Turbulent Pressure Statistics in the Atmospheric Boundary Layer from Large-Eddy Simulation

We use large-eddy simulation (LES) to study the turbulent pressure field in atmospheric boundary layers with free convection, forced convection, and stable stratification. We use the Poisson equation for pressure to represent the pressure field as the sum of mean-shear, turbulence–turbulence, subfilter-scale, Coriolis, and buoyancy contributions. We isolate these contributions and study them separately. We find that in the energy-containing range in the free-convection case the turbulence–turbulence pressure dominates over the entire boundary layer. That part dominates also up to midlayer in the forced-convection case; above that the mean-shear pressure dominates. In the stable case the mean-shear pressure dominates over the entire boundary layer.We find evidence of an inertial subrange in the pressure spectrum in the free and forced-convection cases; it is dominated by the turbulence–turbulence pressure and has a three-dimensional spectral constant of about 4.0. This agrees well with quasi-Gaussian predictions but is a factor of 2 less than recent results from direct numerical simulations at moderate Reynolds numbers. Measurements of the inertial subrange pressure spectral constant at high Reynolds numbers, which might now be possible, would be most useful.     

A Mixed-Layer Model Of The Well-Mixed Stratocumulus-Topped Boundary Layer

Recently a range of sophisticated large-eddy simulations of thecloud-topped boundary layer have been intercompared and furthercompared with observations and single column models. Here we comparethese results with perhaps the simplest model of the cloud-toppedboundary layer, namely a mixed-layer model. Results from the model aredescribed with two aims in mind. Firstly, the good results act as areminder of the success of simple models, and, secondly, we suggestthat a simple mixed-layer model could be used as a baseline for futuremodel intercomparisons.The mixed-layer model is based on two assumptions that follow previousstudies. Firstly, the liquid-water potential temperature and the total waterspecific humidity are assumed to be constant with height in the boundarylayer. Secondly, turbulence entrains air across the inversion into the boundarylayer at a rate that is assumed to be proportional to the jump in radiative flux at the cloud top and inversely proportional to the jump in buoyancy at the inversion. The constant of proportionality is called the entrainment efficiency.Results from the model for the entrainment rate and height evolutionof the boundary layer are compared with the observations and modelsconsidered in a EUCREM intercomparison study. Thepresent mixed-layer model accurately predicts the observed heightevolution of the boundary layer, but over-estimates the entrainmentrate to a similar degree as the large-eddy simulations. We show that,if the subsidence rate is reduced to the value given by observationsrather than the value used in the EUCREM intercomparison study,then the model agrees well with observed value of the entrainment rateif the entrainment efficiency is taken to be 0.6. With this value, themodel also agrees well with a further case study byBechtold et al. An entrainment efficiency of 0.6 is a little higherthan suggested by large eddy simulations, but such simulations do notcurrently resolve the entrainment events explicitly. Hence this pointdeserves further study.     

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.     

Large-Eddy Simulation of air Pollution Dispersion in the Nocturnal Cloud-Topped Atmospheric Boundary Layer

Effects of stratocumulus clouds on the dispersion of contaminants are studied in the nocturnal atmospheric boundary layer. The study is based on a large-eddy simulation (LES) model with a bulk parametrization of clouds. Computations include Lagrangian calculations of atmospheric dispersion of a passive tracer released from point sources at various heights above the ground. The results obtained show that the vertical diffusion is non-Gaussian and depends on the location of a source in the boundary layer.     

A Hybrid Spectral/Finite-Volume Algorithm for Large-Eddy Simulation of Scalars in the Atmospheric Boundary Layer

Pseudospectral methods are frequently used in the horizontal directions in large-eddy simulation of atmospheric flows. However, the same approach often creates unphysical oscillations for scalar fields if there are horizontal heterogeneities in the sources and/or sinks, as is usual in air pollution problems. A hybrid approach is developed to combine the use of pseudospectral representation of the velocity field and bounded finite-volumes for the scalar concentration. An interpolation scheme that yields a divergence-free interpolated velocity field is derived and implemented, and its importance is illustrated by two sample applications.     

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 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.     

A GCSS Boundary-Layer Cloud Model Intercomparison Study Of The First Astex Lagrangian Experiment

Three single-column models (all with an explicit liquid water budget and compara-tively high vertical resolution) and three two-dimensional eddy-resolving models (including one with bin-resolved microphysics) are compared with observations from the first ASTEX Lagrangian experiment. This intercomparison was a part of the second GCSS boundary-layer cloud modelling workshop in August 1995.In the air column tracked during the first ASTEX Lagrangian experiment, a shallow subtropical drizzling stratocumulus-capped marine boundary layer deepens after two days into a cumulus capped boundary layer with patchy stratocumulus. The models are forced with time varying boundary conditions at the sea-surface and the capping inversion to simulate the changing environment of the air column.The models all predict the observed deepening and decoupling of the boundary layer quite well, with cumulus cloud evolution and thinning of the overlying stratocumulus. Thus these models all appear capable of predicting transitions between cloud and boundary-layer types with some skill. The models also produce realistic drizzle rates, but there are substantial quantitative differences in the cloud cover and liquid water path between models. The differences between the eddy-resolving model results are nearly as large as between the single column model results. The eddy resolving models give a more detailed picture of the boundary-layer evolution than the single-column models, but are still sensitive to the choice of microphysical and radiative parameterizations, sub-grid-scale turbulence models, and probably model resolution and dimensionality. One important example of the differences seen in these parameterizations is the absorption of solar radiation in a specified cloud layer, which varied by a factor of four between the model radiation parameterizations.     

An Intercomparison of Large-Eddy Simulations of the Stable Boundary Layer

Results are presented from the first intercomparison of large-eddy simulation (LES) models for the stable boundary layer (SBL), as part of the Global Energy and Water Cycle Experiment Atmospheric Boundary Layer Study initiative. A moderately stable case is used, based on Arctic observations. All models produce successful simulations, in as much as they generate resolved turbulence and reflect many of the results from local scaling theory and observations. Simulations performed at 1-m and 2-m resolution show only small changes in the mean profiles compared to coarser resolutions. Also, sensitivity to subgrid models for individual models highlights their importance in SBL simulation at moderate resolution (6.25 m). Stability functions are derived from the LES using typical mixing lengths used in numerical weather prediction (NWP) and climate models. The functions have smaller values than those used in NWP. There is also support for the use of K-profile similarity in parametrizations. Thus, the results provide improved understanding and motivate future developments of the parametrization of the SBL.     

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 Turbulent Separated Flow Over Rough Hills

Large-eddy simulations (LES) have been performed ofneutral turbulent flow over two-dimensional ridges steepenough to cause separation. Both periodic and isolated ridges havebeen considered. The results are compared with wind-tunnel observations and with the predictions of various turbulence closure models.For the periodic case the LES results are qualitatively reasonable,although the depth of the separated region appears to besensitive to the use of a distributed drag near the lower boundary.The isolated ridge results compare very favourably with the experimentaldata, with the LES performance appearing to be at least as good as that ofthe closure models.     

Large-Eddy Simulation Of Neutral Turbulent Flow Over Rough Sinusoidal Ridges

The requirements for a credible large-eddy simulation of neutral, turbulent flow over hills with an aerodynamically rough surface are discussed, in order to select a suitable case for simulation. As well as providing adequate resolution within the dynamically important inner region, obtaining a realistic upstream or undisturbed mean velocity profile is also of critical importance. A distributed drag canopy formulation has been introduced to the model to allow it to obtain such a profile while resolving very close to the rough surface. Simulations have then been performed of flow over ridges of varying heights. The results from the steepest case, which is just on the verge of separation, are compared with wind-tunnel observations. It is shown that the large-eddy simulation results are in much better agreement with the experimental data than are the results from a simple first-order mixing-length closure model. An encouraging lack of sensitivity of the simulation results to numerical resolution is also demonstrated.     

An Evaluation Of Local Similarity At The Top Of The Mixed Layer Based On Large-Eddy Simulations

Local similarity, referred to as type II similarity,in the interfacial, stably-stratified layer at thetop of the atmospheric (or oceanic) mixed layer isdiscussed. Type II scales for scalars are based onthe local values of scalar gradients. Similaritypredictions are derived from the second-orderclosure model of Yamada and Mellor, and also fromsimilarity arguments. The obtainedformulation is verified for active and passive scalarsbased on the large-eddy simulation model.     

黑河绿洲区不均匀下垫面大气边界层结构的大涡模拟研究

采用RAMS模式中大涡模拟的方法,加入高分辨率的植被和土壤资料,模拟了黑河（张掖地区）不均匀下垫面条件下大气边界层演变过程。分析了模拟的地表通量、边界层的平均结构和湍流二阶量,并用黑河试验的观测资料检验了模式的模拟性能。结果表明,模拟的平均结构较好地展现了不均匀下垫面条件下边界层内从稳定层结到混合层发展,夹卷层形成,底层逆温层出现,混合层过渡到残留层等的演变过程,呈现出了从初始的稳定边界层发展到对流边界层,最后又形成夜问稳定边界层的日变化规律。湍流二阶量的分析显示,在非均匀下垫面条件下边界层内湍流二阶量的垂直分布与边界层的发展相对应,白天湍流二阶量出现两个峰值,分别位于近地层和混合层顶。与观测资料和现有研究的对比表明,RAMS中陆面模块（LEAF）地表参数不能较好地反映黑河地区的植被特征,模拟的白天地表感热和潜热通量偏小,气温白天偏低、夜间偏高,相对湿度也有偏差。     

Large-Eddy Simulation Of Radiation Fog

In order to study the three-dimensional structure of radiation fogand to obtain a basic understanding of its generation mechanism,a numerical experiment is performed with a large-eddysimulation model and compared with the observation at Cabauw in the Netherlands. After confirming that the results are insatisfactory agreement with the observations, the structure of thefog and its generation mechanism are examined in more detail.Before the fog forms, the atmosphere is stable and an inversionlayer exists almost adjacent to the ground surface. As the fog grows, however, the stratification is destabilized and a mixed layerdevelops gradually. The longwave radiative cooling near thefog top contributes to the destabilization more than thecondensational heating does.The evolution of the fog can be classified into three stagesaccording to the behaviour of turbulent kinetic energy (TKE):formation, development, and dissipation stages.The fog layer has different flow structures at each stage.During the formation stage, longitudinal rolls similar tostreaks in channel flows appear near the ground surface.The development stage is characterized by an initiation oftransverse bands due to Kelvin–Helmholtz instability anda sudden increase of TKE. During the dissipation stage, longitudinalrolls and polygonal cells due to convective instability are organized.     

A Large-Eddy Simulation and Lagrangian Stochastic Study of Heavy Particle Dispersion in the Convective Boundary Layer

Large-eddy simulation and Lagrangian stochastic dispersion models were used to study heavy particle dispersion in the convective boundary layer (CBL). The effects of various geostrophic winds, particle diameters, and subgrid-scale (SGS) turbulence were investigated. Results showed an obvious depression in the vertical dispersion of heavy particles in the CBL and major vertical stratification in the distribution of particle concentrations, relative to the passive dispersion. Stronger geostrophic winds tended to increase the dispersion of heavy particles in the lower CBL. The SGS turbulence, particularly near the surface, markedly influenced the dispersion of heavy particles in the CBL. For reference, simulations using passive particles were also conducted; these simulation results agreed well with results from previous convective tank experiments and numerical simulations.     

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.     

Near-Surface Coherent Structures and The Vertical Momentum Flux in a Large-Eddy Simulation of the Neutrally-Stratified Boundary Layer

The near-surface flow of a well-resolved large-eddy simulation of the neutrally-stratified planetary boundary layer is used to explore the relationships between coherent structures and the vertical momentum flux. The near-surface flow is characterized by transient streaks, which are alternating bands of relatively higher and lower speed flow that form parallel to the mean shear direction in the lower part of the boundary layer. Although individual streaks are transient, the overall flow is in a quasi-equilibrium state in which the streaks form, grow, decay and regenerate over lifetimes on the order of tens of minutes. Coupled with the streaky flow is an overturning circulation with alternating bands of updrafts and downdrafts approximately centered on the streaks. The surface stress is dominated by upward ejections of slower moving near-surface air and downward sweeps of higher speed air from higher in the boundary layer. Conditional sampling of the ejection and sweep events shows that they are compact, coherent structures and are intimately related to the streaks: ejections (sweeps) preferentially form in the updrafts (downdrafts) of the three-dimensional streak flow. Hence, consistent with other recent studies, we propose that the streak motion plays an important role in the maintenance of the surface stress by establishing the preferential conditions for the ejections and sweeps that dominate the surface stress. The velocity fluctuation spectra in the model near the surface have a k ⁻¹ spectral slope over an intermediate range of wavenumbers. This behaviour is consistent with recent theoretical predictions that attempt to evaluate the effects of organized flow, such as near-surface streaks, on the variance spectra.     

Two-Point Correlation Analysis Of Neutrally Stratified Flow Within And Above A Forest From Large-Eddy Simulation

Two-point space-time correlations ofvelocities, a passive scalar and static pressure arecalculated using the resolvable flow fields computedby large-eddy simulation (LES) of neutrally stratifiedflow within and above a sparse forest. Zero-time-lagspatial auto-correlation contours in thestreamwise-vertical cross-section for longitudinal andlateral velocities and for a scalar are tilted fromthe vertical in the downstream direction, as istypical in near-wall sheared flow. On the other hand,auto-correlations of vertical velocity and of staticpressure are vertically coherent. Zero-time-lagspatial auto-correlations in the spanwise-verticalcross-section show no distinct tilt, and those forboth longitudinal and vertical velocities demonstratedistinct negative side lobes in the middle forest andabove, while longitudinal velocity in the subcrowntrunk space is laterally in-phase. Static pressureperturbations appear to be spatially coherent in thespanwise direction at all heights, especially insidethe forest. Near the forest floor, longitudinalvelocity is found to be in-phase with static pressureperturbation and to be closely linked to theinstantaneous streamwise pressure gradient, supportinga previous proposal that longitudinal velocity in thisregion is dominantly modulated by the pressurepatterns associated with the coherent sweep/ejectionevents. Near treetop height, a lack of linkage betweenthe pressure gradient and the local time derivative ofthe longitudinal velocity supports the hypothesis ofadvection dominating turbulent flow.The major phase characteristics of the two-pointcorrelations essentially remained the same from fourLES runs with different domain size and/or gridresolution. A larger LES domain yielded betteragreement with field observations in a real forest onboth the magnitudes of the correlations and thesingle-point integral time scales. A finer gridresolution in the LES led to a faster rate of decreaseof correlation with increasing separation in space ortime, as did the higher frequency fluctuations in theturbulent records from field measurements. Convectivevelocities estimated from the lagged two-pointauto-correlations of the calculated flow fields werecompared with similar calculations from wind-tunnelstudies. At the canopy top, estimates from thecorrelation analyses agree with the translationvelocity estimated from instantaneous snapshots of ascalar microfront using both LES and field data. Thistranslation velocity is somewhat higher than the localmean wind speed. Convective velocities estimated fromlagged correlations increase with height above thecanopy. It is suggested that an appropriate filteringprocedure may be necessary to reduce the effects ofsmall-scale random turbulence, as was reported in astudy over an orchard canopy. The mean longitudinalvelocity near the treetops is found to be moreappropriate than the local mean longitudinal velocityat each height to link single-point integral timescales with directly calculated spatial integralstreamwise length scales.