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.     

Some observations of airflow over a large hill of moderate slope

Measurements are presented of mean windspeed and turbulence over Great Dun Fell, which is rather larger than hills investigated in the past, viz., 847 m high, which is comparable to the boundary-layer depth. The Fell is well suited for study, being covered by rough grass with no trees and few other obstructions. It was found that the speed-up of the wind is dominated by the elevated stratification and generally agrees closely with the predictions of the model of Carruthers and Choularton (1982) except when the flow is blocked. On the hill summit, the turbulence is approximately in local equilibrium in at least the lowest 10 m and the turbulence measurements are similar to those obtained within the inner layer at other sites. The transverse and longitudinal components show spectral lags at wavelengths greater than 30 m. This suggests an inner-layer depth of about 1/3 that predicted by Jackson and Hunt (1975). At reduced frequencies (>0.1), a recovery in spectral energy is observed due to gravity wave activity. A large variation in the streamline tilt at the summit is observed depending on whether the airflow regime is supercritical or subcritical.     

Simulation of the Askervein Flow. Part 1: Reynolds Averaged Navier–Stokes Equations (k ∈ Turbulence Model)

The neutrally stratified flow over the Askervein Hill was simulatedusing a terrain-following coordinatesystem and a two-equation(k - ) turbulence model. Calculations were performed on awide range of numerical grids to assess, among other things, theimportance of spatial discretization and the limitations of theturbulence model. Our results showed that a relatively coarse gridwas enough to resolve the flow in the upstream region of the hill;at the hilltop, 10 m above the ground, the speed-up was 10% lessthan the experimental value. The flow's most prominent feature wasa recirculating region in the lee of the hill, which determinedthe main characteristics of the whole downstream flow. This regionhad an intermittent nature and could be fully captured only in the caseof a time-dependent formulation and a third-order discretization ofthe advective terms. The reduction of the characteristic roughnessnear the top of the hill was also taken into account, showing theimportance of this parameter, particularly in the flow close to theground at the summit and in the downstream side of the hill.Calculations involving an enlarged area around the Askervein Hillshowed that the presence of the nearby topography affected the flowneither at the top nor downstream of the Askervein Hill.     

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.     

A wind tunnel study of turbulent flow over model hills

Detailed wind tunnel measurements have been made of mean flow and turbulence over a two-dimensional ridge and a circular hill, both having cosine-squared cross-section and maximum slope about 15 °. The measurements were made in an artificially thickened neutrally stratified boundary layer, and have been compared with results from linear models and rapid distortion theory as appropriate.Our study shows that linear theory gives generally good predictions of the mean flow on the upwind side of the hills, and especially of the flow speedup at the hill top, but that the turbulence is less well predicted. In particular, the measurements show a major increase in the vertical component of turbulence and in the shear stress on the upwind slope of both the two- and three-dimensional hills which is not predicted by either equilibrium or isotropic rapid-distortion theories, although this may be partly due to the effect of streamline curvature. Rapid-distortion theory is successful only in describing the streamwise component of turbulence in the outer region of the flow, while in the upper part of the inner region of the flow, the turbulence measurements show disagreement with both the equilibrium and the rapid-distortion theories. Our experiments also confirm that the equilibrium region is a very thin layer close to the surface, while above this region and below the outer region, there is a transitional region where all terms in the stress equation are important.The measurements over the three-dimensional hill suggest that the mean flow and turbulence are broadly similar to those over the two-dimensional ridge, but with reduced perturbation amplitudes. The major differences between the two cases are found on the upwind slope and in the wake where, respectively, horizontal divergence and convergence of the three-dimensional flow are most pronounced.     

Application of a quasi-nonhydrostatic parameterization for numerically modeling neutral flow over an isolated hill

A parameterization of the nonhydrostatic pressure was modified and adapted to a nonlinear numerical model of the neutral atmospheric boundary layer. A hydrostatic model and the quasinonhydrostatic version were used to simulate neutral flow over a symmetrical hill of uniform roughness. Mean-flow quantities and some turbulence characteristics of the flow from both models are presented. These results were compared with observations, analytic theory, and other numerical models.The quasi-nonhydrostatic method produced qualitative features commonly observed in such flows that the hydrostatic model could not simulate. For instance, the observed velocity reduction at the hill base and the speedup at the summit both were simulated by the quasi-nonhydrostatic model. However, computation of vertical velocities from the incompressible continuity equation is inadequate above regions of recirculation and presents a limitation to the method.Journal Paper No. J-12741 of the Iowa Agriculture and Home Economics Experiment Station, Ames, Iowa. Project No. 2779.     

Stratified airflow over one or two hills

Methods for calculating, interpolating and idealising air flow in complex terrain are reviewed. Then the general structure of stratified airflow over a single hill of height H and length L₁ is studied in detail and shown to be determined by the upwind velocity profile, the magnitude of a characteristic Froude number and the dimensions of the hill. Let N(L₁) be the buoyancy frequency upwind at a height L₁, and u_* and U₀ be the upwind friction and mean velocity respectively; then the flow is effectively neutral if u^*/NL₁>1. But if u_*/NL₁>1 and u₀/NL₁>1, the stratification is weak enough to affect the upwind turbulence and velocity profile but not the dynamics of the flow over the hill. If U₀/NL₁ <1 but U₀/NH>1 the buoyancy forces are strong enough to affect the mean flow over the hill but not strong enough to prevent it passing over the top. In this regime the flow is very sensitive to the form of the upwind temperature profile. If U₀/NH>1, much of the flow passes round the hill. A similar classification, with different flow patterns, is appropriate for unstably stratified flows. When the wind is weak enough, local slope winds can dominate. Results from the analysis of these different regimes are described and compared with laboratory of field measurements where possible. It is shown how some of these results can be extended to groups of hills.     

地形对边界层影响的有限元数值模式

本文在定常和中性层结条件下应用有限元法初步建立了一个能够处理二线复杂地形上边界层问题的数值模式。模式使八节点抛物型等参元,有限元方程组用“波前法”求解。应用模式计算了几种典型地形上的近地层流动。模拟出了风速、气压、湍流动量通量以及湍流交换系数等气象要素的主要分布特征,并将计算结果与有关的观测事实做了比较。     

Large-Eddy Simulations of Atmospheric Flows Over Complex Terrain Using the Immersed-Boundary Method in the Weather Research and Forecasting Model

Atmospheric flow over complex terrain, particularly recirculation flows, greatly influences wind-turbine siting, forest-fire behaviour, and trace-gas and pollutant dispersion. However, there is a large uncertainty in the simulation of flow over complex topography, which is attributable to the type of turbulence model, the subgrid-scale (SGS) turbulence parametrization, terrain-following coordinates, and numerical errors in finite-difference methods. Here, we upgrade the large-eddy simulation module within the Weather Research and Forecasting model by incorporating the immersed-boundary method into the module to improve simulations of the flow and recirculation over complex terrain. Simulations over the Bolund Hill indicate improved mean absolute speed-up errors with respect to previous studies, as well an improved simulation of the recirculation zone behind the escarpment of the hill. With regard to the SGS parametrization, the Lagrangian-averaged scale-dependent Smagorinsky model performs better than the classic Smagorinsky model in reproducing both velocity and turbulent kinetic energy. A finer grid resolution also improves the strength of the recirculation in flow simulations, with a higher horizontal grid resolution improving simulations just behind the escarpment, and a higher vertical grid resolution improving results on the lee side of the hill. Our modelling approach has broad applications for the simulation of atmospheric flows over complex topography.     

Large-eddy Simulations of Flow Over Forested Ridges

Large-eddy simulations (LES) of flow over a series of small forested ridges are performed, and compared with numerical simulations using a one-and-a-half order mixing length closure scheme. The qualitative and quantitative similarity between these results provides some confidence in the results of recent analytical and numerical studies of flow over forested hills using first-order mixing length schemes. Time series of model velocities at various locations within the canopy allow the application of various experimental techniques to study the turbulence in the LES. The application of conditional analysis shows that the structure of the turbulence over a forested hill is broadly similar to that over flat ground, with sweeps and ejections dominating. Differences are seen across the hill, particularly associated with regions of mean flow separation and recirculation near the summit and in the lee of the hill. Detailed comparison of derived mixing lengths from the LES with the assumed values used in mixing-length closure schemes show that the mixing length varies with location across the hill and with height in the canopy. This is consistent with previous wind-tunnel measurements, and demonstrates that a constant mixing-length assumption is not strictly valid within the canopy. Despite this, the first-order mixing-length schemes do give similar results both for the mean flow and the turbulence in such situations.     

山丘地形的陆面过程及边界层特征的模拟

将模式NP-89的陆面过程参数化方法应用到北京大学的三维复杂地形中尺度数值模式中, 得到了一个较理想的三维陆面过程及边界层模式, 利用这个改进的三维模式对20 km×20 km范围的山丘地形的陆面过程及边界层特征进行了数值模拟。模拟结果表明, 由于地形阻挡所造成山后的湍流较山前强, 进而造成近地面温度梯度和感热支出小, 最终造成山后的温度比山前的温度明显偏高; 而且随着山高的增加, 这种现象更加明显, 即该模式对山丘地形条件下的陆面过程和大气边界层特征具有较强的模拟能力; 模拟结果合理, 对研究过山气流形成机制、起伏地形大气边界层物理特征和污染物的扩散具有理论和应用价值。     

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.     

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.     

An experimental study of the airflow over a hill in the atmospheric boundary layer

Between 1975 and 1977, the Centre Scientifique et Technique du Bâtiment (CSTB) carried out a study of the overspeed effect over a hill in the surface boundary layer. The hill in question was situated in open country and had a drop of about 100 m for an average slope of 8%. The experimental equipment consisted of three 25 m high masts placed along the upwind slope of the hill. Each mast was equipped with four Gill Propeller anemometers. The data set analyzed consisted of 65 recordings of strong winds which had an average velocity greater than 6 m s^-1.Near the ground, local topographic effects and inhomogeneous roughness along the slope have the same influence on the overspeed effect as the mean slope of the hill. The overspeed is proportional to the upwind slope, but on the other hand, the turbulence structure does not seem to be disturbed by the hill.     

Turbulent Flow at 190 m Height Above London During 2006–2008: A Climatology and the Applicability of Similarity Theory

Flow and turbulence above urban terrain is more complex than above rural terrain, due to the different momentum and heat transfer characteristics that are affected by the presence of buildings (e.g. pressure variations around buildings). The applicability of similarity theory (as developed over rural terrain) is tested using observations of flow from a sonic anemometer located at 190.3 m height in London, U.K. using about 6500 h of data. Turbulence statistics—dimensionless wind speed and temperature, standard deviations and correlation coefficients for momentum and heat transfer—were analysed in three ways. First, turbulence statistics were plotted as a function only of a local stability parameter z/Λ (where Λ is the local Obukhov length and z is the height above ground); the σ _i /u _* values (i = u, v, w) for neutral conditions are 2.3, 1.85 and 1.35 respectively, similar to canonical values. Second, analysis of urban mixed-layer formulations during daytime convective conditions over London was undertaken, showing that atmospheric turbulence at high altitude over large cities might not behave dissimilarly from that over rural terrain. Third, correlation coefficients for heat and momentum were analyzed with respect to local stability. The results give confidence in using the framework of local similarity for turbulence measured over London, and perhaps other cities. However, the following caveats for our data are worth noting: (i) the terrain is reasonably flat, (ii) building heights vary little over a large area, and (iii) the sensor height is above the mean roughness sublayer depth.     

Large-eddy Simulation of Turbulent Flow Across a Forest Edge. Part I: Flow Statistics

The statistics of turbulent flow across a forest edge have been examined using large-eddy simulation, and results compared with field and wind-tunnel observations. The moorland-to-forest transition is characterized by flow deceleration in the streamwise direction, upward distortion of the mean flow, formation of a high pressure zone immediately in front of the edge, suppression of the standard deviations and covariance of velocity components, and enhancement of velocity skewnesses. For the selected forest density, it is observed that the maximum distortion angle is about 8 degrees from the horizontal. Instead of approaching a downwind equilibrium state in a monotonic manner, turbulence (standard deviations and covariances of velocity components) and mean streamwise velocity undershoot in the transition zone behind the edge. Evolution of flow statistics clearly reveals the growth of an internal boundary layer, and the establishment of an equilibrium layer downwind of the edge. It is evident that lower-order moments generally adjust more quickly over the new rough surface than do higher-order moments. We also show that the streamwise velocity standard deviation at canopy height starts its recovery over the rough surface sooner than does the vertical velocity standard deviation, but completes full adjustment later than the latter. Despite the limited domain size upstream of the edge, large-eddy simulation has successfully reproduced turbulent statistics in good agreement with field and wind-tunnel measurements.     

Turbulence and diffusion over inhomogeneous terrain

This paper provides an overview of some aspects of atmospheric boundary-layer dispersion processes over homogeneous and complex terrain. Special emphasis is placed on a discussion of the boundarylayer scaling regimes over homogeneous terrain and the characteristics of the dispersion processes associated with each of these regimes. The paper points out that vertical concentration profiles usually deviate substantially from a Gaussian distribution. The mean flow and turbulence over a low hill is dealt with, and in the inner layer the turbulence levels are increased due to the mean flow speed-up. In the outer layer the turbulence is modified by the rapid distortion effect. In a middle layer the turbulence is reduced due to the effect of a hill-induced streamline curvature. The paper concludes that the flow perturbations introduced by large-scale hills and valleys invalidate the use of simple approximations for describing atmospheric dispersion processes, and that it is necessary to utilize the full set of equations of motion.     

The stably stratified boundary layer over the great plains

Airplane measurements of the stably stratified boundary layer obtained during the Severe Environmental Storms and Mesoscale Experiment (SESAME) over rolling terrain in south-central Oklahoma indicate that considerable horizontal variability exists in the flow on scales of several kilometers. Much of this wave-like structure appears to be tied to the terrain. The criteria for existence of stationary gravity waves indicate that these waves can exist under the observed conditions. The spectrum of terrain variations also supports the existence of these waves. Observed spectra of the vertical velocity have two peaks: one at wavelengths of several kilometers, which is due to waves and the other at wavelengths of about 100 m, which is due to turbulence. The variance at several kilometers wavelength increases somewhat with height at least up to about 800 m, but the variance contributed by turbulence decreases rapidly with height.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

三维非静力E—ε闭合模式对山体流场及浓度分布的模拟

本文采用三维非静力E-ε闭合模式,在对流层边界层方程组中,加入湍能和耗散率方程描述边界层中的湍流运动。求解孤立三维山地地形上的流场、湍流场和浓度场,并分析地形对气流的影响及对污染物浓度分布的影响。同时做了不同坡度和不同风速下的孤立三维山体的流场、湍流场和浓度场比较。数值计算结果表明,地形能改变气流运动,气流过山时将出现分支现象,山后背坡有反向回流出现,并且回流区大小随着山体坡度的增大而增大。山体对气流的阻挡作用随山体高度的增加而更明显,随风速的增加而减弱。湍能及耗散率随高度衰减较快。随着山体坡度增加,山前气流的垂直速度也增加,湍流运动更强。风速大时湍流运动越显著。污染物在山前出现辐散,迎风坡是浓度高值区,山后背风坡也是相对高值区。山坡度越大,山前迎风坡污物浓度越高。