Surface drag and turbulence over an inhomogeneous land surface

Data collected over an inhomogeneous semi-rural area are presented. The data are compared with previous surface-layer data to determine how representative the fixed-point flux measurements are of area averages. Departures from the standard surface-layer results are found to be relatively small (~10–20%), which supports the concept of a blending height above which the flow ceases to respond to variations in the underlying surface and becomes horizontally homogeneous.Effective roughness lengths are derived for different wind directions and the relationship between the effective roughness length and upwind surface is examined in the light of recent ideas on averaging surface roughness lengths. It is found that by averaging drag coefficients, realistic values of the effective roughness length can be calculated which are not very sensitive to the precise choice of the component roughness lengths.     

Numerical Simulation of Drag Partition over Rough Surfaces

We present a numerical simulation of drag partition over rough surfaces. A computational fluid dynamics model is applied with high resolution to simulatingturbulent flows over arrays of roughness elements positioned on asmooth surface. The skin drag on the surface and the pressure drag on the roughnesselements are computed. The simulated drag partition compares well with wind-tunnelmeasurements and theoretical estimates for similar rough surfaces. This confirms that the computational approach offers an alternative to wind-tunnel and field experiments in studying drag and drag partition. The model is then applied to studying drag partition over rough surfaces with various roughness configurations. It is shown that drag partition depends not only on the magnitude of the roughness frontal area but also on the sizes and arrangement of roughness elements, because (1) the pressure drag coefficient is sensitive to roughness-element dimensions and (2) the arragement of roughness elements lead to different interferences of turbulent wakes. The impact ofthe latter factor is not insignificant.     

Estimates of Roughness Parameters for Arrays of Obstacles

Some methods are evaluated and extended to estimate roughness length and zero plane displacement height for atmospheric flow over arrays of obstacles, typically buildings. It appears that the method proposed by Bottema, with an extension to account for low density obstacle arrays, performs best. Procedures are proposed to represent irregular obstacle arrangements by a representative regular array to which Bottema's method can be applied. It is shown that this can be done without loss of accuracy, in general, roughness length can be predicted within a factor of two in more than 74% of the cases (95% reliability estimate). The methods proposed by Lettau and Raupach have been included in the evaluation. Lettau's model, which only requires input on the frontal area density, predicts roughness length unbiassed for frontal area densities up to 0.3, but predictions will be within a factor of two in more than 59% of the cases only (95% reliability estimate).     

Large-Eddy Simulation of Flows over Random Urban-like Obstacles

Further to our previous large-eddy simulation (LES) of flow over a staggered array of uniform cubes, a simulation of flow over random urban-like obstacles is presented. To gain a deeper insight into the effects of randomness in the obstacle topology, the current results, e.g. spatially-averaged mean velocity, Reynolds stresses, turbulence kinetic energy and dispersive stresses, are compared with our previous LES data and direct numerical simulation data of flow over uniform cubes. Significantly different features in the turbulence statistics are observed within and immediately above the canopy, although there are some similarities in the spatially-averaged statistics. It is also found that the relatively high pressures on the tallest buildings generate contributions to the total surface drag that are far in excess of their proportionate frontal area within the array. Details of the turbulence characteristics (like the stress anisotropy) are compared with those in regular roughness arrays and attempts to find some generality in the turbulence statistics within the canopy region are discussed.     

Influence of Obstacles on the Aerodynamic Roughness of the Netherlands

The aim of this study was to analyse the influence of large- and small-scale obstacles (orography, tree lines, and dikes) on the effective aerodynamic roughness of the Netherlands, a relatively flat, small-scale landscape. The roughness averaging approach was based on drag coefficients. The effective roughness was locally dominated by small-scale obstacles such as tree lines and dikes. Even at a regional scale (40,000 km2), the small-scale obstacle drag was of the same order of magnitude as the shear stress due to landuse. The neglect of those obstacles on a regional scale would result in approximately 10% overestimated averaged windspeed at 10~m above the surface. It was concluded that small-scale obstacles need to be taken into account to calculate the aerodynamic roughness of flat landscapes. Orography was of minor importance in this lowland country.     

Characteristics of the Drag Coefficient in the Roughness Sublayer over a Complex Urban Surface

The statistics of momentum exchange in the urban roughness sublayer are investigated. The analysis focuses on the characteristics of the dimensionless friction velocity, \({u_{*}}/U\) , which is defined as the square root of the drag coefficient. The turbulence observations were made at a height of 47 m above the ground on the 325-m meteorological tower, which is located in a very inhomogeneous urban area in Beijing. Under neutral conditions, the dependence of the drag coefficient on wind speed varies with wind direction. When the airflow is from the area of densely built-up buildings, the drag coefficient does not vary with wind speed, while when the airflow is from the area covered by vegetation, the drag coefficient appears to decrease with increasing wind speed. Also, the drag coefficient does not vary monotonically with the atmospheric stability. Both increasing stability and increasing instability lead to the decrease of the drag coefficient, implying that the roughness length and zero-plane displacement may vary in urban areas.     

Near Wall Flow over Urban-like Roughness

In this study, comprehensive measurements over a number of urban-type surfaces with the same area density of 25% have been performed in a wind tunnel. The experiments were conducted at a free stream velocity of 10 m s^-1 and the main instrumentation was 120 ° x-wire anemometry, but measurement accuracy was checked using laser Doppler anemometry.The results haveconfirmed the strong three-dimensionalityof the turbulent flow inthe roughness sublayer and the depths of the inertial sublayer (log-law region) and roughness sublayer for each surface have been determined. Spatial averaging has been used to remove the variability of the flow in the roughness sublayer due to individual obstacles and it is shown that the spatially averaged mean velocity in the inertial sublayer and roughness sublayer can,together, be described by a single log-law with a mean zero-plane displacement and roughness length for the surface, provided that the proper surface stress is known. The spatially averaged shear stresses in the inertial sublayer and roughness sublayer are compared with the surface stress deduced from form drag measurements on the roughness elements themselves.The dispersive stress arising from the spatial inhomogeneity in the mean flow profiles was deduced from the data and is shown to be negligible compared with the usual Reynolds stresses in the roughness sublayer. Comparisons have been made between a homogeneous (regular element array) surface and one consisting of random height elements of the same total volume. Although the upper limits of the inertial sublayer for both surfaces were almost identical at equivalent fetch, the roughness sublayer was much thicker for the random surface than for the uniform surface, the friction velocity and the roughness length were significantly larger and the `roughness efficiency' was greater. It is argued that the inertial sublayer may not exist at all in some of the more extreme rough urban areas. These results will provide fundamental information for modelling urban air quality and forecasting urban wind climates.     

Pressure drag and effective roughness length with neutral stratification

A two-dimensional numerical mesoscale model is used to determine the pressure drag of sinoidal mountains and valleys in a neutral atmosphere. In the first part, pressure distributions and flow patterns for isolated obstacles are considered. For large aspect ratios, the pressure drag exerted by valleys becomes small compared to that of mountains. In the second part, interactions between several obstacles are investigated. For mountains, the drag on downstream obstacles is reduced considerably by the first obstacle when the obstacles are close together. For valleys there is a slight increase of the average drag exerted by each obstacle. In the limit for a large number of obstacles, average drag exerted by one mountain is equal to average drag for one valley. For smaller aspect ratios, this average drag can be entered into the resistence law from the Rossby number similarity theory to yield an effective roughness length.     

Estimates of effective surface roughness over complex terrain

Turbulence data collected in an area of three-dimensional complex terrain using instruments atteched to the tether cable of a captive balloon together with radiosonde ascents are presented. In addition, data collected using only radiosonde ascents in an area of two-dimensional complex terrain of large slope are also shown. Eddy correlation measurements of the turbulent momentum flux and wind velocity profiles are used to deduce the magnitude of the effective roughness from the drag coefficient and normalised velocity profiles. A relationship connecting the terrain characteristics and the roughness length is compared with the experimental data for both types of terrain plus previous experimental estimates of the roughness length over complex terrain. The formula taken from previous work by Grant and Mason (1990) is found to agree with the data when representing an area of order 100 km².     

Determination of surface layer parameters at the edge of a suburban area

Vertical wind and air temperature profile related parameters in the surface layer at the edge of suburban area of Zagreb (Croatia) have been considered. For that purpose, adopted Monin–Obukhov similarity theory and a set of observations of wind and air temperature at 2 and 10?m above ground, recorded in 2005, have been used. The root mean square differences (errors) principle has been used as a tool to estimate the effective roughness length as well as standard deviations of wind speed and wind gusts. The results of estimation are effective roughness lengths dependent on eight wind direction sectors unknown before. Gratefully to that achievement, representativeness of wind data at standard 10-m height can be clarified more deeply for an area of at least about 1?km in upwind direction from the observation site. Extrapolation of wind data for lower or higher levels from standard 10-m height are thus properly representative for a wider inhomogeneous suburban area and can be used as such in numerical models, flux and wind energy estimation, civil engineering, air pollution and climatological applications.     

A simple unified theory for flow in the canopy and roughness sublayer

The mean flow profile within and above a tall canopy is well known to violate the standard boundary-layer flux–gradient relationships. Here we present a theory for the flow profile that is comprised of a canopy model coupled to a modified surface-layer model. The coupling between the two components and the modifications to the surface-layer profiles are formulated through the mixing layer analogy for the flow at a canopy top. This analogy provides an additional length scale—the vorticity thickness—upon which the flow just above the canopy, within the so-called roughness sublayer, depends. A natural form for the vertical profiles within the roughness sublayer follows that overcomes problems with many earlier forms in the literature. Predictions of the mean flow profiles are shown to match observations over a range of canopy types and stabilities. The unified theory predicts that key parameters, such as the displacement height and roughness length, have a significant dependence on the boundary-layer stability. Assuming one of these parameters a priori leads to the incorrect variation with stability of the others and incorrect predictions of the mean wind speed profile. The roughness sublayer has a greater impact on the mean wind speed in stable than unstable conditions. The presence of a roughness sublayer also allows the surface to exert a greater drag on the boundary layer for an equivalent value of the near-surface wind speed than would otherwise occur. This characteristic would alter predictions of the evolution of the boundary layer and surface states if included within numerical weather prediction models.     

Landscape Roughness Parameters for Sherwood Forest – Validation of Aggregation Models

Various models for calculating the effective or area-averaged roughness length zoe have been tested for a partly forested area. Three types of model are considered: the tile approach for very large scales of inhomogeneity (> 20 km), drag models for very small scales (up to 1 km), and surface-layer methods such as the blending-height method for intermediate scales. Over partly forested areas, where both pressure effects and roughness sub-layer effects may become significant, small-scale models are expected be the most suitable type of model. The various model types were tested against new experimental data that were obtained over the partly forested Sherwood Forest area (UK). The best fit with the data was obtained with the blending-height method, rather than with the different small-scale models. This is remarkable as the surface-layer assumptions of the blending-height method were clearly violated: the calculated blending height was 7 m, as compared to the mean tree height of 20 m. Of the small-scale models, a sparse-canopy approach compared poorly with the experimental data. The drag models overestimated the area-averaged roughness to a lesser degree, but a major point of concern remains the choice of the model parameters. Therefore, suggestions are made for an improved choice of these parameters.     

Pollutant Dispersion in Boundary Layers Exposed to Rural-to-Urban Transitions: Varying the Spanwise Length Scale of the Roughness

Both large-eddy simulations (LES) and water-tunnel experiments, using simultaneous stereoscopic particle image velocimetry and laser-induced fluorescence, have been used to investigate pollutant dispersion mechanisms in regions where the surface changes from rural to urban roughness. The urban roughness was characterized by an array of rectangular obstacles in an in-line arrangement. The streamwise length scale of the roughness was kept constant, while the spanwise length scale was varied by varying the obstacle aspect ratio l / h between 1 and 8, where l is the spanwise dimension of the obstacles and h is the height of the obstacles. Additionally, the case of two-dimensional roughness (riblets) was considered in LES. A smooth-wall turbulent boundary layer of depth 10h was used as the approaching flow, and a line source of passive tracer was placed 2h upstream of the urban canopy. The experimental and numerical results show good agreement, while minor discrepancies are readily explained. It is found that for \(l/h=2\) the drag induced by the urban canopy is largest of all considered cases, and is caused by a large-scale secondary flow. In addition, due to the roughness transition the vertical advective pollutant flux is the main ventilation mechanism in the first three streets. Furthermore, by means of linear stochastic estimation the mean flow structure is identified that is responsible for street-canyon ventilation for the sixth street and onwards. Moreover, it is shown that the vertical length scale of this structure increases with increasing aspect ratio of the obstacles in the canopy, while the streamwise length scale does not show a similar trend.     

Simplified expressions for vegetation roughness length and zero-plane displacement as functions of canopy height and area index

Using a previous treatment of drag and drag partition on rough surfaces, simple analytic expressions are derived for the roughness length (z ₀) and zero-plane displacement (d) of vegetated surfaces, as functions of canopy height (h) and area index (). The resulting expressions provide a good fit to numerous field and wind tunnel data, and are suitable for applications such as surface parameterisations in atmospheric models.     

Are Urban-Canopy Velocity Profiles Exponential?

Using analyses of data from extant direct numerical simulations and large-eddy simulations of boundary-layer and channel flows over and within urban-type canopies, sectional drag forces, Reynolds and dispersive shear stresses are examined for a range of roughness densities. Using the spatially-averaged mean velocity profiles these quantities allow deduction of the canopy mixing length and sectional drag coefficient. It is shown that the common assumptions about the behaviour of these quantities, needed to produce an analytical model for the canopy velocity profile, are usually invalid, in contrast to what is found in typical vegetative (e.g. forest) canopies. The consequence is that an exponential shape of the spatially-averaged mean velocity profile within the canopy cannot normally be expected, as indeed the data demonstrate. Nonetheless, recent canopy models that allow prediction of the roughness length appropriate for the inertial layer’s logarithmic profile above the canopy do not seem to depend crucially on their (invalid) assumption of an exponential profile within the canopy.     

Wind profiles,momentum fluxes and roughness lengths at Cabauw revisited

We describe the results of an experiment focusing on wind speed and momentum fluxes in the atmospheric boundary layer up to 200 m. The measurements were conducted in 1996 at the Cabauw site in the Netherlands. Momentum fluxes are measured using the K-Gill Propeller Vane. Estimates of the roughness length are derived using various techniques from the wind speed and flux measurements, and the observed differences are explained by considering the source area of the meteorological parameters. A clear rough-to-smooth transition is found in the wind speed profiles at Cabauw. The internal boundary layer reaches the lowest k-vane (20 m) only in the south-west direction where the obstacle-free fetch is about 2 km. The internal boundary layer is also reflected in the roughness lengths derived from the wind speed profiles. The lower part of the profile (< 40 m) is not in equilibrium and no reliable roughness analysis can be given. The upper part of the profile can be linked to a large-scale roughness length. Roughness lengths derived from the horizontal wind speed variance and gustiness have large footprints and therefore represent a large-scale average roughness. The drag coefficient is more locally determined but still represents a large-scale roughness length when it is measured above the local internal boundary layer. The roughness length at inhomogeneous sites can therefore be determined best from drag coefficient measurements just above the local internal boundary layers directly, or indirectly from horizontal wind speed variance or gustiness. In addition, the momentum and heat fluxes along the tower are analysed and these show significant variation with height related to stability and possibly surface heterogeneity. It appears that the dimensionless wind speed gradients scale well with local fluxes for the variety of conditions considered, including the unstable cases.     

Aerodynamic drag coefficient and roughness length for three seasons over a tropical western Indian station

Land Surface Processes Experiment (LASPEX) was conducted over semi-arid region of western India in 1997. As a part of this program, wind and temperature observations were taken using slow as well as fast response sensors over a semi-arid station Anand (22°35′N, 72°55′E) situated in Gujarat state of India. Turbulent parameters such as drag coefficient and sensible heat flux were estimated using eddy correlation method and aerodynamic roughness length was estimated using wind profiles. The analysis has been carried out for the data representing summer, monsoon and winter seasons. It was found that the wind speed does not exceed 5 ms^− 1 during the observational period considered in this study. Relationship of aerodynamic drag coefficient and roughness length with wind speed and stability has been investigated. Aerodynamic roughness length was greater in the stable conditions when the wind speed was low and it reduced drastically during convective conditions. The resulting values of aerodynamic roughness length and drag coefficient for the monsoon period agree well with values reported in literature over Indian subcontinent for homogeneous grass covered surfaces.     

Spatial variability of turbulent fluxes and roughness lengths in HAPEX-MOBILHY

Surface-based and aircraft measured fluxes over the heterogeneous surface in HAPEX-MOBILHY are analyzed for the ten flight days when cloud cover above the boundary layer was minimal. The fair-weather climatology of the spatial variation of surface fluxes is estimated to provide an assessment of the generality of previous case studies appearing in the literature. For the 10-day averages, greater heating over the forest generates a forest breeze which leads to rising motion and a modest increase of boundary-layer cloud cover at the forest edge. The exchange coefficients and effective roughness lengths are computed for local averages (15 km scale) and for regional averages (100 km scale) intended to represent a range of grid sizes in numerical models of the atmosphere. The effective roughness length for momentum over the mixed agricultural region for both scales is on the order of 1 m, apparently due to bluff roughness effects associated with scattered trees, edges of small woods and other obstacles. This roughness length value is an order of magnitude larger than values used in numerical models for the same region, which are based on the dominant vegetation type. The spatially varying effective roughness length for heat is computed for use in those models which use surface radiation temperature to estimate surface heat flux. The effective roughness lengths for heat are found to be smaller than those typically used in numerical models of the atmosphere.     

On the parameterization of drag over small-scale topography in neutrally-stratified boundary-layer flow

Predictions of the surface drag in turbulent boundary-layer flow over two-dimensional sinusoidal topography from various numerical models are compared. For simple 2D terrain, the model results show that the drag increases associated with topography are essentially proportional to (slope)² up to the steepness at which the flow separates. For the purposes of boundary-layer parameterisation within larger-scale models, we propose a representation of the effects of simple 2D topography via an effective roughness length, z ₀ ^eff. The form of the varation of z ₀ ^eff with terrain slope and topographic wavelength is established for small slopes from the model results and a semi-empirical formula is proposed.