Aerodynamic Roughness Length of Fresh Snow

This study presents the results from a series of wind-tunnel experiments designed to investigate the aerodynamic roughness length z ₀ of fresh snow under no-drift conditions. A two-component hot-film anemometer was employed to obtain vertical profiles of velocity statistics in a zero pressure gradient turbulent boundary layer for flow over naturally deposited snow surfaces. The roughness of these snow surfaces was measured by means of digital photography to capture characteristic length scales that can be related to z ₀. Our results show that, under aerodynamically rough conditions, the mean value of the roughness length for fresh snow is \({\langle{z}_{0}\rangle= 0.24}\) mm with a standard deviation σ(z ₀) = 0.05 mm. In this study, we show that variations in z ₀ are associated with variations in the roughness geometry. The roughness measurements suggest that the estimated values of z ₀ are consistent with the presence of irregular roughness structures that develop during snowfalls that mimic ballistic deposition processes.     

Momentum Absorption in Rough-Wall Boundary Layers with Sparse Roughness Elements in Random and Clustered Distributions

A wind-tunnel experiment has been used to investigate momentum absorption by rough surfaces with sparse random and clustered distributions of roughness elements. An unusual (though longstanding) method was used to measure the boundary-layer depth δ and friction velocity u _* and thence to infer the functional relationship z ₀/h = f(λ) between the normalised roughness length z ₀/ h and the roughness density λ (where z ₀ is the roughness length and h the mean height of the roughness elements). The method for finding u _* is based on fitting the velocity defect in the outer layer to a functional form for the dimensionless velocity-defect profile in a canonical zero-pressure-gradient boundary layer. For the conditions investigated here, involving boundary layers over sparse roughness with strong local heterogeneity, this velocity-defect-law method is found to be more robust than several alternative methods for finding u _* (uw covariance, momentum integral and slope of the logarithmic velocity profile).The experimental results show that, (1) there is general agreement in the relationship z ₀/h = f(λ) between the present experiment with random arrays and other wind-tunnel experiments with regular arrays; (2) the main effect of clustering is to increase the scatter in the z ₀/h = f(λ) relationship, through increased local horizontal heterogeneity; (3) this scatter obscures any trend in the z ₀/h = f(λ) relationship in response to clustering; and (4) the agreement between the body of wind-tunnel data (taken as a whole) and field data is good, though with scatter for which it is likely that a major contribution stems from local horizontal heterogeneity in the field.     

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.     

Aerodynamic Parameters of a UK City Derived from Morphological Data

Detailed three-dimensional building data and a morphometric model are used to estimate the aerodynamic roughness length z ₀ and displacement height d over a major UK city (Leeds). Firstly, using an adaptive grid, the city is divided into neighbourhood regions that are each of a relatively consistent geometry throughout. Secondly, for each neighbourhood, a number of geometric parameters are calculated. Finally, these are used as input into a morphometric model that considers the influence of height variability to predict aerodynamic roughness length and displacement height. Predictions are compared with estimations made using standard tables of aerodynamic parameters. The comparison suggests that the accuracy of plan-area-density based tables is likely to be limited, and that height-based tables of aerodynamic parameters may be more accurate for UK cities. The displacement heights in the standard tables are shown to be lower than the current predictions. The importance of geometric details in determining z ₀ and d is then explored. Height variability is observed to greatly increase the predicted values. However, building footprint shape only has a significant influence upon the predictions when height variability is not considered. Finally, we develop simple relations to quantify the influence of height variation upon predicted z ₀ and d via the standard deviation of building heights. The difference in these predictions compared to the more complex approach highlights the importance of considering the specific shape of the building-height distributions. Collectively, these results suggest that to accurately predict aerodynamic parameters of real urban areas, height variability must be considered in detail, but it may be acceptable to make simple assumptions about building layout and footprint shape.     

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.     

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.     

Impact of surface variations on the momentum flux above the urban canopy

Based on the momentum flux–wind profile relationship of the Monin–Obukhov Similarity (MOS) theory, the observational data from the urban boundary layer field campaign in Nanjing are used to calculate the friction velocity ( $ {u_*} $ ) at the top of the urban canopy and the calculated results are evaluated. The urban surface roughness parameters (the roughness length z ₀ and zero-plane displacement height z _d) are estimated with the Ba method (Bottema’s morphological method). Two different regimes are employed for the calculations. In the homogeneous approach, z ₀ and z _d are averagely derived from the surface elements in the whole study area; while in the heterogeneous approach, z ₀ and z _d are locally derived from the surface elements in the corresponding upwind fetches (or source areas). The calculated friction velocities are compared to the measurement data. The results show that the calculated friction velocities from the heterogeneous approach are in better agreement with the observed values than those from the homogeneous approach are. This study implies that the local roughness parameters can properly represent the dynamical heterogeneity of urban surface, and its application can significantly improve the performance of parameterizations based on the MOS theory in the urban roughness sublayer.     

An Approximate Analytical Solution Of Flux-Profile Relationships For The Atmospheric Surface Layer With Different Momentum And Heat Roughness Lengths

An approximate method for calculating the relationship between z/L(z = reference height, L = Obukhov length) and the bulk Richardsonnumber is presented. If this relationship is known, the momentum andheat fluxes can be computed easily without any iteration. The avoidance of iteration can speed up computationsin large-scale models considerably (up to 10 times) and cases which do not converge or converge very slowly cannot occur. The proposed formulae take into account the difference between momentum (z_0M) and heat roughnesslengths (z_0H). Because the roughness lengths are not neglected at any step of the derivation, the resulting analytical formulae can be used not only between the surface and the reference height but also between two finite levels z₁ andz₂ (by replacing z_0M and z_0H by z₁ and z by z₂). Theequations remain correct even in the limit z₁ z₂.The formulae are based upon the (partially modified) Businger–Dyer flux–profile relationships and,consequently, they are restricted to predominantly homogeneous terrain.These new approximations are an improvement over the existing solutions because they are simpler than most of the formulae in the literature and are able to match the numerical exact solution for different parameter sets (Businger, Dyer, Högström) with an maximum error of about 2% for a wide range of z/L, z/z_0M and z_0M/z_0H.Furthermore, in stable conditions, schemes with and without a finitecritical bulk Richardson number can be approximated. The possibleambiguity of the exact solution =f(RI_B) in (moderately) stable conditions is discussed briefly. The performance of the new formulae is compared to the exact numerical solution and to different formulae proposed in the literature.     

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.     

Development and Validation of an Evaporation Duct Model.Part Ⅰ:Model Establishment and Sensitivity Experiments

Based on the Coupled Ocean-Atmospheric Response Experiment（COARE）bulk algorithm and the Naval Postgraduate School（NPS）model,a universal evaporation duct（UED）model that can flexibly accommodate the latest improvements in component（such as stability function,velocity roughness,and scalar roughness）schemes for different stratification and wind conditions,is proposed in this paper.With the UED model,the sensitivity of the model-derived evaporation duct height（EDH）to stability function（Ψ）,ocean wave effect under moderate to high wind speeds,and scalar roughness length parameterization,is investigated,and relative contributions of these factors are compared.The results show that the stability function is a key factor influencing the simulated EDH values.Under unstable conditions,the EDH values from stability functions of Fairall et al.（1996）and Hu and Zhang（1992）are generally higher than those from others;while under stable conditions,unreasonably high EDHs can be avoided by use of the stability functions of Hu and Zhang（1992）and Grachev et al.（2007）.Under moderate to high wind speeds,the increase in velocity roughness length z₀ due to consideration of the true ocean wave effect acts to reduce modeled EDH values;this trend is more pronounced under stable conditions.Although the scalar roughness length parameterization has a minor effect on the model-derived EDH,a positive correlation is found between the scalar roughness length z_0qand the model-derived EDH.     

The Effect of Stratification on the Aerodynamic Roughness Length and Displacement Height

The roughness length, z _0u , and displacement height, d _0u , characterise the resistance exerted by the roughness elements on turbulent flows and provide a conventional boundary condition for a wide range of turbulent-flow problems. Classical laboratory experiments and theories treat z _0u and d _0u as geometric parameters independent of the characteristics of the flow. In this paper, we demonstrate essential stability dependences—stronger for the roughness length (especially in stable stratification) and weaker but still pronounced for the displacement height. We develop a scaling-analysis model for these dependences and verify it against experimental data.     

An Improvement of the Louis Scheme for the Surface Layer in an Atmospheric Modelling System

The Louis scheme for calculating the vertical eddy fluxes within the atmospheric surface layer is improved by broadening the original assumptions. In our approach, the momentum and heat transfer roughness lengths (z₀ and z_T respectively) can be different, and z₀ need not be negligibly small compared with the lowest height (z) in modelling. For these conditions, we choose more consistent wind and potential temperature profile forms, then derive new algorithms for calculating fluxes. Improvement is demonstrated for a wide range of z/L (L is the Obukhov length), z/z₀ and z₀ z_T, by comparing these fluxes with those derived from a theoretical surface-layer model. The improved algorithms can be used in atmospheric modelling systems for more varied surfaces and a wide range of atmospheric stability.     

Observed Wind Profiles and Turbulence Fluxes over an ice Surface with Changing Surface Roughness

Wind profile and eddy-correlation data obtained at two sites on a melting glacier surface in Iceland during the summer of 1996 are presented. Throughout the experiment the surface roughness increased rapidly from smooth to very rough, with the largest roughness element height obtained being about 1.7 m. In a layer close to the rough surface we find that the wind speed profiles were disturbed showing horizontal inhomogeneities as in a roughness sublayer. Its height was approximately two times the height of the main roughness elements (h) at both sites throughout the experiment. From the wind profiles and eddy-correlation data we calculated corrections for the displaced zero plane as a function of time and compared these with results obtained from a drag partitioning model. In general, the agreement was reasonable considering the ranges of uncertainty but the results indicate that the increasing horizontal anisotropy of the surface probably limits the use of the model. The values obtained for the roughness lengths are in good agreement with those calculated from a simple linear model, i.e., z₀/h = 0.5 with the frontal area index. Above the roughness sublayer the wind profiles, normalised standard deviations of wind speed, and the balance of the turbulence kinetic energy budget behaved as over an ideal homogeneous surface thereby confirming similarity of the flow.     

Aerodynamic Scaling for Estimating the Mean Height of Dense Canopies

We used an aerodynamic method to objectively determine a representative canopy height, using standard meteorological measurements. The canopy height may change if the tree height is used to represent the actual canopy, but little work to date has focused on creating a standard for determining the representative canopy height. Here we propose the ‘aerodynamic canopy height’ h _a as the most effective means of resolving the representative canopy height for all forests. We determined h _a by simple linear regression between zero-plane displacement d and roughness length z ₀, without the need for stand inventory data. The applicability of h _a was confirmed in five different forests, including a forest with a complex canopy structure. Comparison with stand inventory data showed that h _a was almost equivalent to the representative height of trees composing the crown surface if the forest had a simple structure, or to the representative height of taller trees composing the upper canopy in forests with a complex canopy structure. The linear relationship between d and z ₀ was explained by assuming that the logarithmic wind profile above the canopy and the exponential wind profile within the canopy were continuous and smooth at canopy height. This was supported by observations, which showed that h _a was essentially the same as the height defined by the inflection point of the vertical profile of wind speed. The applicability of h _a was also verified using data from several previous studies.     

Near-Wall Flow Development After A Step Change In Surface Roughness

An experimental study of the initial flow field downstream of a step change in surface roughness is presented. The roughness length of the downstream surface was approximately tenfold that of the upstream roughness and, unlike all previous studies, attention was concentrated on the roughness sublayer region beneath the inertial (log-law) region. The experiments were conducted at a boundary layer Reynolds number of about 6 × 10⁴ (based on layer thickness andfree-stream velocity) and around a longitudinal location where the (downstream) roughness length, z_o2, was about 1% of the boundary-layer thickness atthe roughness change point.The thickness of the roughness sublayer was found for the two roughness. It was observed that the vertical profiles of mean velocity and turbulence characteristics started to show similarity after about 160z₀₂ downstream of the roughness change. The presence of a shear stress overshoot is shown to depend strongly on the precise location (with respect to the roughness elements) at which the measurements are made and the thickness of the equilibrium layer is shown to be very sensitive to the way it is defined. It is demonstrated that the growing equilibrium layer has first to encompass the roughness sublayer before any thickness of inertial sublayer can be developed. It follows that, in somepractical cases, like flows across some urban environments, the latter(log-law) region may never exist at all.     

北京城市下垫面动力学参数的计算与分析

采用北京325 m铁塔2008—2012年的单层超声观测资料,基于莫宁-奥布霍夫相似理论(Monin-Obukhov similarity theory)和前人提出的最小误差分析方法,计算了铁塔周边下垫面的零平面位移高度和动力粗糙度长度。结果表明,由于铁塔位于北京市区,其周边下垫面呈现极其复杂的非均匀性,所以对应铁塔周边不同的扇区,零平面位移高度和动力粗糙度长度各有不同。平均而言,在2008—2012年间,铁塔周边下垫面的零平面位移高度为34.4 m,动力粗糙度长度为1.16 m。此外,综合前人的计算结果发现,铁塔周边的零平面位移高度和动力粗糙度长度在2001年之前呈显著增加的趋势,而在2001年以后并未增长,这一现象与铁塔周边的城市化进程相对应。     

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.     

Influence of a Two-scale Surface Roughness on a Neutral Turbulent Boundary Layer

Flow in the urban boundary layer is strongly influenced by the surface roughness, which is composed principally of isolated buildings or groups of buildings. Previous research has shown that the flow regime depends on the characteristic height of these obstacles (H), and the spacing between them (W). In reality, the urban boundary layer contains roughness elements with a wide range of length scales; in many practical situations these can be classified into large-scale roughness—buildings, or groups of buildings—and small-scale roughness, such as street furniture and elements on the façades and roofs. It is important to understand how the small-scale roughness might modify mass and momentum transfer in the urban boundary layer, but relatively little information is available concerning the potential interaction between large- and small-scale roughness elements in the different flow regimes. This problem has been studied using wind-tunnel experiments, by measuring vertical velocity profiles over a two-dimensional obstacle array, adding small-scale roughness elements to the top of larger parallel square bars. The experiments were performed for different cavity aspect ratios: the results show that the small-scale roughness increases the turbulence intensities and the momentum transfer when the large-scale obstacles are closely packed (H/W > 1) but it has very little effect for more widely-spaced obstacles (H/W < 1).     

Studies on critical Reynolds number indices for wind-tunnel experiments on flow within urban areas

Reynolds-number dependence of flow fields within a modelled urban area was studied in a wind tunnel. We measured flow around a single model building and around model city blocks at various wind speeds, and studied Reynolds number indices more appropriate than the building Reynolds number. Our results led to the following conclusions. Firstly, the flow around the models in the wind tunnel was roughly divided into three parts according to the intensities of viscous stress and Reynolds stress as follows: (1) the flow in the vicinity of the ground or the surfaces of the model, where viscous stress became dominant under certain conditions; (2) the flow detached from the surfaces of the model, where Reynolds stress was always dominant; and (3) the flow around the separation bubble at the leading edge of the building model, where the influences of both viscous stress near the wall and the Reynolds stress in the separated boundary layer were mixed.Secondly, the critical Reynolds number of the flow in the modelled urban area could be defined by using both the roughness Reynolds number Re_z0 (= z₀u_*/) and the dimensionless height z₊ (= zu_*/). Reynolds-number independence could be expected for whole flow fields in the modelled urban areas as long as the critical values of Re_z0 and z₊ were satisfied.