Bridging the Transition from Mesoscale to Microscale Turbulence in Numerical Weather Prediction Models

With a focus towards developing multiscale capabilities in numerical weather prediction models, the specific problem of the transition from the mesoscale to the microscale is investigated. For that purpose, idealized one-way nested mesoscale to large-eddy simulation (LES) experiments were carried out using the Weather Research and Forecasting model framework. It is demonstrated that switching from one-dimensional turbulent diffusion in the mesoscale model to three-dimensional LES mixing does not necessarily result in an instantaneous development of turbulence in the LES domain. On the contrary, very large fetches are needed for the natural transition to turbulence to occur. The computational burden imposed by these long fetches necessitates the development of methods to accelerate the generation of turbulence on a nested LES domain forced by a smooth mesoscale inflow. To that end, four new methods based upon finite amplitude perturbations of the potential temperature field along the LES inflow boundaries are developed, and investigated under convective conditions. Each method accelerated the development of turbulence within the LES domain, with two of the methods resulting in a rapid generation of production and inertial range energy content associated to microscales that is consistent with non-nested simulations using periodic boundary conditions. The cell perturbation approach, the simplest and most efficient of the best performing methods, was investigated further under neutral and stable conditions. Successful results were obtained in all the regimes, where satisfactory agreement of mean velocity, variances and turbulent fluxes, as well as velocity and temperature spectra, was achieved with reference non-nested simulations. In contrast, the non-perturbed LES solution exhibited important energy deficits associated to a delayed establishment of fully-developed turbulence. The cell perturbation method has negligible computational cost, significantly accelerates the generation of realistic turbulence, and requires minimal parameter tuning, with the necessary information relatable to mean inflow conditions provided by the mesoscale solution.     

A Modulated-Gradient Parametrization for the Large-Eddy Simulation of the Atmospheric Boundary Layer Using the Weather Research and Forecasting Model

The performance of the modulated-gradient subgrid-scale (SGS) model is investigated using large-eddy simulation (LES) of the neutral atmospheric boundary layer within the weather research and forecasting model. Since the model includes a finite-difference scheme for spatial derivatives, the discretization errors may affect the simulation results. We focus here on understanding the effects of finite-difference schemes on the momentum balance and the mean velocity distribution, and the requirement (or not) of the ad hoc canopy model. We find that, unlike the Smagorinsky and turbulent kinetic energy (TKE) models, the calculated mean velocity and vertical shear using the modulated-gradient model, are in good agreement with Monin–Obukhov similarity theory, without the need for an extra near-wall canopy model. The structure of the near-wall turbulent eddies is better resolved using the modulated-gradient model in comparison with the classical Smagorinsky and TKE models, which are too dissipative and yield unrealistic smoothing of the smallest resolved scales. Moreover, the SGS fluxes obtained from the modulated-gradient model are much smaller near the wall in comparison with those obtained from the regular Smagorinsky and TKE models. The apparent inability of the LES model in reproducing the mean streamwise component of the momentum balance using the total (resolved plus SGS) stress near the surface is probably due to the effect of the discretization errors, which can be calculated a posteriori using the Taylor-series expansion of the resolved velocity field. Overall, we demonstrate that the modulated-gradient model is less dissipative and yields more accurate results in comparison with the classical Smagorinsky model, with similar computational costs.     

Large-Eddy Simulation of the Daytime Boundary Layer in an Idealized Valley Using the Weather Research and Forecasting Numerical Model

A three-dimensional numerical meteorological model is used to perform large-eddy simulations of the upslope flow circulation over a periodic ridge-valley terrain. The subgrid-scale quantities are modelled using a prognostic turbulence kinetic energy (TKE) scheme, with a grid that has a constant horizontal resolution of 50 m and is stretched along the vertical direction. To account for the grid anisotropy, a modified subgrid length scale is used. To allow for the response of the surface fluxes to the valley-flow circulation, the soil surface temperature is imposed and the surface heat and momentum fluxes are computed based on Monin–Obukhov similarity theory. The model is designed with a symmetrical geometry using periodic boundary conditions in both the x and y directions. Two cases are simulated to study the influence of along-valley geostrophic wind forcing with different intensities. The presence of the orography introduces numerous complexities both in the mean properties of the flow and in the turbulent features, even for the idealized symmetric geometry. Classical definitions for the height of the planetary boundary layer (PBL) are revisited and redefined to capture the complex structure of the boundary layer. Analysis of first- and second-moment statistics, along with TKE budget, highlights the different structure of the PBL at different regions of the domain.     

A grid nesting method for large-eddy simulation of planetary boundary-layer flows

A method for performing nested grid calculations with a large-eddy simulation code is described. A common numerical method is used for all meshes, and the grid architecture consists of a single outer or coarse grid, and nested or fine grids, which overlap in some common region. Inter-grid communication matches the velocity, pressure and potential temperature fields in the overlap region. Resolved and sub-grid scale (SGS) turbulent fluxes and kinetic energy on the fine grid are averaged to the coarse grid using a conservation rule equivalent to Germano's identity used to develop dynamic SGS models.Simulations of a slightly convective, strong shear planetary boundary layer were carried out with varying surface-layer resolutions. Grid refinements in the (x, y, z) directions of up to (5, 5, 2) times were employed. Two-way interaction solutions on the coarse and fine meshes are successfully matched in the overlap region on an instantaneous basis, and the turbulent motions on the fine grid blend smoothly into the coarse grid across the grid interface. With surface-layer grid nesting, significant increases in resolved eddy fluxes and variances are found. The energy-scale content of the vertical velocity, and hence vertical turbulent fluxes, appear to be most influenced by increased grid resolution. Vertical velocity spectra show that the dominant scale shifts towards higher wavenumbers (smaller scales) and the magnitude of the peak energy is increased by more than a factor of 3 with finer resolution. Outside of the nested region the average heat and momentum fluxes and spectra are slightly influenced by the fine resolution in the surface layer. From these results we conclude that fine resolution is required to resolve the details of the turbulent motions in the surface layer. At the same time, however, increased resolution in the surface layer does not appreciably alter the ensemble statistics of the resolved and SGS motions outside of the nested region.     

Large-Eddy Simulation of the Stable Atmospheric Boundary Layer using Dynamic Models with Different Averaging Schemes

Large-eddy simulation (LES) of a stable atmospheric boundary layer is performed using recently developed dynamic subgrid-scale (SGS) models. These models not only calculate the Smagorinsky coefficient and SGS Prandtl number dynamically based on the smallest resolved motions in the flow, they also allow for scale dependence of those coefficients. This dynamic calculation requires statistical averaging for numerical stability. Here, we evaluate three commonly used averaging schemes in stable atmospheric boundary-layer simulations: averaging over horizontal planes, over adjacent grid points, and following fluid particle trajectories. Particular attention is focused on assessing the effect of the different averaging methods on resolved flow statistics and SGS model coefficients. Our results indicate that averaging schemes that allow the coefficients to fluctuate locally give results that are in better agreement with boundary-layer similarity theory and previous LES studies. Even among models that are local, the averaging method is found to affect model coefficient probability density function distributions and turbulent spectra of the resolved velocity and temperature fields. Overall, averaging along fluid pathlines is found to produce the best combination of self consistent model coefficients, first- and second-order flow statistics and insensitivity to grid resolution.     

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.     

Modeling Arctic Boundary Layer Cloud Streets at Grey-zone Resolutions

To better understand how model resolution affects the formation of Arctic boundary layer clouds, we investigated the influence of grid spacing on simulating cloud streets that occurred near Utqia?vik(formerly Barrow), Alaska, on 2 May2013 and were observed by MODIS(the Moderate Resolution Imaging Spectroradiometer). The Weather Research and Forecasting model was used to simulate the clouds using nested domains with increasingly fine resolution ranging from a horizontal grid spacing of 27 km in t...     

Comparison of Kansas Data with High-resolution Large-eddy Simulation Fields

The surface layer of an atmospheric boundary layer (ABL) is most accessible to field measurements and hence its ensemble-mean structure has been well established. The Kansas field measurements were the first detailed study of this layer, providing numerous benchmark statistical profiles for a wide range of stability states. Large-eddy simulation (LES), in contrast, is most suitable for studying the mixed layer of the ABL where the energy-containing range of the vertical velocity field is well resolved. In the surface layer, typical large-eddy simulations barely resolve the energy-containing vertical-velocity fields and hence do not provide sufficient data for a detailed analysis.We carried out a nested-mesh simulation of a moderately convective ABL (-z_i/L = 8) in which the lower 6% of the boundary layer had an effective grid resolution of 512³. We analyze the LES fields above the 6th vertical grid level (z = 23 m) where the vertical velocity field has a well formed inertial subrange, for a detailed comparison with the Kansas results. Various terms in the budgets of turbulent kinetic energy, temperature variance, Reynolds stress, temperature flux, and some higher order moments are compared. The agreement is generally quite good; however, we do observe certain discrepancies, particularly in the terms involving pressure fluctuations.     

Morning Boundary-Layer Turbulent Kinetic Energy by Theoretical Models

A major factor that influences the diurnal variation of turbulent kinetic energy (TKE) is the sensible heat flux at the surface. Here, the TKE variations are analysed during the morning transition phase because subsequent to the neutral or stable stratification during the night, peaks of concentration of scalars develop. The characteristics of the TKE during the growth phase of convection are analysed with the help of two analytical models. For this purpose, a three-dimensional spectral model of the growth of convection, starting from a neutral layer, and other formulations of micrometeorological parameters such as the convective and neutral spectra, velocity variance and dissipation rates are utilised. The peak values in the TKE spectra in the lower, middle and upper levels of the convective boundary layer showed a migration to higher wavelengths as the convection increased with time. The TKE evolutions generated by the analytical models agree fairly well with the results of large-eddy simulation for three vertical levels.     

Study of near-surface models for large-eddy simulations of a neutrally stratified atmospheric boundary layer

In large-eddy simulations (LES) of the atmospheric boundary layer (ABL), near-surface models are often used to supplement subgrid-scale (SGS) turbulent stresses when a major fraction of the energetic scales within the surface layer cannot be resolved with the temporal and spatial resolution at hand. In this study, we investigate the performance of both dynamic and non-dynamic eddy viscosity models coupled with near-surface models in simulations of a neutrally stratified ABL. Two near-surface models that are commonly used in LES of the atmospheric boundary layer are considered. Additionally, a hybrid Reynolds- averaged/LES eddy viscosity model is presented, which uses Prandtl’s mixing length model in the vicinity of the surface, and blends in with the dynamic Smagorinsky model away from the surface. Present simulations show that significant portions of the modelled turbulent stresses are generated by the near-surface models, and they play a dominant role in capturing the expected logarithmic wind profile. Visualizations of the instantaneous vorticity field reveal that flow structures in the vicinity of the surface depend on the choice of the near-surface model. Among the three near-surface models studied, the hybrid eddy viscosity model gives the closest agreement with the logarithmic wind profile in the surface layer. It is also observed that high levels of resolved turbulence stresses can be maintained with the so-called canopy stress model while producing good agreement with the logarithmic wind profile.     

The Budget of Turbulent Kinetic Energy in the Urban Roughness Sublayer

Full-scale observations from two urban sites in Basel, Switzerland were analysed to identify the magnitude of different processes that create, relocate, and dissipate turbulent kinetic energy (TKE) in the urban atmosphere. Two towers equipped with a profile of six ultrasonic anemometers each sampled the flow in the urban roughness sublayer, i.e. from street canyon base up to roughly 2.5 times the mean building height. This observational study suggests a conceptual division of the urban roughness sublayer into three layers: (1) the layer above the highest roofs, where local buoyancy production and local shear production of TKE are counterbalanced by local viscous dissipation rate and scaled turbulence statistics are close to to surface-layer values; (2) the layer around mean building height with a distinct inflexional mean wind profile, a strong shear and wake production of TKE, a more efficient turbulent exchange of momentum, and a notable export of TKE by transport processes; (3) the lower street canyon with imported TKE by transport processes and negligible local production. Averaged integral velocity variances vary significantly with height in the urban roughness sublayer and reflect the driving processes that create or relocate TKE at a particular height. The observed profiles of the terms of the TKE budget and the velocity variances show many similarities to observations within and above vegetation canopies.     

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.     

Comparison of Measured and Numerically Simulated Turbulence Statistics in a Convective Boundary Layer Over Complex Terrain

The Weather Research and Forecasting (WRF) model can be used to simulate atmospheric processes ranging from quasi-global to tens of m in scale. Here we employ large-eddy simulation (LES) using the WRF model, with the LES-domain nested within a mesoscale WRF model domain with grid spacing decreasing from 12.15 km (mesoscale) to 0.03 km (LES). We simulate real-world conditions in the convective planetary boundary layer over an area of complex terrain. The WRF-LES model results are evaluated against observations collected during the US Department of Energy-supported Columbia Basin Wind Energy Study. Comparison of the first- and second-order moments, turbulence spectrum, and probability density function of wind speed shows good agreement between the simulations and observations. One key result is to demonstrate that a systematic methodology needs to be applied to select the grid spacing and refinement ratio used between domains, to avoid having a grid resolution that falls in the grey zone and to minimize artefacts in the WRF-LES model solutions. Furthermore, the WRF-LES model variables show large variability in space and time caused by the complex topography in the LES domain. Analyses of WRF-LES model results show that the flow structures, such as roll vortices and convective cells, vary depending on both the location and time of day as well as the distance from the inflow boundaries.     

Subgrid-Scale Dynamics of Water Vapour, Heat, and Momentum over a Lake

We examine the dynamics of turbulence subgrid (or sub-filter) scales over a lake surface and the implications for large-eddy simulations (LES) of the atmospheric boundary layer. The analysis is based on measurements obtained during the Lake-Atmosphere Turbulent EXchange (LATEX) field campaign (August–October, 2006) over Lake Geneva, Switzerland. Wind velocity, temperature and humidity profiles were measured at 20 Hz using a vertical array of four sonic anemometers and open-path gas analyzers. The results indicate that the observed subgrid-scale statistics are very similar to those observed over land surfaces, suggesting that the effect of the lake waves on surface-layer turbulence during LATEX is small. The measurements allowed, for the first time, the study of subgrid-scale turbulent transport of water vapour, which is found to be well correlated with the transport of heat, suggesting that the subgrid-scale modelling of the two scalars may be coupled to save computational resources during LES.     

城市建筑动力学效应对对流边界层影响的敏感性试验

本文将大涡模拟应用于城市对流边界层(CBL)湍流结构和流场特征的研究,在大涡模式中,拖曳系数取与建筑物高度及建筑物高度标准差有关的表达式以考虑次网格建筑物对风速和湍流动能(TKE)的面积平均影响.模拟结果表明,由于城市建筑物对气流的拖曳作用,使建筑物冠层及整个CBL内风速大幅度减小,城市冠层内部风速减小尤为明显,在夹卷层内,风速有一明显的跃变.在边界层中部对流运动已经发展成为较强的热泡,城市建筑物的动力学效应使热泡的水平尺度增大,CBL内平均上升气流速度和下沉气流速度减小,同时使CBL中上升气流所占比例比平坦地面增大.城市建筑物使CBL低层热通量、动量通量、速度方差和位温方差明显增大,但对近地层高度以上的湍流量影响不大.     

Third-Order Moments for Shear Driven Boundary Layer

A new third-order model for shear driven boundary layer is presented and tested against large-eddy simulation (LES) data. Numerical solutions are obtained using mean flow components and second-order moments as input. The calculated vertical profiles of the variances and turbulent kinetic energy fluxes and those provided by a LES experiment are compared and discussed     

Large-Eddy Simulation of Flow and Pollutant Transport in Urban Street Canyons with Ground Heating

Our study employed large-eddy simulation (LES) based on a one-equation subgrid-scale model to investigate the flow field and pollutant dispersion characteristics inside urban street canyons. Unstable thermal stratification was produced by heating the ground of the street canyon. Using the Boussinesq approximation, thermal buoyancy forces were taken into account in both the Navier–Stokes equations and the transport equation for subgrid-scale turbulent kinetic energy (TKE). The LESs were validated against experimental data obtained in wind-tunnel studies before the model was applied to study the detailed turbulence, temperature, and pollutant dispersion characteristics in the street canyon of aspect ratio 1. The effects of different Richardson numbers (Ri) were investigated. The ground heating significantly enhanced mean flow, turbulence, and pollutant flux inside the street canyon, but weakened the shear at the roof level. The mean flow was observed to be no longer isolated from the free stream and fresh air could be entrained into the street canyon at the roof-level leeward corner. Weighed against higher temperature, the ground heating facilitated pollutant removal from the street canyon.     

Resolution Sensitivity and Scaling of Large-Eddy Simulations of the Stable Boundary Layer

Large-eddy simulations (LES) of the continuously turbulent quasi-equilibrium stable boundary layer (SBL) are conducted with grid lengths in the range of 12.5 m to 2 m, in order to explore resolution sensitivity, and determine at what point grid convergence occurs. The structure of the mean potential temperature, winds, and turbulent fluxes varies significantly over this resolution range. The highest resolution simulations show a significant degree of convergence. The dimensionless momentum diffusivity asymptotes to a value of 0.06, corresponding to a limiting flux Richardson number of 0.15.Using the converged simulations, some scaling hypotheses underpinning first-order and second-order closure models are revisited. The effective Richardson number stability functions of the LES are compared with the forms often used in numerical weather prediction (NWP). The mixing implied by the LES is less than that used in NWP. The commonly used similarity profiles for heat and momentum fluxes, and the scalings for dissipation and pressure covariances are compared with the LES. This information could provide guidance for the next generation of SBL parametrization schemes.