When the turbulence intensity, wind shear and covariance are strong, the present solution is better than simpler solutions (Taylor, 1921; Durbin, 1983) and as good as any numerical Lagrangian stochastic model yet reported.     

Stratified airflow over one or two hills

Methods for calculating, interpolating and idealising air flow in complex terrain are reviewed. Then the general structure of stratified airflow over a single hill of height H and length L₁ is studied in detail and shown to be determined by the upwind velocity profile, the magnitude of a characteristic Froude number and the dimensions of the hill. Let N(L₁) be the buoyancy frequency upwind at a height L₁, and u_* and U₀ be the upwind friction and mean velocity respectively; then the flow is effectively neutral if u^*/NL₁>1. But if u_*/NL₁>1 and u₀/NL₁>1, the stratification is weak enough to affect the upwind turbulence and velocity profile but not the dynamics of the flow over the hill. If U₀/NL₁ <1 but U₀/NH>1 the buoyancy forces are strong enough to affect the mean flow over the hill but not strong enough to prevent it passing over the top. In this regime the flow is very sensitive to the form of the upwind temperature profile. If U₀/NH>1, much of the flow passes round the hill. A similar classification, with different flow patterns, is appropriate for unstably stratified flows. When the wind is weak enough, local slope winds can dominate. Results from the analysis of these different regimes are described and compared with laboratory of field measurements where possible. It is shown how some of these results can be extended to groups of hills.     

Markov chain simulations of vertical dispersion from elevated sources into the neutral planetary boundary layer

A Lagrangian statistical-trajectory model based on a Markov chain relation is used to investigate vertical dispersion from elevated sources into the neutral planetary boundary layer. The model is fully two-dimensional, in that both vertical and longitudinal velocity fluctuations, and their correlation, are simulated explicitly. The best observational information currently available is used to characterize the mean and turbulent structure of the neutral boundary layer. In particular, a realistic vertical profile of the Lagrangian integral time scale is proposed, based partly on a review of direct measurements and partly on a comparison of the model predictions with published diffusion data. The model predictions are shown to agree well with a variety of dispersion observations. The model is used to study vertical diffusion as a function of release height H, friction velocity u* and surface roughness z ₀ for downwind distances up to 10 km from the source. The equivalent Gaussian dispersion parameter Σ _z is shown to decrease slightly with an increase in H, and to increase with increases in z ₀ or u*. It is demonstrated that relationships valid in a field of homogeneous turbulence can be applied to vertical dispersion in the atmosphere if the release occurs above the region of strongest gradients in the mean and turbulent parameters. Scaling in terms of the standard deviation in elevation angle of the wind at the release point leads to a universal curve which provides accurate estimates of Σ _z over a wide range of values of H, z ₀ and the meteorological parameters.     

Estimation of Roughness Parameters Within Sparse Urban-Like Obstacle Arrays

We conduct wind-tunnel experiments on three different uniform roughness arrays composed of sparsely distributed rectangular cylinders for the estimation of surface parameters. Roughness parameters such as the roughness length z ₀ and zero-plane displacement d are extracted using a best-fit approximation of the measured wind velocity. We also perform a large-eddy simulation (LES) to confirm that four sampling points are sufficient to surrogate a space average above the canopy layer of the sparse roughness arrays. We propose a new morphological model from a systematic analysis of experimental data on the arrays. The friction velocity predicted by the proposed model agrees well with the peak value of the measured Reynolds shear stress ${(-\left<\overline{u'w'}\right>)^{0.5}}${(-\left<\overline{u'w'}\right>)^{0.5}}. The proposed model is further validated in an additional wind-tunnel experiment conducted on a scaled configuration of a real urban area exposed to four wind directions. The proposed model is found to perform very well particularly in the estimation of the friction velocity, readily leading to a better estimation of turbulence, which is essential for an accurate prediction of pollutant dispersion.