Shear-Stress Partitioning in Live Plant Canopies and Modifications to Raupach’s Model

The spatial peak surface shear stress t_S^￠￠{\tau _S^{\prime\prime}} on the ground beneath vegetation canopies is responsible for the onset of particle entrainment and its precise and accurate prediction is essential when modelling soil, snow or sand erosion. This study investigates shear-stress partitioning, i.e. the fraction of the total fluid stress on the entire canopy that acts directly on the surface, for live vegetation canopies (plant species: Lolium perenne) using measurements in a controlled wind-tunnel environment. Rigid, non-porous wooden blocks instead of the plants were additionally tested for the purpose of comparison since previous wind-tunnel studies used exclusively artificial plant imitations for their experiments on shear-stress partitioning. The drag partitioning model presented by Raupach (Boundary-Layer Meteorol 60:375–395, 1992) and Raupach et al. (J Geophys Res 98:3023–3029, 1993), which allows the prediction of the total shear stress τ on the entire canopy as well as the peak (t_S ^￠￠/t)^1/2{(\tau _S ^{\prime\prime}/\tau )^{1/2}} and the average (t_S^￠/t)^1/2{(\tau _S^{\prime}/\tau )^{1/2}} shear-stress ratios, is tested against measurements to determine the model parameters and the model’s ability to account for shape differences of various roughness elements. It was found that the constant c, needed to determine the total stress τ and which was unspecified to date, can be assumed a value of about c = 0.27. Values for the model parameter m, which accounts for the difference between the spatial surface average t_S^￠{\tau _S^{\prime}} and the peak t_S ^￠￠{\tau _S ^{\prime\prime}} shear stress, are difficult to determine because m is a function of the roughness density, the wind velocity and the roughness element shape. A new definition for a parameter a is suggested as a substitute for m. This a parameter is found to be more closely universal and solely a function of the roughness element shape. It is able to predict the peak surface shear stress accurately. Finally, a method is presented to determine the new a parameter for different kinds of roughness elements.     

Experimental Investigation on Shear-Stress Partitioning for Flexible Plants with Approximately Zero Basal-to-Frontal Area Ratio in a Wind Tunnel

Shear-stress partitioning is investigated for one type of flexible plant for very small values of the basal-to-frontal area ratio σ (0.001–0.007). The plant model is made of plastic with irregular structures, which are different from previously investigated rigid regular or flexible roughness elements with larger σ values. The distribution of the surface shear stress and the total shear stress at four plant densities with five plant heights are measured in a wind tunnel using Irwin-type sensors and a load cell, respectively. The wind-tunnel experiments prove that, for these flexible plants, the plant height and lateral cover usually decrease with increasing friction velocity, especially for taller plants, while the plant coverage generally increases. However, these characteristics may be inconsistent with flexible roughness elements with very large σ values (and usually very low aspect ratios) because these elements are less flexible. The present flexible plants generally result in lower shear-stress ratios compared with other roughness elements, which is also proven by the higher values of β (the ratio of the drag coefficient of an isolated roughness element to that of the bare surface) and a constant m (accounting for the difference between the average and peak surface shear stresses) from the present experiments (β?=?184–210 and m?=?0.68–0.79). The peak mean stress ratio of the present flexible plants is not a constant (1.07–1.54) because it is affected by the lateral cover, which is different from previous studies that consider the ratio to be constant without regard for the lateral cover.     

Observations of the barotropic Ekman layer over an urban terrain

Data from low-level soundings over Cambridge, U.S.A. were selected on the basis of an Ekman-like variation of the wind vector with altitude combined with evidence of a barotropic atmosphere. The method of geostrophic departure was used to determine the shear-stress distribution. The analysis yields the dimensionless properties of the barotropic Ekman layer under neutral and stable stratification. Some important results include: the geostrophic drag coefficient displays no dependence on the degree of static stability; the dimensionless height of the boundary layer decreases with increasing stability in agreement with the prediction of Zilitinkevich; the properties of the urban surface layer, where the roughness elements are multistory buildings, show no dependence on atmospheric stability under the moderate wind conditions which display the Ekman-like wind profile; and the directions of the horizontal shear stress and the vertical derivative of the velocity vector usually tend to be parallel only near the surface layer. Values of the two constants of the Rossby number similarity theory are found for the neutral barotropic Ekman layer at a surface Rossby number equal to 2 × 10⁵. The implications of the work with respect to wind-tunnel simulation of the flow over models of urban areas are discussed.     

Drag Partition for Regularly-Arrayed Rough Surfaces

Vegetation and other roughness elements distributed across a surface can providesignificant protection against wind erosion by extracting momentum from the flowand thereby reducing the shear stress acting at the surface. A theoretical model haspreviously been presented to specify the partition of drag forces for rough surfacesand to predict required vegetation density to suppress wind erosion. However, themodel parameters have not yet been constrained and the predictive capacity of themodel has remained uncertain. A wind-tunnel study was conducted to measure thedrag partition for a range of roughness densities and to parameterise the model inorder to improve its range of potential applicability. The drag forces acting on bothan array of roughness elements and the intervening surface were measured independentlyand simultaneously using new drag balance instrumentation. A detailed measure of thespatial heterogeneity of surface shear stresses was also made using Irwin sensors. Thedata agreed well with previous results and confirmed the general form of the model.Analysis of the drag partition confirmed the parameter definition = C_R/C_S(where C_R and C_S are roughness element and surface drag coefficients,respectively) and a constant proportional difference between the mean and maximumsurface shear stress was found. The results of this experiment suggest that the definitionfor m, the surface shear stress inhomogeneity parameter, should be revised, although thetheoretical and physical reasons for including this parameter in the model appear to bevalid. Best-fit values for m ranged from 0.53 to 0.58.     

The Askervein Hill Project: Wind-tunnel simulations at three length scales

Wind-tunnel simulations of neutrally-stable atmospheric boundary-layer flow over an isolated, low hill (Askervein) have been carried out at three different length scales in two wind-tunnel facilities. The objectives of these simulations were to assess the reliability with which changes in mean wind and turbulence structure induced by the prototype hill on boundary-layer flow can be reproduced in the wind tunnel, and to determine the relative impact of certain modelling approaches (surface roughness, model scale, measurement techniques, etc.) on the quality of the simulations. The wind-tunnel results are compared with each other and with full-scale data and are shown in general to model the prototype flow very well. The effects of relaxing the criterion of aerodynamic roughness of the model surface were limited to certain regions in the lee of the hill and were linked to separation phenomena.     

A wind-tunnel boundary-layer study of the effects of a surface roughness change: Rough to smooth

The changes imposed on mean velocities and turbulence statistics in the lower atmosphere by an abrupt change in surface roughness, from very rough to smooth, were modelled in a wind tunnel. The influence of a change in the effective surface level, which often accompanies such a variation in surface roughness, was also studied. A deep, turbulent flow was generated upstream of the change, which had a logarithmic mean velocity profile and constant shear-stress for approximately 200 mm above the floor, except for a region near the surface which was influenced by the three-dimensional nature of the random rough surface.When the surface roughness change coincided with a change in surface level, the downstream flow close to the surface was in the wake of the upstream roughness elements, and measured Reynolds shear-stress values were lower than those obtained when the downstream surface was raised. Otherwise, the influence of a change in surface level was small.In all cases, Reynolds shear-stress varied approximately linearly with height in the lower two-thirds of the internal layer and no constant stress region was apparent near the surface, even 2 m downstream of the roughness change. When the roughness change was not accompanied by a change in level, Reynolds shear-stress values extrapolated to the surface agreed well with surface shear-stress inferred from the law of the wall.Changes in mean squares of vertical and lateral velocity fluctuations and in integral time scales, as the flow passed downstream of the roughness change, were surprisingly small.     

Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

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.     

Turbulent flow over a very rough,random surface

A knowledge of the nature of turbulent flow over very rough surfaces is important for an understanding of the environment of crops, forests, and cities. For this reason, a wind-tunnel investigation was carried out on the variations in mean velocity, Reynolds shear-stress, and other turbulence quantities in a deep turbulent flow over a rough surface having a fair degree of randomness in the shapes, sizes, and positions of its elements.There was a layer close to the surface with considerable variations in both mean velocity and shear-stress, and the horizontal scale over which the mean velocity varied was much larger than the average distance between roughness elements. Above this layer, whose depth was of the order of the spacing between roughness elements, shear stress was constant with height, and the velocity profile had a logarithmic form. The usefulness of both mean profile and eddy-correlation methods for estimating fluxes above very rough terrain is discussed in the light of these findings.     

Field And Wind-Tunnel Studies Of Aerodynamic Roughness Length

The aerodynamic roughness length (z₀) values of three Gobi desert surfaces were obtained by measurement of the boundary-layer wind profile in the field. To clarify the factors affecting the Gobi surface aerodynamic roughness length, a wind-tunnel experiment was conducted. The wind-tunnel simulation shows that z₀ values increase with increasingsize and coverage of roughness elements. Especially, the shape and height of roughnesselements are more important than other factors in affecting roughness length. The roughness length increases with decreasing values of the geometric parameter (the ratio of element horizontal surface area to height, ) of roughness elements. But at a higher free stream velocity, the height is more important than the shape in affecting roughness length.     

A Simple Model for Spatially-averaged Wind Profiles Within and Above an Urban Canopy

This paper deals with the modelling of the flow in the urban canopy layer. It critically reviews a well-known formula for the spatially-averaged wind profile, originally proposed by Cionco in 1965, and provides a new interpretation for it. This opens up a number of new applications for modelling mean wind flow over the neighbourhood scale. The model is based on a balance equation between the obstacle drag force and the local shear stress as proposed by Cionco for a vegetative canopy. The buildings within the canopy are represented as a canopy element drag formulated in terms of morphological parameters such as λ _f and λ _p (the ratios of plan area and frontal area of buildings to the lot area). These parameters can be obtained from the analysis of urban digital elevation models. The shear stress is parameterised using a mixing length approach. Spatially-averaged velocity profiles for different values of building packing density corresponding to different flow regimes are obtained and analysed. The computed solutions are compared with published data from wind-tunnel and water-tunnel experiments over arrays of cubes. The model is used to estimate the spatially-averaged velocity profile within and above neighbourhood areas of real cities by using vertical profiles of λ _f .     

Observations of Boundary-Layer Wind-Tunnel Flow over Isolated Ridges of Varying Steepness and Roughness

Boundary-layer wind-tunnel flow is measured over isolated ridges of varyingsteepness and roughness. The steepness/roughness parameter space is chosento produce flows that range from fully attached to strongly separated. Measurementsshow that maximum speedup at the hill crest is significantly lower than predictedby linear theory and that recovery in the lee of the hill is much slower for stronglyseparated flow over steep terrain. The measurements also show that behaviour ofthe mean and turbulent components of the flow on the downwind side of the ridgeis fundamentally different between separated and non-separated flows. This suggeststhe dominance of much increased turbulence time and length scales in the lee of thehill in association with a production mechanism that scales with the hill length ratherthan the proximity to the surface as on the windward side of the hill crest.     

Aerodynamic Parameters of Regular Arrays of Rectangular Blocks with Various Geometries

The aerodynamic effects of various configurations of an urban array were investigated in a wind-tunnel experiment. Three aerodynamic parameters characterising arrays—the drag coefficient (C _d ), roughness length (z _o) and displacement height (d)—are used for analysis. C _d is based on the direct measurement of the total surface shear using a floating element, and the other two parameters are estimated by logarithmic fitting of the measured wind profile and predetermined total drag force. The configurations of 63 arrays used for measurement were designed to estimate the effects of layout, wind direction and the height variability of the blocks on these parameters for various roughness packing densities. The results are summarised as follows: (1) The estimated C _d and z _o of the staggered arrays peak against the plan area index (λ _p ) and frontal area index (λ _f ), in contrast with values for the square arrays, which are less sensitive to λ _p and λ _f . In addition, the square arrays with a wind direction of 45° have a considerably larger C _d , and the wind direction increases z _o/H by up to a factor of 2. (2) The effect of the non-uniformity of roughness height on z _o is more remarkable when λ _f exceeds 20%, and the discrepancy in z _o is particularly remarkable and exceeds 200%. (3) The effect of the layout of tall blocks on C _d is stronger than that of short blocks. These results indicate that the effects of both wind direction and the non-uniformity of the heights of buildings on urban aerodynamic parameters vary greatly with λ _p and λ _f ; hence, these effects should be taken into account by considering the roughness packing density.     

Effect of static stability on the pattern of three-dimensional baroclinic lee wave across a meso scale elliptical barrier

Summary In this paper, an attempt has been made to examine the effect of static stability on the pattern of three dimensional (3-D) baroclinic lee wave across a meso-scale elliptical barrier. For this purpose first a 3-D meso scale lee wave model has been developed. Then the model is applied to the Western Ghats (WG) using real time radio sonde data of Santacruz (19°7′N, 72°51′E) (here after SCZ), a station on the windward side of WG, on the days when dynamic and thermodynamic conditions of the atmosphere were favourable to generate lee waves. It is found that the pattern of 3-D baroclinic lee wave is very much sensitive to the value of the static stability parameter N². It is found that during southwest monsoon season trapped lee waves are convergent type (contours of perturbation vertical velocity w′ are crescent shaped convex down wind) and during winter they are divergent type (contours of w′ are crescent shaped concave down wind). The study shows that for a given profile of wind, the value of N² must exceed certain threshold value to obtain divergent type lee wave, otherwise convergent type lee waves are found. It is also found that in the southwest monsoon season, when atmosphere is neutrally stratified, a single divergent lee wave corresponds to a single transverse lee wave, whereas in the winter season, when atmosphere is strongly stratified, a single divergent lee wave corresponds to a number of transverse lee wave. Furthermore, in the former case long (or short) divergent lee wave corresponds to short (or long) transverse lee wave, whereas in the later case long (or short) divergent lee wave, in general, corresponds to long (or short) transverse lee wave. This revised version was published online in November 2004 with corrected captions of Figs. 1 and 2.     

Aerodynamic roughness of the sea surface at high winds

The role of the surface roughness in the formation of the aerodynamic friction of the water surface at high wind speeds is investigated. The study is based on a wind-over-waves coupling theory. In this theory waves provide the surface friction velocity through the form drag, while the energy input from the wind to waves depends on the friction velocity and the wind speed. The wind-over-waves coupling model is extended to high wind speeds taking into account the effect of sheltering of the short wind waves by the air-flow separation from breaking crests of longer waves. It is suggested that the momentum and energy flux from the wind to short waves locally vanishes if they are trapped into the separation bubble of breaking longer waves. At short fetches, typical for laboratory conditions, and strong winds the steep dominant wind waves break frequently and provide the major part of the total form drag through the air-flow separation from breaking crests, and the effect of short waves on the sea drag is suppressed. In this case the dependence of the drag coefficient on the wind speed is much weaker than would be expected from the standard parameterization of the roughness parameter through the Charnock relation. At long fetches, typical for the field, waves in the spectral peak break rarely and their contribution to the air-flow separation is weak. In this case the surface form drag is determined predominantly by the air-flow separation from breaking of the equilibrium range waves. As found at high wind speeds up to 60 m s⁻¹ the modelled aerodynamic roughness is consistent with the Charnock relation, i.e. there is no saturation of the sea drag. Unlike the aerodynamic roughness, the geometrical surface roughness (height of short waves) could be saturated or even suppressed when the wind speed exceeds 30 m s⁻¹.     

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.     

Subfilter-scale Fluxes over a Surface Roughness Transition. Part I: Measured Fluxes and Energy Transfer Rates

A wind-tunnel experiment was designed and carried out to study the effect of a surface roughness transition on subfilter-scale (SFS) physics in a turbulent boundary layer. Specifically, subfilter-scale stresses are evaluated that require parameterizations and are key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. The surface transition considered in this study consists of a sharp change from a rough, wire-mesh covered surface to a smooth surface. The resulting magnitude jump in aerodynamic roughnesses, M = ln(z ₀₁/z ₀₂), where z ₀₁ and z ₀₂ are the upwind and downwind aerodynamic surface roughnesses respectively, is similar to that of past experimental studies in the atmospheric boundary layer. The two-dimensional velocity fields used in this study are measured using particle image velocimetry and are acquired at several positions downwind of the roughness transition as well as over a homogeneous smooth surface. Results show that the SFS stress, resolved strain rate and SFS transfer rate of resolved kinetic energy are dependent on the position within the boundary layer relative to the surface roughness transition. A mismatch is found in the downwind trend of the SFS stress and resolved strain rate with distance from the transition. This difference of behaviour may not be captured by some eddy-viscosity type models that parameterize the SFS stress tensor as proportional to the resolved strain rate tensor. These results can be used as a benchmark to test the ability of existing and new SFS models to capture the spatial variability SFS physics associated with surface roughness heterogeneities.     

Effect of Roughness on Surface Boundary Conditions for Large-Eddy Simulation

An important parameterization in large-eddy simulations (LESs) of high- Reynolds-number boundary layers, such as the atmospheric boundary layer, is the specification of the surface boundary condition. Typical boundary conditions compute the fluctuating surface shear stress as a function of the resolved (filtered) velocity at the lowest grid points based on similarity theory. However, these approaches are questionable because they use instantaneous (filtered) variables, while similarity theory is only valid for mean quantities. Three of these formulations are implemented in simulations of a neutral atmospheric boundary layer with different aerodynamic surface roughness. Our results show unrealistic influence of surface roughness on the mean profile, variance and spectra of the resolved velocity near the ground, in contradiction of similarity theory. In addition to similarity-based surface boundary conditions, a recent model developed from an a priori experimental study is tested and it is shown to yield more realistic independence of the results to changes in surface roughness. The optimum value of the model parameter found in our simulations matches well the value reported in the a priori wind-tunnel study.     

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.     

Flow around a windbreak in oblique wind

Wind speed was measured near the surface, along a line normal to a single, 50 % porous windbreak. The results for near-neutral atmospheric conditions were strongly dependent on the incidence angle of the wind, a, and slightly dependent on the roughness of the surface. A measure of the shelter effect - the protected distance - was found to decrease faster than cos . The drag coefficient of the windbreak decreased proportionally with cos . The effect of increased roughness was to increase the wind speed near the surface in the lee of the windbreak.