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.     

Numerical studies of neutrally stratified planetary boundary-layer flow above gentle topography

A numerical model of planetary boundary-layer flow above two-dimensional gentle topography is developed as an extension of the surface-layer model described by Taylor (1977). Comparisons are made with surface-layer predictions for flow over Gaussian hills; and the flow at various angles above hills, valleys and escarpments is modelled. Some simple case studies of the influence of gentle two-dimensional topography on pollutant dispersion are made which indicate relatively minor effects on surface pollutant concentrations in comparison with results for dispersion above a plane surface.     

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.     

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.     

A simple model of neutrally stratified boundary-layer flow over complex terrain with surface roughness modulations (MS3DJH/3R)

The MS3DJH series of simple models of flow over low hills and other terrain features described in earlier papers (see Taylor et al., 1983) required that the terrain was of uniform surface roughness. In the present paper, we describe an approximate theory of flow above variations in surface roughness using a similar structure to that established by Jackson and Hunt (1975) for flow over hills. This then allows us to include the calculation of flow perturbations due to roughness variations within a modified version of our model which we designate as MS3DJH/3R. Comparisons are made with alternative calculations for simple two-dimensional flows; and sample three-dimensional calculations are presented. The model retains its essential features of high spatial resolution and low computing cost.Summer student, 1981     

Wind flow over ridges in simulated atmospheric boundary layers

The flows over four two-dimensional triangular hills and three two-dimensional bell-shaped hills have been investigated in a simulated rural atmospheric boundary layer modelled to a scale of 1:300: Further measurements were made over two of the triangular hills in a simulated rural boundary layer of 1: 3000 scale and in a simulated urban boundary layer modelled to a scale of 1:400. The effect of the model hill surface roughness was also investigated. Flow measurements were restricted to the mean velocity U, RMS velocity fluctuations u and the energy spectra for the streamwise velocity component Measurements were made at a number of longitudinal positions in the approach flow, over the model hills and downstream of the model hills. For each model hill, the crest was the region of largest mean velocity and smallest velocity fluctuations. The largest mean velocities over the model hills occurred for hills of intermediate slope rather than for the steepest hills. A decrease in the scale of the simulated atmospheric boundary layer led to a reduction in the amplification factors at the hill crests, whereas an increase in the surface roughness of the approach flow resulted in increased amplification factors at the hill crests.     

Surface Characteristics Observed over the Central Tropical Indian Ocean During Indoex IFP99

The present study is based on the observations carried out over the IndianOcean from the Indian research vessel ORV Sagar Kanya during the intensive field phase of the Indian Ocean Experiment in January–March 1999. The study area spanned from 15°N to 20°S in the central Indian Ocean. Near surface variations and surface fluxes along the cruise track are presented. A comparison of near surface characteristics over the Indian Ocean and tropical west Pacific has been made. It is observed that the average difference between the sea surface temperature and air temperature at 10 m height was 0.7 °C over the study area, nearly half of that observed over the tropical west Pacific. A comparison between observed and NCEP reanalysissurface data has been made. We find good agreement between ship measured andNCEP reanalysis surface pressure, specific humidity and wind fields.On the other hand, surface air temperature in the reanalysis tends to be lowcompared to observations. The components of the net surface heat flux comparebetter in the north Indian Ocean than in the southern Indian Ocean.     

Estimation of bulk transfer coefficient for latent heat flux (Ce)

The bulk transfer coefficient for latent heat flux (Ce) has been estimated over the Arabian Sea from the moisture budget during the pre-monsoon season of 1988.The computations have been made over two regions (A: 0–8 ° N; 60–68 ° E; B: 0–4 ° N; 56–60 ° E) with the upper computational boundary fixed at the 300 mb level. The precipitation amount (P) was negligible for region A while the observed values of P have been used for region B. The Ce estimates have been compared with those obtained with other available schemes (Kondo, 1975: Bunker, 1976). which are based on wind speed and atmospheric stability within the surface layer. Our value of Ce is higher in region A and lower in region B than the other estimates.     

A wind tunnel study of turbulent dispersion over two- and three-dimensional gentle hills from upwind point sources in neutral flow

A study of turbulent dispersion over hills for upstream, elevated sources was conducted, based on wind tunnel tracer gas (CO₂) experiments over a gentle 2-D ridge and a 3-D circular hill, both having a cosine-square cross-section. The concentration measurements were made with four different source locations for each hill case (2-D or 3-D), and the study focused on dispersion parameters under the influence of the presence of the hills in order to provide a better understanding of the mechanisms involved.The wind tunnel measurements show that, in the case of gentle hills, the topographic impact on turbulent dispersion from upstream sources is only moderate and is more pronounced for the 3-D than for the 2-D hill. The perturbation in mean flow introduced by the hills, including streamline divergence/convergence, is shown to dominate the changes in the dispersion due to the hills in this case. The plume spread, both in the lateral and the vertical, is enhanced over the upwind hill foot and reduced over the hill top in response to the mean flow slow-down and speed-up at these places, and is further enhanced or reduced due to streamline divergence/convergence in the vertical over the hills as well as in the horizontal over the 3-D hill. These results are also compared with cases of turbulent dispersion over more steep hills (Snyder and Britter, 1987).     

Some evidence of organized flow over natural waves

Measurements of the flow characteristics at 2 m over unobstructed wave surfaces on Lake Michigan were made using an anemometer-bivane as a velocity sensor. During one 40-min period of measurement, significant energy concentration was observed at the frequency of dominant surface waves in the vertical and cross wind spectra. Cross spectra between the surface elevation and vertical motions in the flow indicate that the surface lags the vertical motions by about 55 ° at the frequency of dominant waves.     

The Askervein hill project: A finite control volume prediction of three-dimensional flows over the hill

A three-dimensional nonlinear numerical model, that has been extensively used previously to predict environmental water flows, was applied to predict the flow over an isolated hill, Askervein. Predictions are reported for winds approaching the hill from 210 ° and 180 ° clockwise from north, both under almost neutral atmospheric conditions.The model predictions were compared with data collected during a major field study in 1983. From the comparisons it was concluded that the model predicts the mean flow variables with good accuracy. Larger discrepancies were found for quantities related to the turbulence, pointing to deficiencies in the turbulence model, and perhaps in some of the measurements.     

Pre-monsoon surface pressure and summer monsoon rainfall over India

Summary The relationship between the surface air pressure field during the pre-monsoon months and the Indian summer monsoon rainfall is analysed using climate data from 105 stations situated in Eurasia between 0°–60° N and 20°–100° E. Moreover, grid-point data for the whole northern hemisphere are used. Pressure during April over an area around 50° N and 35° E is found to show a significant negative correlation with the subsequent monsoon rainfall. During May the pressure over a large part of the study area south of 40° N shows a significant correlation with its highest value in the heat low region over Pakistan. It is assumed that monitoring of pressure variations over this region may be useful in predicting monsoon rainfall, particularly the rainfall during the first half of the season. Certain limitations of the climate data in this region are also discussed.With 5 Figures     

A new nonlinear analytical model for canopy flow over a forested hill

A new nonlinear analytical model for canopy flow over gentle hills is presented. This model is established based on the assumption that three major forces (pressure gradient, Reynolds stress gradient, and nonlinear canopy drag) within canopy are in balance for gentle hills under neutral conditions. The momentum governing equation is closed by the velocity-squared law. This new model has many advantages over the model developed by Finnigan and Belcher (Quart J Roy Meteorol Soc 130: 1–29 2004, hereafter referred to as FB04) in predicting canopy wind velocity profiles in forested hills in that: (1) predictions from the new model are more realistic because surface drag effects can be taken into account by boundary conditions, while surface drag effects cannot be accounted for in the algebraic equation used in the lower canopy layer in the FB04 model; (2) the mixing length theory is not necessarily used because it leads to a theoretical inconsistency that a constant mixing length assumption leads to a nonconstant mixing length prediction as in the FB04 model; and (3) the effects of height-dependent leaf area density (a(z)) and drag coefficient (C _d ) on wind velocity can be predicted, while both a(z) and C _d must be treated as constants in FB04 model. The nonlinear algebraic equation for momentum transfer in the lower part of canopy used in FB04 model is height independent, actually serving as a bottom boundary condition for the linear differential momentum equation in the upper canopy layer. The predicting ability of the FB04 model is largely restricted by using the height-independent algebraic equation in the bottom canopy layer. This study has demonstrated the success of using the velocity-squared law as a closure scheme for momentum transfer in forested hills in comparison with the mixing length theory used in FB04 model thus enhancing the predicting ability of canopy flows, keeping the theory consistent and simple, and shining a new light into land-surface parameterization schemes in numerical weather and climate models.     

Numerical Simulation of Flow over Two-Dimensional Hills Using a Second-Order Turbulence Closure Model

We study turbulent flow over two-dimensional hills. The Reynolds stresses are represented by a second-order closure model, where advection, diffusion, production and dissipation processes are all accounted for. We solve a full set of primitive non-hydrostatic dynamic equations for mean flow quantities using a finite-difference numerical method. The model predictions for the mean velocity and Reynolds stresses are compared with the measured data from a wind-tunnel experiment that simulates the atmospheric boundary layer. The agreement is good. The performance of the second-order closure model is also compared withthat of lower level turbulence models, including the eddy-viscositymodel and algebraic Reynolds stress models. It is concluded that thepresent closure is a considerable improvement over the other modelsin representing various physical effects in flow over hills. Thefeasibility of running a finite-difference numerical simulationincorporating a full second-order closure model on an IBM workstationis also demonstrated.     

Water tank and numerical model studies of flow over steep smooth two-dimensional hills

The present work investigates the role of different treatments of the lower boundary condition on the numerical prediction of flows over two-dimensional, smooth, steep hills. Four different law of the wall formulations are tested when a large recirculating region is formed on the lee side of the hill. Numerical implementation of the near-wall functions was made through a finite elements code. The standard κ–ε model was used to close the averaged Navier–Stokes equations. Results are validated through original data obtained in a water tank. Measurements resorted to laser Doppler anemometry. The experiment provide detailed data for the characterization of the reverse flow in the region between the separation and the reattachment points, with emphasis on the near wall region. The experimental wall shear stress distribution is compared with the results provided by the different laws of the wall showing good agreement. The numerical predictions are shown to vary markedly between different formulations.     

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 global monthly climatology of soil moisture and water balance

Global monthly climatology of available soil moisture content is derived on a 4° by 5° grid from observed precipitation and air surface temperature by use of a simple water budget model. The governing equations and methods of calculation for deriving these fields, which follow the formulation of Thornthwaite, are first described and the importance of the various assumptions and simplifications of this approach are discussed. The derived global fields are then presented. A comparison of some of the derived fields with other calculations is also made in order to permit an evaluation of the results: For example, our indirect estimate of the river run-off is generally in good agreement with more direct estimates, except for high latitude regions where the freezing of the soil may play an important role.Yale Mintz died on 27 April 1991. This work was carried out jointly over a number of years preceding his death     

Thermodynamic structure of the boundary layer in relation to a monsoon depression over the Bay of Bengal — A case study

Aerological observations carried out on board ORV Sagarkanya at a stationary location (20° N, 89° E) over the Head Bay of Bengal during August 18–21, 1990 were analysed to study the thermodynamic structure of the marine boundary layer in relation to a monsoon depression which formedin situ with its centre at 20° N, 88° E. The q(mixing ratio) reversal observed at 850 hPa prior to formation of the low pressure area shifted to a higher level (h<700 hPa) with the formtion of the low. Positive buoyancy below 850 hPa prior to the formation of the low indicated conditions favourable for deep convection. When the low pressure area intensified into a depression, negative buoyancy was observed at lower levels.     

Turbulence modelling over two-dimensional hills using an Algebraic Reynolds Stress Expression

We carry out model studies of turbulence quantities for flow over two-dimensional hills using a non-hydrostatic version of the Regional Atmospheric Modeling System (RAMS). We test two turbulence closure models: the first one is an explicit Algebraic Reynolds Stress Model (ARSM) and the second one is a combination of the ARSM and a transport equation for the shear stress {ovuw}. Model predictions for the turbulent stresses are compared with data from a wind-tunnel experiment containing isolated two-dimensional hills of varying slope. From the comparison, it is concluded that the first model can only predict the normal stresses adequately while the second model provides satisfactory predictions for the normal stresses as well as giving an improved result for the shear stress {ovuw}.     

Flow Over Partially Forested Ridges

Numerical simulations of flow over hills that are partially covered with a forest canopy are performed. This represents a much more realistic situation than previous studies that have generally concentrated on hills that are fully-forested. The results show that the flow over the hill is sensitive to where on the hill the forest is positioned. In particular, for low slopes flow separation is predominantly located within the forest on the lee slope. This has implications for the transport of scalars in the forest canopy. For large hills the results show more variability in scalar concentrations within the canopy compared to either a fully-forested hill or a patch of forest over flat terrain. These results are likely to have implications for a range of applications including the siting and interpretation of flux measurements over forests in complex terrain, predicting wind damage to trees and wind-farm developments. Calculation of the hill-induced pressure drag and canopy-plus-surface stress shows a strong sensitivity to the position of the forest relative to the hill. Depending on the position of the forest the individual drag terms may be strongly enhanced or reduced and may even change sign. The net impact is generally to reduce the total drag compared to an equivalent fully-forested hill, but the amount of the reduction depends strongly on the position of the forest canopy on the hill. In many cases with large, wide hills there is a clear separation of scales between the adjustment of the canopy to a forest edge (of order 6 ? 8L _c, where L _c is the canopy adjustment length scale) and the width of the hill. This separation means that the hill-induced pressure and flow fields and the forest-edge induced pressure and flow fields can in some sense be considered as acting separately. This provides a means of explaining the combined effects of partial forestation and terrain. It also offers a simple method for modelling the changes in drag over a hill due to partial forest cover by considering the impact of the hill and the partial canopy separately. Scaling arguments based on this idea successfully collapse the modelled drag over a range of different hill widths and heights and for different canopy parameters. This offers scope for a relatively simple parametrization of the effects of partial forest cover on the drag over a hill.