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.     

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.     

Estimation Of The Lagrangian Structure Function Constant C0 From Surface-Layer Wind Data

Eulerian turbulence observations, madein the surface layer under unstable conditions (z/L > 0),by a sonic anemometer were used to estimatethe Lagrangian structure function constant _O. Twomethods were considered. The first one makes use of arelationship, widely used in the Lagrangian stochasticdispersion models, relating _O to the turbulent kineticenergy dissipation rate , wind velocity variance andLagrangian decorrelation time. The second one employsa novel equation, connecting _O to the constant of thesecond-order Eulerian structure function. Beforeestimating _O, the measurements were processed in orderto discard non-stationary cases at least to a firstapproximation and cases in which local isotropy couldnot be assumed. The dissipation was estimated eitherfrom the best fit of the energy spectrum in theinertial subrange or from the best fit of the third-orderlongitudinal Eulerian structure function. Thefirst method was preferred and applied to the subsequentpart of the analysis. Both methods predict thepartitioning of _O in different spatial components as aconsequence of the directional dependence of theEulerian correlation functions due to the isotropy.The _O values computed by both methods are presented anddiscussed. In conclusion, both methods providerealistic estimates of _O that compare well withprevious estimations reported in the literature, evenif a preference is to be attributed to the second method.     

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.     

Turbulence Scale Dependence of the Richardson Constant in Lagrangian Stochastic Models

We investigate the relative dispersion properties of the well-mixed class of Lagrangian stochastic models. Dimensional analysis shows that, given a model in the class, its properties depend solely on a non-dimensional parameter, which measures the relative weight of Lagrangian-to-Eulerian scales. This parameter is formulated in terms of Kolmogorov constants, and model properties are then studied by modifying its value in a range that contains the experimental variability. Large variations are found for the quantity, g* = 2gC₀^{− 1}, where g is the Richardson constant.     

UNIVERSALITY OF THE LAGRANGIAN VELOCITY STRUCTURE FUNCTION CONSTANT (C0) ACROSS DIFFERENT KINDS OF TURBULENCE

In this paper, we evaluate the Lagrangian velocity structure function constant, C0, in the inertial subrange by comparing experimental diffusion data and simulation results obtained with applicable Lagrangian stochastic models. We find in several different flows (grid turbulence, laboratory boundary-layer flow and the atmospheric surface layer under neutral stratification) the value for C0 is 3.0 ± 0.5. We also identify the reasons responsible for earlier studies having not reached the present result.     

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.     

Coherent Structures near the Surface in a Strongly Sheared Convective Boundary Layer Generated by Large-Eddy Simulation

Well-developed low speed and high temperature streaks in association with the alignment of convection cells are observed in a large-eddy-simulation (LES) generated strongly sheared convective boundary-layer flow, which is driven by a geostrophic wind speed of 15 m s^-1 and a surface kinematic heat flux of 0.05 K m s^-1. Vortices that drive streaky structures are identified through an eigenvalue method (lambda;₂method) near the surface. These vortices are highly elongated along the quasi-streamwise direction alternating sign of the x-component of vorticity (_x). By conditional sampling of fully developed vortices, a statistically significant coherent structure is educed. The educed vortex is elongated to the streamwise direction with the elevation angle of about 17° above the horizontal surface. However, the horizontal tilting is not clearly demonstrated in the present simulation. Fluctuation fields in the domain of the educed vortex show the existence of a low speed and high temperature streak as a direct consequence of momentum and heat transport by vortical motions. The strong ejection(upward transport of low momentum or high temperature)occurring at the higher level than that of the strong sweep (downward transport of high momentum and low temperature) can be explained from the spatial distribution of the fluctuationfields of velocity and temperature. The contribution of ejection to the Reynolds stress at z/h₁ = 0.18 is about 75%, which is slightly greater than that (70% at z/h₁ = 0.173) for the neutrally stratified atmospheric boundary layer. Ejection is also found to be dominant for the turbulent heat flux.     

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 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.     

Non-Gaussian Lagrangian Stochastic Model for Wind Field Simulation in the Surface Layer

Wind field simulation in the surface layer is often used to manage natural resources in terms of air quality, gene flow(through pollen drift), and plant disease transmission(spore dispersion). Although Lagrangian stochastic(LS) models describe stochastic wind behaviors, such models assume that wind velocities follow Gaussian distributions. However,measured surface-layer wind velocities show a strong skewness and kurtosis. This paper presents an improved model, a non-Gaussian LS model, which inco...     

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.     

Forward-in-time and Backward-in-time Dispersion in the Convective Boundary Layer: the Concentration Footprint

The turbulence field obtained using a large-eddy simulation model is used to simulate particle dispersion in the convective boundary layer with both forward-in-time and backward-in-time modes. A Lagrangian stochastic model is used to treat subgrid-scale turbulence. Results of forward dispersion match both laboratory experiments and previous numerical studies for different release heights in the convective boundary layer. Results obtained from backward dispersion show obvious asymmetry when directly compared to results from forward dispersion. However, a direct comparison of forward and backward dispersion has no apparent physical meaning and might be misleading. Results of backward dispersion can be interpreted as three-dimensional or generalized concentration footprints, which indicate that sources in the entire boundary layer, not only sources at the surface, may influence a concentration measurement at a point. Footprints at four source heights in the convective boundary layer corresponding to four receptors are derived using forward and backward dispersion methods. The agreement among footprints derived with forward and backward methods illustrates the equivalence between both approaches. The paper shows explicitly that Lagrangian simulations can yield identical footprints using forward and backward methods in horizontally homogeneous turbulence.     

A Homogeneous Langevin Equation Model, Part i: Simulation of Particle Trajectories in Turbulence with a Skewed Velocity Distribution

A Lagrangian stochastic model for the time evolution of the velocity of a fluid particle is presented. This model is based on a one-dimensional generalized Langevin equation, and assumes the velocity probability distribution of the turbulent fluid is skewed and spatially homogeneous. This has been shown to be an effective approach to simulating vertical dispersion in the convective boundary layer. We use a form of the Langevin equation that has a linear (in velocity) deterministic acceleration and a random acceleration that is a non-Gaussian, skewed process. For the case of homogeneous fluid velocity statistics, this 'linear-skewed' Langevin equation can be integrated explicitly, resulting in an efficient numerical simulation method. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity are known. Results of these tests show that, for homogeneous turbulence, a linear-skewed Langevin equation model can overcome the difficulties encountered in applying a Langevin equation with a skewed random acceleration. The linear-skewed Langevin equation model results are compared to results of a 'nonlinear-Gaussian' Langevin equation model, and show that the linear-skewed model is significantly more efficient.     

Large-Eddy Simulations of the Stable Boundary Layer Using the Standard Kolmogorov Theory: Range of Applicability

Large-eddy simulations (LES) of the Stable Atmospheric Boundary Layer (SBL) are difficult because the turbulence is not isotropic for strong stratification and the Kolmogorov theory might be no longer valid. This fact compells us to work on modifications to the subgrid turbulence schemes, although there is not any widely accepted theory on anisotropic turbulence. In this work, a LES model is used to see what range of stable stratification can still be simulated with a subgrid turbulence scheme using the Kolmogorov theory for the dissipation. Twenty simulations of increasing stability have been performed using a horizontal resolution of 5 m. The model is able to simulate weakly and moderately stable conditions and experiences runaway cooling for strong stability. The goodness of the successful simulations is inspected through comparison to observations from the experimental campaigns SABLES-98 and CASES-99. Other supplementary tests have been performed on the resolution and the surface boundary condition.     

A Homogeneous Langevin Equation Model, Part ii: Simulation of Dispersion in the Convective Boundary Layer

We present a Lagrangian stochastic model of vertical dispersion in the convective boundary layer (CBL). This model is based on a generalized Langevin equation that uses the simplifying assumption that the skewed vertical velocity probability distribution is spatially homogeneous. This approach has been shown to account for two key properties of CBL turbulence associated with large-scale coherent turbulent structures: skewed vertical velocity distributions and long velocity correlation time. A 'linear-skewed' form of the generalized Langevin equation is used, which has a linear (in velocity) deterministic acceleration and a skewed random acceleration. 'Reflection' boundary conditions for selecting a new velocity for a particle that encounters a boundary were investigated, including alternatives to the standard assumption that the magnitudes of the particle incident and reflected velocities are positively correlated. Model simulations were tested using cases for which exact, analytic statistical properties of particle velocity and position are known, i.e., well-mixed spatial and velocity distributions. Simulations of laboratory experiments of CBL dispersion show that (1) the homogeneous linear-skewed Langevin equation model (as well as an alternative 'nonlinear-Gaussian' Langevin equation model) can simulate the important aspects of dispersion in the CBL, and (2) a negatively-correlated-speed reflection boundary condition simulates the observed dispersion of material near the surface in the CBL significantly better than alternative reflection boundary conditions. The homogeneous linear-skewed Langevin equation model has the advantage that it is computationally more efficient than the homogeneous nonlinear-Gaussian Langevin equation model, and considerably more efficient than inhomogeneous Langevin equation models.     

热浮升烟流扩散的拉格朗日粒子模拟

本文建立了一个处理对流边界层热浮升烟流扩散的拉格朗日粒子模式。模式既考虑了对流边界层的特殊气流结构，并作了均匀湍流参数化的简化；同时提出了在拉格朗日模式中合理计入热浮升烟流抬升影响的近似方法。模拟计算结果表明:烟流热浮力的影响使得地面最大浓度值远比被动烟流的低，而且出现位置离源更远。模式计算与外场试验结果合理地一致。模式物理概念明确合理，输入参数少，计算量小，具有简单实用的优点，适合日常环境应用需要。     

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.     

Large-Eddy Simulations of the Baroclinic Mixed Layer

The effects of baroclinicity, imposed on the dry mixed layer by the presenceof large-scale, horizontal temperature gradients, have been investigated basedon a large-eddy simulation model. The purpose of this investigation is to examinesimultaneous impacts of thermal stratification and shear in the atmospheric boundarylayer. For this purpose, five cases are considered – one barotropic, and four baroclinic.Based on the performed simulations, a new parametrization of the interfacial layer isproposed. The parameterization employs new interfacial scaling, which is valid at thetop of the mixed layer. In terms of new scales, dimensionless moments characterizingturbulence at the top of the shearless mixed layer are universal constants. In the shearedcase, dimensionless statistics of turbulence are shown to be functions of the interfacialRichardson number.