Very-Large-Scale Motions in the Atmospheric Boundary Layer Educed by Snapshot Proper Orthogonal Decomposition

Large-eddy simulations of the atmospheric boundary layer (ABL) under a wide range of stabilities are conducted to educe very-large-scale motions and then to study their dynamics and how they are influenced by buoyancy. Preliminary flow visualizations suggest that smaller-scale motions that resemble hairpins are embedded in much larger scale streamwise meandering rolls. Using simulations that represent more than 150 h of physical time, many snapshots in the \(xy\) -, \(yz\) - and \(xz\) -planes are then collected to perform snapshot proper orthogonal decomposition and further investigate the large structures. These analyses confirm that large streamwise rolls that share several features with the very-large-scale motions observed in laboratory studies arise as the dominant modes under most stabilities, but the effect of the surface kinematic buoyancy flux on the energy content of these dominant modes is very significant. The first two modes in the \(yz\) -plane in the neutral case contain up to 3 % of the total turbulent kinetic energy; they also have a vertical tilt angle in the \(yz\) -plane of about 0 to 30 \(^\circ \) due to the turning effect associated with the Coriolis force. Unstable cases also feature streamwise rolls, but in the convective ABL they are strengthened by rising plumes in between them, with two to four rolls spanning the whole domain in the first few modes; the Coriolis effect is much weaker in the unstable ABL. These rolls are no longer the dominant modes under stable conditions where the first mode is observed to contain sheet-like motions with high turbulent kinetic energy. Using these proper orthogonal decomposition modes, we are also able to extract the vertical velocity fields corresponding to individual modes and then to correlate them with the horizontal velocity or temperature fields to obtain the momentum and heat flux carried by individual modes. Structurally, the fluxes are explained by the topology of their corresponding modes. However, the fraction of the fluxes produced by the modes is invariably smaller than the fraction of energy they contain, particularly under stable conditions where the first modes are found to perform weak counter-gradient fluxes.     

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.     

A Large-Eddy Simulation Study of the Influence of Subsidence on the Stably Stratified Atmospheric Boundary Layer

The influence of the large-scale subsidence rate, S, on the stably stratified atmospheric boundary layer (ABL) over the Arctic Ocean snow/ice pack during clear-sky, winter conditions is investigated using a large-eddy simulation model. Simulations of two 24-h periods are conducted while varying S between 0, 0.001 and 0.002 ms⁻¹, and the resulting quasi-equilibrium ABL structures and evolutions are examined. Simulations conducted with S = 0 yield a boundary layer that is deeper, more strongly mixed and cools more rapidly than the observations. Simulations conducted with S > 0 yield improved agreement with the observations in the ABL height, potential temperature gradients and bulk heating rates. We also demonstrate that S > 0 limits the continuous growth of the ABL observed during quasi-steady conditions, leading to the formation of a nearly steady ABL of approximately uniform depth and temperature. Subsidence reduces the magnitudes of the stresses, as well as the implied eddy-diffusivity coefficients for momentum and heat, while increasing the vertical heat fluxes considerably. Subsidence is also observed to increases the Richardson number to values in excess of unity well below the ABL top.     

Three-Dimensional Lagrangian Simulation of Suspended Particles in the Neutrally Stratified Atmospheric Surface Layer

A three-dimensional (3-D) inertial particle – Lagrangian stochastic model for heavy particles in turbulent flows has been constructed. In this model, particle velocities are computed by adopting a non-linear drag law, while fluid velocity in the vicinity of a particle is calculated using a 3-D Langevin equation. Our model results have shown that the inclusion of the horizontal fluid velocity fluctuation computations and a non-linear drag law have an impact on the statistics of both fluid and particles when compared with our earlier one-dimensional (1-D) model with a linear drag law. Model results are compared and contrasted with Businger’s 1965 theory in terms of effective settling velocity.     

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.     

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.     

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.     

Study of the Probability Density Functions From a Large-Eddy Simulation for a Stably Stratified Boundary Layer

Turbulence in a non-strongly stably stratified large-eddy simulation (LES) case is studied through probability density functions (PDFs) to obtain additional information than that provided by classical LES averages. The PDFs are computed for one hour within the steady-state regime at three different levels: near the surface, in the middle and at the top of the boundary layer, for the wind components and the temperature. The physical significance of these PDFs from LES is discussed and they are compared to those obtained from observations. The analysis of the eddy structures within the stably stratified boundary layer is made through the combined study of the fields, the spectra and the statistical moments obtained from the PDFs and joint PDFs. The homogeneity of the fields is inspected through a comparison of the ensemble to the temporal and the spatial PDFs, showing that the ergodic theorem is not fulfilled. To this end, the sensitivity of the PDF moments to the LES resolution is explored.     

Subfilter-Scale Modelling Using Transport Equations: Large-Eddy Simulation of the Moderately Convective Atmospheric Boundary Layer

We perform large-eddy simulation (LES) of a moderately convective atmospheric boundary layer (ABL) using a prognostic subfilter-scale (SFS) model obtained by truncating the full conservation equations for the SFS stresses and fluxes. The truncated conservation equations contain production mechanisms that are absent in eddy-diffusivity closures and, thus, have the potential to better parametrize the SFS stresses and fluxes. To study the performance of the conservation-equation-based SFS closure, we compare LES results from the surface layer with observations from the Horizontal Array Turbulence Study (HATS) experiment. For comparison, we also show LES results obtained using an eddy-diffusivity closure. Following past studies, we plot various statistics versus the non-dimensional parameter, Λ _w /Δ, where Λ _w is the wavelength corresponding to the peak in the vertical velocity spectrum and Δ is the filter width. The LES runs are designed using different domain sizes, filter widths and surface fluxes, in order to replicate partly the conditions in the HATS experiment. Our results show that statistics from the different LES runs collapse reasonably and exhibit clear trends when plotted against Λ _w /Δ. The trends exhibited by the production terms in the modelled SFS conservation equations are qualitatively similar to those seen in the HATS data with the exception of SFS buoyant production, which is underpredicted. The dominant production terms in the modelled SFS stress and flux budgets obtained from LES are found to approach asymptotically constant values at low Λ _w /Δ. For the SFS stress budgets, we show that several of these asymptotes are in good agreement with their corresponding theoretical values in the limit Λ _w /Δ → 0. The modelled SFS conservation equations yield trends in the mean values and fluctuations of the SFS stresses and fluxes that agree better with the HATS data than do those obtained using an eddy-diffusivity closure. They, however, underpredict considerably the level of SFS anisotropy near the wall when compared to observations, which could be a consequence of the shortcomings in the model used for the pressure destruction terms. Finally, we address the computational cost incurred due to the use of additional prognostic equations.     

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 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.     

A Large-Eddy Simulation Study of Water Vapour and Carbon Dioxide Isotopes in the Atmospheric Boundary Layer

A large-eddy simulation model developed at the National Center for Atmospheric Research (NCAR) is extended to simulate the transport and diffusion of C¹⁸OO, H₂¹⁸O and ¹³CO₂ in the atmospheric boundary layer (ABL). The simulation results show that the ¹⁸O compositions of leaf water and the ABL CO₂ are moderately sensitive to wind speed. The variations in the ¹⁸O composition of water vapour are an order of magnitude greater than those in the ¹³C and ¹⁸O compositions of CO₂ both at turbulent eddy scales and across the capping inversion. In a fully-developed convective ABL, these isotopic compositions are well mixed as with other conserved atmospheric quantities. The Keeling intercepts determined with the simulated high-frequency turbulence time series do not give a reliable estimate of the ¹⁸O composition of the surface water vapour flux and may be a reasonable approximation to the ¹³C and ¹⁸O compositions of the surface CO₂ flux in the late afternoon only after a deep convective ABL has developed. We suggest that our isotopic large-eddy simulation (ISOLES) model should be a useful tool for testing and formulating research hypotheses on land–air isotopic exchanges.     

On the Development of a Dynamic Non-linear Closure for Large-Eddy Simulation of the Atmospheric Boundary Layer

A dynamic procedure is developed to compute the model coefficients in the recently introduced modulated gradient models for both momentum and scalar fluxes. The magnitudes of the subgrid-scale (SGS) stress and the SGS flux are estimated using the local equilibrium hypothesis, and their structures (relative magnitude of each of the components) are given by the normalized gradient terms, which are derived from the Taylor expansion of the exact SGS stress/flux. Previously, the two model coefficients have been specified on the basis of theoretical arguments. Here, we develop a dynamic SGS procedure, wherein the model coefficients are computed dynamically according to the statistics of the resolved turbulence, rather than provided a priori or ad hoc. Results show that the two dynamically calculated coefficients have median values that are approximately constant throughout the turbulent atmospheric boundary layer (ABL), and their fluctuations follow a near log-normal distribution. These findings are consistent with the fact that, unlike eddy-viscosity/diffusivity models, modulated gradient models have been found to yield satisfactory results even with constant model coefficients. Results from large-eddy simulations of a neutral ABL and a stable ABL using the new closure show good agreement with reference results, including well-established theoretical predictions. For instance, the closure delivers the expected surface-layer similarity profiles and power-law scaling of the power spectra of velocity and scalar fluctuations. Further, the Lagrangian version of the model is tested in the neutral ABL case, and gives satisfactory results.     

Large-Eddy Simulation Of A Nocturnal Stratocumulus-Topped Marine Atmospheric Boundary Layer: An Uncertainty Analysis

A large-eddy simulation (LES) model has been used to study a nocturnalstratocumulus-topped marine atmospheric boundary layer. The main objectivesof our study have been first to investigate the statistical significance of LES-derived data products. Second, to test the sensitivity of our LES results with respect to the representation of subgrid-scale mixing and microphysical processes, and third to evaluate and to quantify the parametric uncertainty arising from the incomplete knowledge of the environmental parameters that are required to specify the initial and boundary conditions of a particular case study. Model simulations were compared with observations obtained in solid stratocumulus during the third flight of the first 'Lagrangian' experiment of the Atlantic Stratocumulus Transition Experiment (ASTEX). Based on these simulations the following conclusions could be drawn. Resolution(50 × 50 × 25 m³) and domain size (3.2 × 3.2 × 1.5 km³) of the LES calculations were adequate from a numerical point of view to represent the essential features of the stratocumulus-topped boundary layer. However, the ensemble runs performed in our study to investigate the statistical significance of LES-derived data products demonstrate that the area-time averaging procedure for the second-order moments produces only a low degree of statistical reliability in the model results. This illustratesthe necessity of having LES model results that are not only of adequate resolution but also of sufficiently large domain. The impact of different subgrid schemes was small, but the primary effects of drizzle were found to influence the boundary-layer structure in a climatologically significant way. The parametric uncertainty analysis revealed that the largest contribution to the variance of the LES-derived data products is due to theuncertainties in the cloud-top jump of total water mixing ratio and the net radiative forcing. The differences between the model and measurements for most of the simulated quantities were within the modelling uncertainties, but the calculated precipitation rate was found to differ significantly from that derived in the observations.     

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.     

Some Aspects of Atmospheric Dispersion in the Stratified Atmospheric Boundary Layer over Homogeneous Terrain

The ability to simulate atmospheric dispersion with models developed for applied use under stable atmospheric stability conditions is discussed. The paper is based on model simulations of three experimental data sets reported in the literature. The Hanford data set covered weakly stable conditions, the Prairie Grass experiments covered both weakly stable and very stable atmospheric conditions, and the Lillestrøm experiment was carried out during very stable conditions. Simulations of these experiments reported in the literature for eight different models are discussed. Applied models based on the Gaussian plume model concept with the spread parameters described in terms of the Pasquill stability classification or Monin–Obukhov similarity relationships are used. Other model types are Lagrangian particle models which also are parameterized in terms of Monin–Obukhov similarity relationships. The applied models describe adequately the dispersion process in a weakly stable atmosphere, but fail during very stable atmospheric conditions. This suggests that Monin–Obukhov similarity theory is an adequate tool for the parameterization of the input parameters to atmospheric dispersion models during weakly stable conditions, but that more detailed parameterisations including other physical processes than those covered by the Monin–Obukhov theory should be developed for the very stable atmosphere.     

Neutrally Stratified Turbulent Ekman Boundary Layer: Universal Similarity for a Transitional Rough Surface

The geostrophic Ekman boundary layer for large Rossby number (Ro) has been investigated by exploring the role played by the mesolayer (intermediate layer) lying between the traditional inner and outer layers. It is shown that the velocity and Reynolds shear stress components in the inner layer (including the overlap region) are universal relations, explicitly independent of surface roughness. This universality of predictions has been supported by observations from experiment, field and direct numerical simulation (DNS) data for fully smooth, transitionally rough and fully rough surfaces. The maxima of Reynolds shear stresses have been shown to be located in the mesolayer of the Ekman boundary layer, whose scale corresponds to the inverse square root of the friction Rossby number. The composite wall-wake universal relations for geostrophic velocity profiles have been proposed, and the two wake functions of the outer layer have been estimated by an eddy viscosity closure model. The geostrophic drag and cross-isobaric angle predictions yield universal relations, which are also supported by extensive field, laboratory and DNS data. The proposed predictions for the geostrophic drag and the cross-isobaric angle compare well with data for Rossby number Ro ≥ 10⁵. The data show low Rossby number effects for Ro < 10⁵ and higher-order effects due to the mesolayer compare well with the data for Ro ≥ 10³.     

Single-Column Model Intercomparison for a Stably Stratified Atmospheric Boundary Layer

The parameterization of the stably stratified atmospheric boundary layer is a difficult issue, having a significant impact on medium-range weather forecasts and climate integrations. To pursue this further, a moderately stratified Arctic case is simulated by nineteen single-column turbulence schemes. Statistics from a large-eddy simulation intercomparison made for the same case by eleven different models are used as a guiding reference. The single-column parameterizations include research and operational schemes from major forecast and climate research centres. Results from first-order schemes, a large number of turbulence kinetic energy closures, and other models were used. There is a large spread in the results; in general, the operational schemes mix over a deeper layer than the research schemes, and the turbulence kinetic energy and other higher-order closures give results closer to the statistics obtained from the large-eddy simulations. The sensitivities of the schemes to the parameters of their turbulence closures are partially explored.     

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.