The Kettles Hill Project: Field observations,wind-tunnel simulations and numerical model predictions for flow over a low hill

Field observations of the influence of topography on steady, neutrally-stratified boundary-layer flow were carried out in February 1981 and March 1984 on Kettles Hill near Pincher Creek, Alberta, Canada. The primary measurements were of wind speed at 3,6, and 10 m levels at stations in linear arrays along and across the major axis of this gentle, 1 km long and 100 m high, elliptical hill. Wind profile measurements up to heights of 200 m were made with TALA kites and tethersondes on the hilltop and at a reference site located about 3.7 km west of the hilltop. In addition, AIRsondes were flown and tracked from the reference site to provide additional data. The field observations provided the basic data for a comparison with wind-tunnel and numerical model simulations of the same flow. The wind-tunnel investigation was carried out in the Atmospheric Environment Service Boundary-Layer Wind Tunnel while the numerical model used was MS3DJH. For horizontal profiles of normalized mean wind speed at given heights above the prototype terrain, model results agree reasonably well with the field data. The wind-tunnel predictions are slightly high in most cases. For vertical profiles of wind speed up to 200 m above the hilltop, the numerical and wind-tunnel values are higher than were observed. The sensitivity of the normalized wind speed at the hilltop to deviations from non-logarithmic upwind profiles is demonstrated with data from the March 1984 experiment. A comparison of prototype with numerical-model mean-wind-direction perturbations at the 10 m level shows reasonable agreement except near the summit of the hill.Contractor: 24 Heslop Drive, Toronto.     

Relaxation Factor Effects in the Non-Linear Mixed Spectral Finite Difference Model of Flow Over Topographic Features

The nonlinear version of the mixed spectral finite difference model of atmospheric boundary-layer flow over topography is reviewed. The relations between the stability of the iteration scheme and its relaxation parameter are discussed. Suitable choice of the relaxation factor improves the computational stability on terrain with maximum slope up to 0.5 or 0.6 in certain circumstances. Examples of relatively high slope terrain are used to test the stability. A two-dimensional version of the model is considered. More detailed simulations are studied and analyzed for a comparison with wind-tunnel flow over periodic sinusoidal surfaces. An application on real topography is given for Bolund hill in Roskilde, Denmark.     

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 model of atmospheric boundary-layer flow above an isolated two-dimensional ‘hill’; an example of flow above ‘gentle topography’

A numerical model is developed for two-dimensional turbulent boundary-layer flow above gentle topography — defined as not giving rise to mean flow separation. Although the model is formulated in a framework of mixing length and turbulent energy equation models for the surface layer of the atmospheric boundary layer, it could be modified to include higher-order closure hypotheses and/or extended to model gentle topography for the planetary boundary layer or on the sea bed. Results are presented for flow above a specific shape of hill and the effects of surface roughness and hill height are investigated.     

Large-Eddy Simulation of Stably-Stratified Flow Over a Steep Hill

Large-eddy simulation (LES) is used to simulate stably-stratified turbulent boundary-layer flow over a steep two-dimensional hill. To parametrise the subgrid-scale (SGS) fluxes of heat and momentum, three different types of SGS models are tested: (a) the Smagorinsky model, (b) the Lagrangian dynamic model, and (c) the scale-dependent Lagrangian dynamic model (Stoll and Porté-Agel, Water Resour Res 2006, doi:). Simulation results obtained with the different models are compared with data from wind-tunnel experiments conducted at the Environmental Flow Research Laboratory (EnFlo), University of Surrey, U.K. (Ross et al., Boundary-Layer Meteorol 113:427–459, 2004). It is found that, in this stably-stratified boundary-layer flow simulation, the scale-dependent Lagrangian dynamic model is able to account for the scale dependence of the eddy-viscosity and eddy-diffusivity model coefficients associated with flow anisotropy in flow regions with large mean shear and/or strong flow stratification. As a result, simulations using this tuning-free model lead to turbulence statistics that are more realistic than those obtained with the other two models.     

Some numerical studies of surface boundary-layer flow above gentle topography

A numerical model of two-dimensional surface boundary-layer flow based on a non orthogonal coordinate mapping is developed. Results show good agreement with previous computations using conformal mapping techniques for flow over a periodic wavy surface and over an isolated hill. Results are presented for flow over Gaussian hills and valleys and over smooth sloping escarpments. For a 1 in 4 Sine ramp, good agreement is obtained with Freeston's (1974) wind-tunnel measurements.Presented under the title Atmospheric boundary-layer flow above gentle topography at the 10th Annual Congress of the Canadian Meteorological Society, Quebec City, May 26–28, 1976.     

Comparison of Speed-Up Over Hills Derived from Wind-Tunnel Experiments,Wind-Loading Standards,and Numerical Modelling

We evaluate the accuracy of the speed-up provided in several wind-loading standards by comparison with wind-tunnel measurements and numerical predictions, which are carried out at a nominal scale of 1:500 and full-scale, respectively. Airflow over two- and three-dimensional bell-shaped hills is numerically modelled using the Reynolds-averaged Navier–Stokes method with a pressure-driven atmospheric boundary layer and three different turbulence models. Investigated in detail are the effects of grid size on the speed-up and flow separation, as well as the resulting uncertainties in the numerical simulations. Good agreement is obtained between the numerical prediction of speed-up, as well as the wake region size and location, with that according to large-eddy simulations and the wind-tunnel results. The numerical results demonstrate the ability to predict the airflow over a hill with good accuracy with considerably less computational time than for large-eddy simulation. Numerical simulations for a three-dimensional hill show that the speed-up and the wake region decrease significantly when compared with the flow over two-dimensional hills due to the secondary flow around three-dimensional hills. Different hill slopes and shapes are simulated numerically to investigate the effect of hill profile on the speed-up. In comparison with more peaked hill crests, flat-topped hills have a lower speed-up at the crest up to heights of about half the hill height, for which none of the standards gives entirely satisfactory values of speed-up. Overall, the latest versions of the National Building Code of Canada and the Australian and New Zealand Standard give the best predictions of wind speed over isolated hills.     

Flow over Hills: A Large-Eddy Simulation of the Bolund Case

Simulation of local atmospheric flows around complex topography is important for several applications in wind energy (short-term wind forecasting and turbine siting and control), local weather prediction in mountainous regions and avalanche risk assessment. However, atmospheric simulation around steep mountain topography remains challenging, and a number of different approaches are used to represent such topography in numerical models. The immersed boundary method (IBM) is particularly well-suited for efficient and numerically stable simulation of flow around steep terrain. It uses a homogenous grid and permits a fast meshing of the topography. Here, we use the IBM in conjunction with a large-eddy simulation (LES) and test it against two unique datasets. In the first comparison, the LES is used to reproduce experimental results from a wind-tunnel study of a smooth three-dimensional hill. In the second comparison, we simulate the wind field around the Bolund Hill, Denmark, and make direct comparisons with field measurements. Both cases show good agreement between the simulation results and the experimental data, with the largest disagreement observed near the surface. The source of error is investigated by performing additional simulations with a variety of spatial resolutions and surface roughness properties.     

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.     

细网格非静力二维高阶闭合模式对山体流场特征的模拟分析

本文采用二阶矩湍流闭合方案，分别就非静力和准静力两种条件建立ＰＢＬ数值模式，并模拟了二维山脊流场的结构，计算了二维山体对气流平均场和湍流场的影响。计算结果表明，无论是平均场还是湍流场，采用准静力假设都会造成模拟结果的较大偏差，且对平均场的影响比对湍流场的影响更为显著。两种模式计算结果的差别还随地形坡度和背景风增大而增大。     

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.     

Measurements of flow over an elongated ridge and its thermal stability dependence: The mean field

Measurements of mean wind flow and turbulence parameters have been made over Cooper's Ridge, a 115 m high elongated ridge with low surface roughness. This paper describes measurements of the streamwise and vertical variations in the mean field for a variety of atmospheric stability conditions. In near-neutral conditions, the normalised speedup over the ridge compares well with measurements from Askervein (Mickleet al., 1988). The near-neutral results are also compared to an analytical flow model based on that of Huntet al. (1988a). Measured streamwise variations show less deceleration at the foot of the hill and slightly more acceleration at the crest of the hill than does the model. In non-neutral conditions, the speedup over the ridge reduces slightly in unstable conditions and increases by up to a factor of two in stable conditions. The model is modified to allow boundary-layer stability to change the upwind wind profile and the depths of the inner and middle layers. Such a modification is shown to describe the observations of speedup well in unstable and weakly stable conditions but to overestimate the speedup in moderate to strongly stable conditions. This disagreement can be traced to the model's overestimation of the upstream scaling velocity at the height of the middle layer through its use of a stable wind profile form which has greater shear than that of the observed profiles, in possible combination with the three-dimensionality of the ridge which would allow enhanced flow around, rather than over, the feature in more stable conditions.     

Non-Linear Numerical Model Predictions of Flow Over an Isolated Hill of Moderate Slope

Non-linear model simulations of atmospheric boundary-layer flow over the hill called Blashaval have been compared with observations and linear model predictions. Previous studies have shown that linear models can give good predictions of wind speed at the summit and on the upwind slopes of Blashaval. The non-linear model provided wind speed predictions of similar accuracy when compared with the mean observed values at these locations.The published experimental data showed that on the lee-slope the wind speeds at 8m were reduced to approximately 10% of their upstream value at the same height. This was associated with an 180° change in wind direction compared with the upstream flow, suggesting that flow separation had occurred. The non-linear model predictions of lee-slope wind speed, when used with high-resolution topography data, were significantly better than linear model predictions. However, the non-linear model predicted lee-slope wind speeds that were still stronger than observed. The non-linear model simulated flow separation more readily with a 1 1/2-order turbulence closure than with a first-order, mixing-length closure. The configuration of the non-linear model that gave best agreement with observations predicted an 8m lee-slope wind speed that was around 50% of the upstream value.     

A comparison of wind-tunnel experiments and numerical simulations of neutral and stratified flow over a hill

A comparison is made of numerical and experimental results for flow over two-dimensional hills in both neutral and stably stratified flow. The numerical simulations are carried out using a range of one-and-a-half order and second-order closure schemes. The performance of the various turbulence schemes in predicting both the mean and turbulent quantities over the hill is assessed by comparing the results with new wind-tunnel measurements. The wind-tunnel experiments include both neutral and stably stratified flow over two different hills with different slopes, one of which is steep enough to induce flow separation. The dataset includes measurements of the mean and turbulent parts of the flow using laser Doppler anemometry. Pressure measurements are also made across the surface of the hill. These features make the dataset an excellent test of the model performance. In general second-order turbulence schemes provide the best agreement with the experimental data, however, they can be numerically unstable for steep hills. Some modifications can be made to the standard one-and-a-half order closure scheme, which results in improved performance at a fraction of the computation cost of the second-order schemes.     

Local Log-Law-of-the-Wall in Neutrally-Stratified Boundary-Layer Flows

It is well known that in a neutrally-stratified turbulent flow in a deep constant-stress layer above a flat surface,the horizontal mean velocity varies logarithmically with height (the so-called `log-law-of-the-wall').More recently, the same logarithmic law has also been foundin the presence of non-flat surfaces, where it governs thedynamics of the areally-averagedvelocity and involves renormalized effective parameters.Here, we analyze wind profiles over two-dimensional sinusoidal hillsobtained both from numerical simulations performed with a primitiveequation model and from wind-tunnel measurements. We showthat also the local velocity profiles behave to a verygood approximation logarithmically, for a distance from the surface of the order of the maximum hill height almost to the top of the boundary layer. Such alocal log-law-of-the-wall involves effective parameters smoothly depending on theposition along the underlying topography.This dependence looks very similar to the topography itself.     

A boundary-layer analysis of atmospheric motion over a semi-elliptical surface obstruction

Flow over surface obstructions can produce significantly large wind shears such that adverse flying conditions can occur for aeronautical systems (helicopters, V/STOL vehicles, etc.). The purpose of this analysis is to determine the kinds of flow fields that can result from surface obstructions in an otherwise horizontally homogeneous statistically stationary flow. The technique is based on the boundary-layer/Boussinesq-approximated equations of motion. The pressure gradient resulting from the surface obstruction is that consistent with a potential flow over a two-dimensional cylinder with elliptical cross-section, an approach commonly used for boundary-layer analyses in the engineering community. The dissipative effects of atmospheric turbulence on the mean flow are represented with eddy-viscosity models of the Reynolds stresses. The upstream flow is a neutral one and is characterized by a logarithmic profile for the mean wind. The following conclusions result from the analysis: (1) localized maxima in wind speed occur at the top of a surface obstruction, which are expected in physically real flow situations, (2) an increase in the elliptical aspect ratio decreases the wind speed within the boundary layer at the top of the ellipse and returns it to the logarithmic distribution characteristic of undisturbed flow, (3) increases in surface roughness affect the flow by decreasing the velocity in the boundary layer, with the most pronounced effect occurring near the surface of the smaller aspect-ratio ellipse, (4) Reynolds number has a negligible effect on the overall flow for the range of Reynolds numbers considered in this study, (5) a decrease in the elliptical aspect ratio and an increase in the surface roughness cause larger separation regions.     

A Statistical Model for the Prediction of Wind-Speed Probabilities in the Atmospheric Surface Layer

Wind fields in the atmospheric surface layer (ASL) are highly three-dimensional and characterized by strong spatial and temporal variability. For various applications such as wind-comfort assessments and structural design, an understanding of potentially hazardous wind extremes is important. Statistical models are designed to facilitate conclusions about the occurrence probability of wind speeds based on the knowledge of low-order flow statistics. Being particularly interested in the upper tail regions we show that the statistical behaviour of near-surface wind speeds is adequately represented by the Beta distribution. By using the properties of the Beta probability density function in combination with a model for estimating extreme values based on readily available turbulence statistics, it is demonstrated that this novel modelling approach reliably predicts the upper margins of encountered wind speeds. The model’s basic parameter is derived from three substantially different calibrating datasets of flow in the ASL originating from boundary-layer wind-tunnel measurements and direct numerical simulation. Evaluating the model based on independent field observations of near-surface wind speeds shows a high level of agreement between the statistically modelled horizontal wind speeds and measurements. The results show that, based on knowledge of only a few simple flow statistics (mean wind speed, wind-speed fluctuations and integral time scales), the occurrence probability of velocity magnitudes at arbitrary flow locations in the ASL can be estimated with a high degree of confidence.     

Particle-Image Velocimetry Measurements of Separation and Re-attachment of Airflow over Two-Dimensional Hills with Various Slope Angles and Approach-Flow Characteristics

Airflow over two-dimensional hills was investigated in a wind tunnel using particle image velocimetry. We focus on the flow separation behaviour. A trapezoidal hill shape was used in most of the experimental runs, but the critical slope angle for flow separation was approximately the same as that established for smooth hill shapes. The re-attachment point of the separated flow became farther from the hill as the slope angle $\theta $ increased, reaching a saturation of about seven times the hill height for $\theta \gtrsim 60^\circ $ . Increasing the upwind surface roughness length was found to suppress flow separation. This tendency is analogous to the previous experimental results for turbulent boundary layers on flat plates. The boundary-layer thickness varied by the presence or absence of Counihan-type spires and a castellated fence at the test-section entrance had negligible effect on the flow separation.     

Boundary-layer pollutant concentrations over complex terrain

Given the incident profiles of wind velocity and pollutant concentration, we seek to determine the 3-dimensional concentration field of a pollutant upon a region with complex terrain. The analytic solution of the wind velocity in a 3-dimensional boundary-layer model by Walmsley et al. (1980) is utilized as a forcing function in the simplified concentration perturbation equation for a pollutant. The resulting solution applies to an isolated cosine-squared hill in a neutrally stratified boundary-layer flow with a surface type which absorbs the pollutant totally. The solution shows that the concentration perturbation field is organized in accordance with the wind field. In particular, the east-west cross-section is 180° out of phase with the velocity perturbation field. The vertical profiles of the concentration perturbations for selected grid points approach the value of the upper boundary condition very rapidly.     

Spatio-Temporal Surface Shear-Stress Variability in Live Plant Canopies and Cube Arrays

This study presents spatiotemporally-resolved measurements of surface shear-stress τ _s in live plant canopies and rigid wooden cube arrays to identify the sheltering capability against sediment erosion of these different roughness elements. Live plants have highly irregular structures that can be extremely flexible and porous resulting in considerable changes to the drag and flow regimes relative to rigid imitations mainly used in other wind-tunnel studies. Mean velocity and kinematic Reynolds stress profiles show that well-developed natural boundary layers were generated above the 8 m long wind-tunnel test section covered with the roughness elements at four different roughness densities (λ = 0, 0.017, 0.08, 0.18). Speed-up around the cubes caused higher peak surface shear stress than in experiments with plants at all roughness densities, demonstrating the more effective sheltering ability of the plants. The sheltered areas in the lee of the plants are significantly narrower with higher surface shear stress than those found in the lee of the cubes, and are dependent on the wind speed due to the plants ability to streamline with the flow. This streamlining behaviour results in a decreasing sheltering effect at increasing wind speeds and in lower net turbulence production than in experiments with cubes. Turbulence intensity distributions suggest a suppression of horseshoe vortices in the plant case. Comparison of the surface shear-stress measurements with sediment erosion patterns shows that the fraction of time a threshold skin friction velocity is exceeded can be used to assess erosion of, and deposition on, that surface.