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.     

Subfilter-Scale Fluxes over a Surface Roughness Transition. Part II: A priori Study of Large-Eddy Simulation Models

The ability of subfilter-scale (SFS) models to reproduce the statistical properties of SFS stresses and energy transfers over heterogeneous surface roughness is key to improving the accuracy of large-eddy simulations of the atmospheric boundary layer. In this study, several SFS models are evaluated a priori using experimental data acquired downwind of a rough-to-smooth transition in a wind tunnel. The SFS models studied include the eddy-viscosity, similarity, non-linear and a mixed model consisting of a combination of the eddy-viscosity and non-linear models. The dynamic eddy-viscosity model is also evaluated. The experimental data consist of vertical and horizontal planes of high-spatial-resolution velocity fields measured using particle image velocimetry. These velocity fields are spatially filtered and used to calculate SFS stresses and SFS transfer rates of resolved kinetic energy. Coefficients for each SFS model are calculated by matching the measured and modelled SFS energy transfer rates. For the eddy-viscosity model, the Smagorinsky coefficient is also evaluated using a dynamic procedure. The model coefficients are found to be scale dependent when the filter scales are larger than the vertical measurement height and fall into the production subrange of the turbulence where the flow scales are anisotropic. Near the surface, the Smagorinsky coefficient is also found to decrease with distance downwind from the transition, in response to the increase in mean shear as the flow adjusts to the smooth surface. In a priori tests, the ability of each model to reproduce statistical properties of the SFS stress is assessed. While the eddy-viscosity model has low spatial correlation with the measured stress, it predicts mean stresses with the same accuracy as the other models. However, the deficiency of the eddy-viscosity model is apparent in the underestimation of the standard deviation of the SFS stresses and the inability to predict transfers of kinetic energy from the subfilter scales to the resolved scales. Overall, the mixed model is found to have the best performance.     

The Bolund Experiment,Part II: Blind Comparison of Microscale Flow Models

Bolund measurements were used for a blind comparison of microscale flow models. Fifty-seven models ranging from numerical to physical were used, including large-eddy simulation (LES) models, Reynolds-averaged Navier–Stokes (RANS) models, and linearized models, in addition to wind-tunnel and water-channel experiments. Many assumptions of linearized models were violated when simulating the flow around Bolund. As expected, these models showed large errors. Expectations were higher for LES models. However, of the submitted LES results, all had difficulties in applying the specified boundary conditions and all had large speed-up errors. In contrast, the physical models both managed to apply undisturbed ‘free wind’ boundary conditions and achieve good speed-up results. The most successful models were RANS with two-equation closures. These models gave the lowest errors with respect to speed-up and turbulent kinetic energy (TKE) prediction.     

Boundary-layer flow over topography: Impacts of the Askervein study

One of the objectives of the Askervein Hill Project was to obtain a comprehensive and accurate dataset for verification of models of flow and turbulence over low hills. In the present paper, a retrospective of the 1982 and 1983 Askervein experiments is presented. The field study is described in brief and is related to similar studies conducted in the early 1980s. Data limitations are discussed and applications of numerical and wind-tunnel models to Askervein are outlined. Problems associated with model simulations are noted and model results are compared with the field measurements.     

Simulation of the Askervein flow. Part 2: Large-eddy simulations

Large-eddy simulations of the neutrally stratified flow over the Askervein Hill were performed, to improve the knowledge of the flow obtained from field measurements and numerical simulations with Reynolds averaged Navier-Stokes (RANS) methods. A Lagrangian dynamic subgrid model was used but, to avoid the underdissipative character near the ground, it was merged with a damped Smagorinsky model. Simulations of a flat boundary-layer flow with this subgrid model showed that the turbulent vertical motions and shear stress were better resolved using grids with a stream to spanwise aspect ratio Δx / Δy = 2 than with an aspect ratio Δx / Δy = 1. Regarding the flow over the Askervein Hill, it was found that large-eddy simulations provide an acceptable solution for the mean-velocity field and better predictions of the turbulent kinetic energy in the upstream side of the hill than the model. However, as with the model, grid convergence was not achieved in the lee side and the size of the zone with reversed flow increased with the grid refinement. Nevertheless, the existence of the intermittent separation predicted with unsteady RANS in part one of this work seems unquestionable, due to the deceleration of the flow. In our opinion, a better modelling of the decelerating boundary layer in the lee side is required to improve the results obtained using equilibrium assumptions and achieve grid convergence.     

A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows

A long-standing problem in large-eddy simulations (LES) of the planetary boundary layer (PBL) is that the mean wind and temperature profiles differ from the Monin-Obukhov similarity forms in the surface layer. This shortcoming of LES has been attributed to poor grid resolution and inadequate sub-grid-scale (SGS) modeling. We study this deficiency in PBL LES solutions calculated over a range of shear and buoyancy forcing conditions. The discrepancy from similarity forms becomes larger with increasing shear and smaller buoyancy forcing, and persists even with substantial horizontal grid refinement. With strong buoyancy forcing, however, the error is negligible.In order to achieve better agreement between LES and similarity forms in the surface layer, a two-part SGS eddy-viscosity model is proposed. The model preserves the usual SGS turbulent kinetic energy formulation for the SGS eddy viscosity, but it explicitly includes a contribution from the mean flow and a reduction of the contributions from the turbulent fluctuations near the surface. Solutions with the new model yield increased fluctuation amplitudes near the surface and better correspondence with similarity forms out to a distance of 0.1–0.2 times the PBL depth, i.e., a typical surface-layer depth. These results are also found to be independent of grid anisotropy. The new model is simple to implement and computationally inexpensive.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

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.     

NUMERICAL SIMULATIONS OF TURBULENT FLOW IN AND ABOVE PLANT CANOPIES

The turbulent flow in and above plant canopies is of fundamental importance to the understanding oftransport processes of momentum,heat and mass between plant canopies and atmosphere,and to microme-teorology.The Reynolds stress equation model(RSM)has been applied to calculate the turbulence in cano-pies in this paper.The calculated mean wind velocity profiles,Reynolds stress,turbulent kinetic energy andviscous dissipation rate in a corn canopy and a spruce forest are compared with field observed data and withWilson's and Shaw's model.The velocity profiles and Rynolds stress calculated by both models are in goodagreement,and the length scale of turbulence appears to be similar.     

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.     

植被内部及其上方湍流场的数值模拟

植被内部及其上方的湍流流场对于了解植被与大气之间的动量、热量和质量交换过程极其重要。本文把高阶湍流封闭模型的Reynolds应力方程模型(RSM)应用于植被湍流的计算,得到了风速、湍流动能、Reynolds应力及能量耗散率的垂直分布,与现场观测数据比较,甚为满意。     

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.     

Large-Eddy Simulation of the Wind Field and Plume Dispersion Within Different Obstacle Arrays Using a Dynamic Mixing Length Subgrid-Scale Model

A novel dynamic mixing length (DML) subgrid-scale (SGS) model is proposed to improve the large-eddy simulations of the wind field and contaminant dispersion around a group of buildings. Wind field and contaminant dispersion in two kinds of building array geometries are simulated using the model, with wind-tunnel experimental data used to validate the model. The relative errors in the lateral profiles of the streamwise mean velocities behind the sixth row of the buildings of the staggered obstacle array and the aligned obstacle array at the half height of the building are 15 and 9%, respectively. The DML velocity fluctuations in the staggered and aligned obstacle arrays are in agreement with those of the experiment. The results indicate that the DML model can make a more accurate prediction of the mean velocity and velocity fluctuations. The DML model is highly suitable for the simulation of multi-scale turbulent flow in urban canyons, of high Reynolds number turbulent flow and of complex turbulent flow.     

Effects of Thermal Stability and Incoming Boundary-Layer Flow Characteristics on Wind-Turbine Wakes: A Wind-Tunnel Study

Wind-tunnel experiments were carried out to study turbulence statistics in the wake of a model wind turbine placed in a boundary-layer flow under both neutral and stably stratified conditions. High-resolution velocity and temperature measurements, obtained using a customized triple wire (cross-wire and cold wire) anemometer, were used to characterize the mean velocity, turbulence intensity, turbulent fluxes, and spectra at different locations in the wake. The effect of the wake on the turbulence statistics is found to extend as far as 20 rotor diameters downwind of the turbine. The velocity deficit has a nearly axisymmetric shape, which can be approximated by a Gaussian distribution and a power-law decay with distance. This decay in the near-wake region is found to be faster in the stable case. Turbulence intensity distribution is clearly non-axisymmetric due to the non-uniform distribution of the incoming velocity in the boundary layer. In the neutral case, the maximum turbulence intensity is located above the hub height, around the rotor tip location and at a distance of about 4–5.5 rotor diameters, which are common separations between wind turbines in wind farms. The enhancement of turbulence intensity is associated with strong shear and turbulent kinetic energy production in that region. In the stable case, the stronger shear in the incoming flow leads to a slightly stronger and larger region of enhanced turbulence intensity, which extends between 3 and 6 rotor diameters downwind of the turbine location. Power spectra of the streamwise and vertical velocities show a strong signature of the turbine blade tip vortices at the top tip height up to a distance of about 1–2 rotor diameters. This spectral signature is stronger in the vertical velocity component. At longer downwind distances, tip vortices are not evident and the von Kármán formulation agrees well with the measured velocity spectra.     

Large-eddy Simulation of Turbulent Flow across a Forest Edge. Part II: Momentum and Turbulent Kinetic Energy Budgets

Momentum and turbulent kinetic energy (TKE) budgets across a forest edge have been investigated using large-eddy simulation (LES). Edge effects are observed in the rapid variation of a number of budget terms across this vegetation transition. The enhanced drag force at the forest edge is largely balanced by the pressure gradient force and by streamwise advection of upstream momentum, while vertical turbulent diffusion is relatively insignificant. For variance and TKE budgets, the most important processes at the forest edge are production due to the convergence (or divergence) of the mean flow, streamwise advection, pressure diffusion and enhanced dissipation by canopy drag. Turbulent diffusion, pressure redistribution and vertical shear production, which are characteristic processes in homogeneous canopy flow, are less important at the forest transition. We demonstrate that, in the equilibrated canopy flow, a substantial amount of TKE produced in the streamwise direction by the vertical shear of the mean flow is redistributed in the vertical direction by pressure fluctuations. This redistribution process occurs in the upper canopy layers. Part of the TKE in the vertical velocity component is transferred by turbulent and pressure diffusion to the lower canopy levels, where pressure redistribution takes place again and feeds TKE back to the streamwise direction. In this TKE cycle, the primary source terms are vertical shear production for streamwise velocity variance and pressure redistribution for vertical velocity variance. The evolution of these primary source terms downwind of the forest edge largely controls the adjustment rates of velocity variances.     

On extension of Malkus' theory of turbulence to stably stratified shear flow

Malkus' theory of turbulent shear flow and turbulent convection is extended to stably stratified shear flow. The local Richardson number is found to be close to its critical value throughout the turbulent flow. Assuming a strong interaction between velocity and density fields requires that their profiles depend linearly on height. From this, for stratified shear flow at sufficiently high Reynolds numbers, a combination of logarithmic and linear profiles is expected. The purely linear and the log-linear profile are both observed in laboratory channel flow and in atmospheric boundary layer flow.Work undertaken while at the Department of Meteorology and Physical Oceanography, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A.     

Characteristics of turbulent structures in the unstable atmospheric surface layer

An atmospheric surface-layer (ASL) experiment conducted at a meteorological site in the Oostelijk-Flevoland polder of the Netherlands is described. Turbulent fluctuations of wind velocity, air temperature and static pressure were measured, using three 10 m towers.Simultaneous turbulent signals at several heights on the towers were used to investigate the properties of the turbulent structures which contribute most significantly to the turbulent vertical transports in the unstable ASL. These turbulent structures produce between 30 and 50% of the mean turbulent vertical transport of horizontal alongwind momentum and they contribute to between 40 and 50% of the mean turbulent vertical heat transport; in both cases this occurs during 15 to 20% of the total observation time.The translation speed of the turbulent structures equals the wind speed averaged over the depth of the ASL, which scales on the surface friction velocity. The inclination angle of the temperature interface at the upstream edge of the turbulent structures to the surface is significantly smaller than that of the internal shear layer, which is associated with the temperature interface. The turbulent structures in the unstable ASL are determined by a large-scale temperature field: Convective motions, which encompass the whole depth of the planetary boundary layer (PBL), penetrate into the ASL. The curvature of the vertical profile of mean horizontal alongwind velocity forces the alignment of the convective cells in the flow direction (Kuettner, 1971), which have an average length of several hundreds of metres and an average width of a few tens of metres. This mechanism leads to the formation of turbulent structures, which extend throughout the depth of the ASL.     

Geophysical applications of heat and mass transfer in turbulent pipe flow

The theory of heat and mass transfer in turbulent pipe flow is applied to a semi-infinite moist-walled cylindrical pipe to determine the longitudinal distributions of both temperature and moisture content as functions of external conditions, pipe radius and wall temperature, and flow velocity. Since many cave and mine passages approximate this model, the results are directly applicable to cave microclimate studies and mine ventilation problems. The results are found to agree well with previously published microclimate observations. The theory is also applicable to water flow in free-flow karst aquifers; specifically to the study of temperature variations and of solution kinetics under turbulent flow conditions.