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.     

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.     

Neutral Flow Over A Series Of Rough Hills: A Laboratory Experiment

This paper presents laboratory experiments of aerodynamically fully rough, neutral flow over a series of sinusoidal hills. Two sets of hills, with maximum gradients (slopes) of 0.2 (10°) and 0.4 (20°), were considered.The flow remained attached in the former case while separation occurredin the latter. Characteristics of the mean flow and turbulence statistics are discussed and compared with profiles over a flat surface covered with the same roughness as the hills. Comparisons are made with linear theory predictions for the flow in the inner region and aloft. Accurate measurements of the surface pressure were also made, enabling the comparison between the measured pressure drag and predictions from theoretical and computational work with different turbulent closure schemes. Organised secondary flow in the spanwise direction, observed previously in both experimental and computational studies, was also observed here over the small hills.     

Drag due to regular arrays of roughness elements of varying geometry

Comparisons are made of experimental studies on the drag, at high Reynolds number, due to regular arrays of roughness elements of various shapes immersed in a turbulent boundary layer. Using a variant of Millikan's dimensional analysis, the form of the velocity profile is deduced in terms of the dimensions and concentration of the roughness elements. A drag formula results which is shown to be in good agreement with data. Available measurements of the partition of drag between the elements and the intervening surface indicates that equipartition occurs at quite low concentrations. The interaction between elements is then small, so that the drag coefficient of a typical roughness element is nearly constant. A re-examination of some of O'Loughlin's velocity-profile data, obtained below the tops of the roughness elements, suggests the existence of a nearly constant-stress layer scaled to the shear stress of the intervening surface. Above the roughness elements, the mean-velocity profile undergoes a transition to the form appropriate to the total shear stress exerted by the roughened surface. A formula is given which describes the one-dimensional velocity profile over the entire range, excluding the viscous sublayer on the intervening surface. The viscous sublayer appears to correspond quite closely to that on a smooth plate. This work was initiated while the authors were with the Division of Plant Industry, CSIRO. At present on leave at the Natural Resource Ecology Laboratory, Colorado State University, Fort Collins, Colorado, U.S.A.     

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.     

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.     

Observations and parametrization of momentum transfer in heterogeneous terrain consisting of regularly spaced obstacles

Tethered balloon data collected over a heterogeneous, semi-rural area of southern England are presented. The terrain within which the observations were taken is dominated by regularly spaced bluff obstacles that form the boundaries to grass fields. The data are compared with previous surface data to assess how representative these fixed-point measurements are of area-averaged values. It is found that there is a vertical height above which the flow approximates to being homogeneous and observations made above it are representative of the area average. The effective roughness length for momentum is then compared with that derived from a model describing the drag partition around isolated obstacles that are either non-porous or porous to the incident flow. It is shown that the method chosen to partition the drag is of the right order to produce reasonable predictions of the effective roughness length for different roughness densities.     

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.     

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.     

On the effective roughness length for use in numerical three-dimensional models

We present analytical and numerical calculations of the effective roughness length (ERL) over a flat surface with varying roughness elements, for use in large-scale models. It is shown that ERL is mostly determined by the roughest elements present inside the averaging domain and that, more surprisingly, the ERL increases as the first level of the numerical model gets closer to the surface and its altitude approaches the value of the largest local roughness length. This effect further increases the drag coefficient, in addition to the well-known increase due to the lowering of the first model level.     

Wave-dependence of friction velocity,roughness length,and drag coefficient over coastal and open water surfaces by using three databases

The parameterization of friction velocity, roughness length, and the drag coefficient over coastal zones and open water surfaces enables us to better understand the physical processes of air-water interaction. In context of measurements from the Humidity Exchange over the Sea Main Experiment (HEXMAX), we recently proposed wave-parameter dependent approaches to sea surface friction velocity and the aerodynamic roughness by using the dimensional analysis method. To extend the application of these approaches to a range of natural surface conditions, the present study is to assess this approach by using both coastal shallow (RASEX) and open water surface measurements (Lake Ontario and Grand Banks ERS-1 SAR) where wind speeds were greater than 6.44 m s^-1. Friction velocities, the surface aerodynamic roughness, and the neutral drag coefficient estimated by these approaches under moderate wind conditions were compared with the measurements mentioned above. Results showed that the coefficients in these approaches for coastal shallow water surface differ from those for open water surfaces, and that the aerodynamic roughness length in terms of wave age or significant wave height should be treated differently for coastal shallow and open water surfaces.     

Measurements of turbulence structure in the boundary layer on a rough surface

Mean products of velocity fluctuations up to fourth order have been measured in a wind tunnel at the trailing edge of a flat plate, one side of which was covered with floor-sanding paper to produce a fully rough surface. This set-up permits easy comparison of structural parameters in smooth-wall and rough-wall boundary layers. The Reynolds-stress profiles and second-order parameters are closely the same on the rough and smooth surfaces; in particular the decrease in Reynolds shear stress near the rough surface, encountered by several other laboratory workers, was not found in the present results. The triple products are spectacularly altered for a distance of up to 10 roughness heights from the rough surface, and imply a large net rate of transport of turbulent energy and shear stress towards the surface. Comparison with other published data shows that the behaviour of this modified region depends on roughness geometry as well as on the roughness height itself; for example, the mean cube of the normal-component fluctuation remains positive (energy transport away from the surface) over sand or gravel roughness but goes negative, like the other energy-transport terms, over crop canopies.     

On the impact of thermal stability on some rough flow effects over mobile surfaces

Calculations are made of the effects of thermal stability under a range of conditions, over the sea and land, on the physical factors (including the critical wind speed) affecting dust-storm generation, snow drift, and rough sea conditions. The computational procedure involves the surface friction velocity, u _*, and its relation with the aerodynamic roughness over aerodynamically rough, mobile surfaces. The results indicated that even at relatively high wind speeds, thermal effects under extreme advection situations may be significant, particularly for those properties of the agitated surface dependent on u _* ³ and u _* ⁴.     

Experimental Study on Effects of Ground Roughness on Flow Characteristics of Tornado-Like Vortices

The three-dimensional wind velocity and dynamic pressure for stationary tornado-like vortices that developed over ground of different roughness categories were investigated to clarify the effects of ground roughness. Measurements were performed for various roughness categories and two swirl ratios. Variations of the vertical and horizontal distributions of velocity and pressure with roughness are presented, with the results showing that the tangential, radial, and axial velocity components increase inside the vortex core near the ground under rough surface conditions. Meanwhile, clearly decreased tangential components are found outside the core radius at low elevations. The high axial velocity inside the vortex core over rough ground surface indicates that roughness produces an effect similar to a reduced swirl ratio. In addition, the pressure drop accompanying a tornado is more significant at elevations closer to the ground under rough compared with smooth surface conditions. We show that the variations of the flow characteristics with roughness are dependent on the vortex-generating mechanism, indicating the need for appropriate modelling of tornado-like vortices.     

Roughness-Length Model for Organized Rough Walls

A model for the roughness length and its correlation with the roughness shear stress on organized rough walls of varying geometry are presented and verified. The roughness length is nondimensionalized by the characteristic roughness length and is expressed as a function of roughness density with a wake-interference parameter. The dimensionless roughness length is independent of Reynolds number. When the model is applied to the whole range of roughness densities, the rough walls can be smooth, transitionally rough, and fully rough. A large number of data from classical experiments and recent simulations are analyzed to evaluate the proposed correlations, which are found to be consistent with the analyzed datasets. The proposed expression for the dimensionless roughness length and the expression for the dimensionless roughness shear stress, proposed previously by the author (Boundary-Layer Meteorology, 2020, Vol. 174, 393–410), are found to be identical in form. Numerous extant measurements of the two roughness parameters can be reproduced when the wake-interference parameters in the two models are treated as identical. The parameters of the roughness-length model are closely related to the geometry of the roughness elements. Different types of roughness elements can be distinguished by the values of the parameters. These results provide the foundation for constructing the unified roughness model for organized rough walls of varying geometry.

     

A wind-tunnel study of turbulent flow close to regularly arrayed rough surfaces

Recent observations of flux-gradient anomalies in atmospheric flow close to forests, and similar rough surfaces, prompted a wind-tunnel investigation in which cross-wire anemometry was used to study the vertical development and horizontal variability of adiabatic flow over five regularly arrayed rough surfaces, encompassing a 32-fold range of roughness concentration . The roughness elements were cylinders, 6 mm in both height and diameter.Below a layer in which the velocity profile is semi-logarithmic, two surface influences upon the mean velocity field can be distinguished: wake diffusion and horizontal inhomogeneity. The wake diffusion effect causes non-dimensional vertical velocity gradients to be smaller than in the semi-logarithmic region; at least for elements with aspect ratios l/h 1, it is governed by the transverse dimension l of the roughness elements, and is observed when z > h + 1.5l (where z is height above the underlying surface, and h is the height of the roughness elements). A simple diffusivity model successfully describes the horizontally averaged velocity profiles in the region of wake influence, despite conceptual disadvantages. The horizontal inhomogeneity of the flow is negligible when z > h + D (D being the inter-element spacing), and does not entirely mask the wake diffusion effect except over very sparsely roughened surfaces ( 0.02). A criterion for negligibility of both effects, and hence for applicability of conventional turbulent diffusivity theory for momentum, is z > h + 1.5D. These results are compared with atmospheric data, and indicate that wake diffusion may well cause some underestimation of the zero-plane displacement d over typical vegetated surfaces.     

Study on diurnal variation of bulk drag coefficient over different landsurfaces

Summary The magnitude and diurnal change of turbulent bulk drag coefficients over land have been analysed using mean velocity and temperature gradient data of the planetary boundary layer. The turbulent drag coefficients can be about an order of magnitude larger over the rough land surface than over the sea surface. We computed these coefficients by the same method for three typical underlying surfaces represented by urban, grassland and Gobi desert. The results show that there are significant differences in the turbulent transfer among the three typical underlying surfaces.With 6 Figures     

The Characteristics and Parameterization of Aerodynamic Roughness Length over Heterogeneous Surfaces

Aerodynamic roughness length (z0m is a key factor in surface flux estimations with remote sensing algorithms and/or land surface models. This paper calculates z0m over several land surfaces, with 3 years of experimental data from Xiaotangshan. The results show that z0m is direction-dependent, mainly due to the heterogeneity of the size and spatial distribution of the roughness elements inside the source area along different wind directions. Furthermore, a heuristic parameterization of the aerodynamic roughness length for heterogeneous surfaces is proposed. Individual z0m over each surface component (patch) is calculated firstly with the characteristic parameters of the roughness elements (vegetation height, leaf area index, etc.), then z0m over the whole experimental field is aggregated, using the footprint weighting method.     

Pollutant Plume Dispersion in the Atmospheric Boundary Layer over Idealized Urban Roughness

The Gaussian model of plume dispersion is commonly used for pollutant concentration estimates. However, its major parameters, dispersion coefficients, barely account for terrain configuration and surface roughness. Large-scale roughness elements (e.g. buildings in urban areas) can substantially modify the ground features together with the pollutant transport in the atmospheric boundary layer over urban roughness (also known as the urban boundary layer, UBL). This study is thus conceived to investigate how urban roughness affects the flow structure and vertical dispersion coefficient in the UBL. Large-eddy simulation (LES) is carried out to examine the plume dispersion from a ground-level pollutant (area) source over idealized street canyons for cross flows in neutral stratification. A range of building-height-to-street-width (aspect) ratios, covering the regimes of skimming flow, wake interference, and isolated roughness, is employed to control the surface roughness. Apart from the widely used aerodynamic resistance or roughness function, the friction factor is another suitable parameter that measures the drag imposed by urban roughness quantitatively. Previous results from laboratory experiments and mathematical modelling also support the aforementioned approach for both two- and three-dimensional roughness elements. Comparing the UBL plume behaviour, the LES results show that the pollutant dispersion strongly depends on the friction factor. Empirical studies reveal that the vertical dispersion coefficient increases with increasing friction factor in the skimming flow regime (lower resistance) but is more uniform in the regimes of wake interference and isolated roughness (higher resistance). Hence, it is proposed that the friction factor and flow regimes could be adopted concurrently for pollutant concentration estimate in the UBL over urban street canyons of different roughness.