Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-eddy Simulations. Part 1: Free Convection

Convection in a quasi-steady, cloud-free, shear-free atmospheric boundary layer is investigated based on a large-eddy simulation model. The performed tests indicate that the characteristic (peak) values of statistical moments at the top of the mixed layer are proportional to the interfacial scales (from gradients of scalars in the interfacial layer). Based on this finding a parameterization is proposed for profiles of scalar variances. The parameterization employs two, semi-empirical similarity functions F_m(z/z_i) andF_i(z/z_i), multiplied by a combination of the mixed-layer scales and the interfacial scales.     

Effect of Roughness on Surface Boundary Conditions for Large-Eddy Simulation

An important parameterization in large-eddy simulations (LESs) of high- Reynolds-number boundary layers, such as the atmospheric boundary layer, is the specification of the surface boundary condition. Typical boundary conditions compute the fluctuating surface shear stress as a function of the resolved (filtered) velocity at the lowest grid points based on similarity theory. However, these approaches are questionable because they use instantaneous (filtered) variables, while similarity theory is only valid for mean quantities. Three of these formulations are implemented in simulations of a neutral atmospheric boundary layer with different aerodynamic surface roughness. Our results show unrealistic influence of surface roughness on the mean profile, variance and spectra of the resolved velocity near the ground, in contradiction of similarity theory. In addition to similarity-based surface boundary conditions, a recent model developed from an a priori experimental study is tested and it is shown to yield more realistic independence of the results to changes in surface roughness. The optimum value of the model parameter found in our simulations matches well the value reported in the a priori wind-tunnel study.     

A Scale-Dependent Dynamic Model for Scalar Transport in Large-Eddy Simulations of the Atmospheric Boundary Layer

An important challenge in large-eddy simulationsof the atmospheric boundarylayer is the specification of the subgrid-scale(SGS) model coefficient(s)and, in particular, how to account for factorssuch as position in the flow,grid/filter scale and atmospheric stability.A dynamic SGS model (thatassumes scale invariance of the coefficients)is implemented in simulationsof a neutral boundary layer with a constantand uniform surface flux of apassive scalar. Results from our simulationsshow evidence that the lumpedcoefficient in the eddy-diffusion modelcomputed with the dynamic proceduredepends on scale. This scale dependence isstronger near the surface, and itis more important for the scalar than for thevelocity field (Smagorinskycoefficient) due to the stronger anisotropicbehaviour of scalars. Based onthese results, a new scale-dependent dynamicmodel is developed for theeddy-diffusion lumped coefficient. The newmodel, which is similar to theone proposed earlierfor the Smagorinsky coefficient,is fully dynamic, thus not requiring anyparameter specification or tuning.Simulations with the scale-dependent dynamicmodel yield the expected trendsof the coefficients as functions of positionand filter/grid scale.Furthermore, in the surface layer the newmodel gives improved predictionsof mean profiles and turbulence spectra ascompared with the traditionalscale-invariant dynamic model.     

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.     

A Theoretical Model for the Study of Convective Turbulence Decay and Comparison with Large-Eddy Simulation Data

The development of a theoretical model fora decaying convective boundary layeris considered. The model relies on thedynamical energy spectrumequation in which the buoyancy andinertial transfer terms are retained,and a closure assumptionmade for both. The parameterization for thebuoyancy term is given providing a factorizationbetween the energy source termand its temporal decay. Regarding the inertialtransfer term a hypothesis ofsuperposition is used to describe theconvective energy source and time variationof velocity correlation separately.The solution of the budget equation for theturbulent kinetic energy spectrum is possible,given the three-dimensional initial energyspectrum. This is doneutilizing a version of the Kristensen et al.(see Boundary-Layer Meteorol. 47, 149–193)model valid for non-isotropic turbulence. During thedecay the locus of the spectralpeak remains at about the sameposition as the heat flux decreases.Comparison of the theoretical modelis performed against large-eddy simulationdata for a decaying convectiveboundary layer.     

Application of Dynamic Subgrid-scale Models for Large-eddy Simulation of the Daytime Convective Boundary Layer over Heterogeneous Surfaces

The sensitivity of large-eddy simulation (LES) to the representation of subgrid-scale (SGS) processes is explored for the case of the convective boundary layer (CBL) developing over surfaces with varying degrees of spatial heterogeneity. Three representations of SGS processes are explored: the traditional constant Smagorinsky–Lilly model and two other dynamic models with Lagrangian averaging approaches to calculate the Smagorinsky coefficient (C _S ) and SGS Prandtl number (Pr). With initial data based roughly on the observed meteorology, simulations of daytime CBL growth are performed over surfaces with characteristics (i.e. fluxes and roughness) ranging from homogeneous, to striped heterogeneity, to a realistic representation of heterogeneity as derived from a recent field study. In both idealized tests and the realistic case, SGS sensitivities are mostly manifest near the surface and entrainment zone. However, unlike simulations over complex domains or under neutral or stable conditions, these differences for the CBL simulation, where large eddies dominate, are not significant enough to distinguish the performance of the different SGS models, irrespective of surface heterogeneity.     

Velocity and Surface Shear Stress Distributions Behind a Rough-to-Smooth Surface Transition: A Simple New Model

A simple new model is proposed to predict the distribution of wind velocity and surface shear stress downwind of a rough-to-smooth surface transition. The wind velocity is estimated as a weighted average between two limiting logarithmic profiles: the first log law, which is recovered above the internal boundary-layer height, corresponds to the upwind velocity profile; the second log law is adjusted to the downwind aerodynamic roughness and local surface shear stress, and it is recovered near the surface, in the equilibrium sublayer. The proposed non-linear form of the weighting factor is equal to ln(z/z ₀₁)/ln(δ _i /z ₀₁), where z, δ _i and z ₀₁ are the elevation of the prediction location, the internal boundary-layer height at that downwind distance, and the upwind surface roughness, respectively. Unlike other simple analytical models, the new model does not rely on the assumption of a constant or linear distribution for the turbulent shear stress within the internal boundary layer. The performance of the new model is tested with wind-tunnel measurements and also with the field data of Bradley. Compared with other existing analytical models, the proposed model shows improved predictions of both surface shear stress and velocity distributions at different positions downwind of the transition.     

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.     

Large-Eddy Simulation of Turbulent Flow Over a Rough Surface

A family of wall models is proposed that exhibits moresatisfactory performance than previousmodels for the large-eddy simulation (LES) of the turbulentboundary layer over a rough surface.The time and horizontally averaged statistics such asmean vertical profiles of windvelocity, Reynolds stress, turbulent intensities, turbulentkinetic energy and alsospectra are compared with wind-tunnel experimental data.The purpose of the present study is to obtain simulatedturbulent flows that are comparable with wind-tunnelmeasurements for use as the wind environment for thenumerical prediction by LES of source dispersion in theneutral atmospheric boundary layer.     

An Analysis Of Secondary Circulations And Their Effects Caused By Small-Scale Surface Inhomogeneities Using Large-Eddy Simulation

A parallelized large-eddy simulation model has been used to investigate the effects of two-dimensional, discontinuous, small-scale surface heterogeneities on the turbulence structure of the convective boundary layer.Heterogeneities had a typical size of about the boundary-layer heightz_i. They were produced by a surface sensible heat flux pattern ofchessboard-type and of strong amplitude as typical, e.g., for the marginalice zone. The major objectives of this study were to determinethe effects of such strong amplitude heat flux variations and to specify theinfluence of different speeds and directions of the background wind.Special emphasis has been given to investigate the secondary circulations induced by the heterogeneities by means of three-dimensional phase averages.Compared with earlier studies of continuous inhomogeneities, the same sizeddiscontinuous inhomogeneities in this study show similar but stronger effects.Significant changes compared with uniform surface heating are only observedwhen the scale of the inhomogeneities is increased to z_i. Especially the vertical energy transport is much more vigorous and even the mean emperature profile shows a positive lapse rate within the whole mixed layer. However, the effects are not directly caused by the different shape of the inhomogeneities but can mainly be attributed to the large amplitude of the imposed heat flux,as it is typical for the partially ice covered sea during cold air outbreaks.The structure of the secondary flow is found to be very sensitive to the wavelength and shape of the inhomogeneities as well as to the heatflux amplitude, wind speed and wind direction. The main controlling parameter is the near-surface temperature distribution and the related horizontal pressure gradient perpendicular to the main flow direction. The secondary flow varies from a direct circulation with updraughts mainly above the centre of the heated regions to a more indirect circulation with updraughts beneath the centre and downdraughts above it. For background winds larger than 2.5 m s^–1 a roll-like circulation pattern is observed.From previous findings it has often been stated that moderate backgroundwinds of 5 m s^–1 eliminate all impacts of surface inhomogeneitiesthat could potentially be produced in realistic landscapes. However, this studyshows that the effects caused by increasing the wind speed stronglydepend on the wind direction relative to the orientation of theinhomogeneities. Secondary circulations remain strong, even for abackground wind of 7.5 m s^–1, when the wind direction is orientatedalong one of the two diagonals of the chessboard pattern. On the otherhand, the effects of inhomogeneities are considerably reduced, even undera modest background wind of 2.5 m s^–1, if the wind direction isturned by 45°. Mechanisms for the different flow regimesare discussed.     

Simulation of a Stably Stratified Atmospheric Boundary Layer Using One-Dimensional Turbulence

One-dimensional turbulence (ODT) is a single-column simulation in which vertical motions are represented by an unsteady advective process, rather than their customary representation by a diffusive process. No space or time averaging of mesh-resolved motions is invoked. Molecular-transport scales can be resolved in ODT simulations of laboratory-scale flows, but this resolution of these scales is prohibitively expensive in ODT simulations of the atmospheric boundary layer (ABL), except possibly in small subregions of a non-uniform mesh.Here, two methods for ODT simulation of the ABL on uniform meshes are described and applied to the GABLS (GEWEX Atmospheric Boundary Layer Study; GEWEX is the Global Energy and Water Cycle Experiment) stable boundary-layer intercomparison case. One method involves resolution of the roughness scale using a fixed eddy viscosity to represent subgrid motions. The other method, which is implemented at lower spatial resolution, involves a variable eddy viscosity determined by the local mesh-resolved flow, as in multi-dimensional large-eddy simulation (LES). When run at typical LES resolution, it reproduces some of the key high-resolution results, but its fidelity is lower in some important respects. It is concluded that a more elaborate empirically based representation of the subgrid physics, closely analogous to closures currently employed in LES of the ABL, might improve its performance substantially, yielding a cost-effective ABL simulation tool. Prospects for further application of ODT to the ABL, including possible use of ODT as a near-surface subgrid closure framework for general circulation modeling, are assessed.     

Application of a Large-Eddy Simulation Database to Optimisation of First-Order Closures for Neutral and Stably Stratified Boundary Layers

Large-eddy simulation (LES) is a well-established numerical technique, resolving the most energetic turbulent fluctuations in the planetary boundary layer. By averaging these fluctuations, high-quality profiles of mean quantities and turbulence statistics can be obtained in experiments with well-defined initial and boundary conditions. Hence, LES data can be beneficial for assessment and optimisation of turbulence closure schemes. A database of 80 LES runs (DATABASE64) for neutral and stably stratified planetary boundary layers (PBLs) is applied in this study to optimize first-order turbulence closure (FOC). Approximations for the mixing length scale and stability correction functions have been made to minimise a relative root-mean-square error over the entire database. New stability functions have correct asymptotes describing regimes of strong and weak mixing found in theoretical approaches, atmospheric observations and LES. The correct asymptotes exclude the need for a critical Richardson number in the FOC formulation. Further, we analysed the FOC quality as functions of the integral PBL stability and the vertical model resolution. We show that the FOC is never perfect because the turbulence in the upper half of the PBL is not generated by the local vertical gradients. Accordingly, the parameterised and LES-based fluxes decorrelate in the upper PBL. With this imperfection in mind, we show that there is no systematic quality deterioration of the FOC in the strongly stable PBL provided that the vertical model resolution is better than 10 levels within the PBL. In agreement with previous studies, we found that the quality improves slowly with the vertical resolution refinement, though it is generally wise not to overstretch the mesh in the lowest 500 m of the atmosphere where the observed, simulated and theoretically predicted stably stratified PBL is mostly located. The submission to a special issue of the “Boundary-Layer Meteorology” devoted to the NATO advanced research workshop “Atmospheric Boundary Layers: Modelling and Applications for Environmental Security”.     

Statistics of Scalar Fields in the Atmospheric Boundary Layer Based on Large-Eddy Simulations. Part II: Forced Convection

Forced convection in a quasi-steady atmospheric boundary layer is investigated based on a large-eddy simulation (LES) model. The performed simulations show that in the upper portion of the mixed layer the dimensionless (in terms of mixed layer scales) vertical gradients of temperature, humidity, and wind velocity depend on the dimensionless height z/z _i and the Reech number Rn. The peak values of variances and covariances at the top of the mixed layer, scaled in terms of the interfacial scales, are functions of the interfacial Richardson number Ri. As a result expressions for the entrainment rates, in the case when the interfacial layer has a finite depth, and a condition for the presence of moistening or drying regimes in the mixed layer, are derived. Profiles of dimensionless scalar moments in the mixed layer are proposed to be expressed in terms of two empirical similarity functions F _m and F _i , dependent on dimensionless height z/z _i , and the interfacial Richardson number Ri. The obtained similarity expressions adequately approximate the LES profiles of scalar statistics, and properly represent the impact of stability, shear, and entrainment. They are also consistent with the parameterization proposed for free convection in the first part of this paper.     

Some Basic Properties of the Surrogate Subgrid-Scale Heat Flux in the Atmospheric Boundary Layer

The development of improved subgrid-scale (SGS) models for large-eddy simulation of scalar transport in the atmospheric boundary layer requires an improved understanding of basic properties of the SGS fluxes. High frequency atmospheric wind speed and temperature data sampled at a height of 1.7 m are used to measure SGS heat fluxes and dissipation of temperature variance, by means of one-dimensional filtering and invoking Taylor's hypothesis. Conditional averaging is used to isolate interesting features of the SGS signals, and to relate them to the large-scale characteristics of the flow, such as the presence of coherent structures. Both mean and conditionally averaged SGS quantities are compared with those obtained using a standard eddy-diffusivity model. Within the limitations imposed by the one-dimensional data analysis, we observe that the model appears unable to reproduce important features of the real signals, such as the negative dissipation of temperature variance associated with strong negative resolved temperature gradients due to the ejection of warm air under unstable atmospheric stability conditions.     

The Effects of Vegetation Density on Coherent Turbulent Structures within the Canopy Sublayer: A Large-Eddy Simulation Study

Large-eddy simulation has become an important tool for the study of the atmospheric boundary layer. However, since large-eddy simulation does not simulate small scales, which do interact to some degree with large scales, and does not explicitly resolve the viscous sublayer, it is reasonable to ask if these limitations affect significantly the ability of large-eddy simulation to simulate large-scale coherent structures. This issue is investigated here through the analysis of simulated coherent structures with the proper orthogonal decomposition technique. We compare large-eddy simulation of the atmospheric boundary layer with direct numerical simulation of channel flow. Despite the differences of the two flow types it is expected that the atmospheric boundary layer should exhibit similar structures as those in the channel flow, since these large-scale coherent structures arise from the same primary instability generated by the interaction of the mean flow with the wall surface in both flows. It is shown here that several important similarities are present in the two simulations: (i) coherent structures in the spanwise-vertical plane consist of a strong ejection between a pair of counter-rotating vortices; (ii) each vortex in the pair is inclined from the wall in the spanwise direction with a tilt angle of approximately 45°; (iii) the vortex pair curves up in the streamwise direction. Overall, this comparison adds further confidence in the ability of large-eddy simulation to produce large-scale structures even when wall models are used. Truncated reconstruction of instantaneous turbulent fields is carried out, testing the ability of the proper orthogonal decomposition technique to approximate the original turbulent field with only a few of the most important eigenmodes. It is observed that the proper orthogonal decomposition reconstructs the turbulent kinetic energy more efficiently than the vorticity.     

A Variable Mesh Spacing for Large-Eddy Simulation Models in the Convective Boundary Layer

A variable vertical mesh spacing for large-eddy simulation (LES) models in a convective boundary layer (CBL) is proposed. The argument is based on the fact that in the vertical direction the turbulence near the surface in a CBL is inhomogeneous and therefore the subfilter-scale effects depend on the relative location between the spectral peak of the vertical velocity and the filter cut-off wavelength. From the physical point of view, this lack of homogeneity makes the vertical mesh spacing the principal length scale and, as a consequence, the LES filter cut-off wavenumber is expressed in terms of this characteristic length scale. Assuming that the inertial subrange initial frequency is equal to the LES filter cut-off frequency and employing fitting expressions that describe the observed convective turbulent energy one-dimensional spectra, it is feasible to derive a relation to calculate the variable vertical mesh spacing. The incorporation of this variable vertical grid within a LES model shows that both the mean quantities (and their gradients) and the turbulent statistics quantities are well described near to the ground level, where the LES predictions are known to be a challenging task.     

Large-Eddy Simulation Of The Stably Stratified Planetary Boundary Layer

In this work, we study the characteristics of a stably stratifiedatmospheric boundary layer using large-eddy simulation (LES).In order to simulate the stable planetary boundary layer, wedeveloped a modified version of the two-part subgrid-scalemodel of Sullivan et al. This improved version of themodel is used to simulate a highly cooled yet fairly windy stableboundary layer with a surface heat flux of(W)_o = -0.05 m K s^-1and a geostrophic wind speed of U_g = 15 m s^-1.Flow visualization and evaluation of the turbulencestatistics from this case reveal the development ofa continuously turbulent boundary layer with small-scalestructures. The stability of the boundary layercoupled with the presence of a strong capping inversionresults in the development of a dominant gravity wave atthe top of the stable boundary layer that appears to be relatedto the most unstable wave predicted by the Taylor–Goldsteinequation. As a result of the decay of turbulence aloft,a strong-low level jet forms above the boundary layer.The time dependent behaviour of the jet is compared with Blackadar'sinertial oscillation analysis.     

Alignment Trends of Velocity Gradients and Subgrid-Scale Fluxes in the Turbulent Atmospheric Boundary Layer

Field experimental data in the atmospheric surface layer are analyzed using toolsfrom statistical geometry. The data consist of velocity measurements from sonicanemometer arrays. In the context of large eddy simulations (LES), these arrayspermit the spatial filtering needed to separate large from small scales. Time seriesof various quantities relevant to LES are evaluated from the data. Results show thatthe preferred filtered fluid deformation is axisymmetric extension and the preferredsubgrid stress state is axisymmetric contraction. The filtered fluctuating vorticityshows preferred alignments with the mean vorticity, with the streamwise direction,and with the intermediate strain-rate eigenvector. The alignment between eigenvectorsof the subgrid-scale stress and filtered strain rate is used to test eddy viscosity andmixed model formulations. In qualitative agreement with prior laboratory measurements at much lower Reynolds numbers, a bimodal distribution is observed, which can be reduced to good alignment with eddy viscosity closure using the mixed model.     

Footprints in Homogeneously and Heterogeneously Driven Boundary Layers Derived from a Lagrangian Stochastic Particle Model Embedded into Large-Eddy Simulation

A Lagrangian stochastic (LS) model, which is embedded into a parallelised large-eddy simulation (LES) model, is used for dispersion and footprint evaluations. For the first time an online coupling between LES and LS models is applied. The new model reproduces concentration patterns, which were obtained in prior studies, provided that subgrid-scale turbulence is included in the LS model. Comparisons with prior studies show that the model evaluates footprints successfully. Streamwise dispersion leads to footprint maxima that are situated less far upstream than previously reported. Negative flux footprints are detected in the convective boundary layer (CBL). The wide range of applicability of the model is shown by applying it under neutral and stable stratification. It is pointed out that the turning of the wind direction with height leads to a considerable dependency of source areas on height. First results of an application to a heterogeneously heated CBL are presented, which emphasize that footprints are severely affected by the inhomogeneity.