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.     

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.     

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 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 Modelling Study of Flux Imbalance and the Influence of Entrainment in the Convective Boundary Layer

It is frequently observed in field experiments that the eddy covariance heat fluxes are systematically underestimated as compared to the available energy. The flux imbalance problem is investigated using the NCAR’s large-eddy simulation (LES) model imbedded with an online scheme to calculate Reynolds-averaged fluxes. A top–down and a bottom–up tracer are implemented into the LES model to quantify the influence of entrainment and bottom–up diffusion processes on flux imbalance. The results show that the flux imbalance follows a set of universal functions that capture the exponential decreasing dependence on u _*/w _*, where u _* and w _* are friction velocity and the convective velocity scale, respectively, and an elliptic relationship to z/z _i , where z _i is the mixing-layer height. The source location in the boundary layer is an important factor controlling the imbalance magnitude and its horizontal and vertical distributions. The flux imbalance of heat and the bottom–up tracer is tightly related to turbulent coherent structures, whereas for the top–down diffusion, such relations are weak to nonexistent. Our results are broadly consistent with previous studies on the flux imbalance problem, suggesting that the published results are robust and are not artefacts of numerical schemes.     

A Lagrangian Decorrelation Time Scale in the Convective Boundary Layer

A new method for deriving the Lagrangian decorrelation time scales for inhomogeneous turbulence is described. The expression for the time scales here derived for the convective boundary layer is compared to those estimated by Hanna during the Phoenix experiment. Then the values of C₀, the Lagrangian velocity structure function constant, and of B_i, the Lagrangian velocity spectrum constant, were evaluated from the Eulerian velocity spectra and from the Lagrangian time scales derived, under unstable conditions, from Taylor's statistical diffusion theory. The numerical coefficient of the lateral and vertical Lagrangian spectra in the inertial subrange was found equal to 0.21, in good agreement with previous experimental estimates.     

Nesting Turbulence in an Offshore Convective Boundary Layer Using Large-Eddy Simulations

The applicability of the one-way nesting technique for numerical simulations of the heterogeneous atmospheric boundary layer using the large-eddy simulation (LES) framework of the Weather Research and Forecasting model is investigated. The focus of this study is on LES of offshore convective boundary layers. Simulations were carried out using two subgrid-scale models (linear and non-linear) with two different closures [diagnostic and prognostic subgrid-scale turbulent kinetic energy (TKE) equations]. We found that the non-linear backscatter and anisotropy model with a prognostic subgrid-scale TKE equation is capable of providing similar results when performing one-way nested LES to a stand-alone domain having the same grid resolution but using periodic lateral boundary conditions. A good agreement is obtained in terms of velocity shear and turbulent fluxes, while velocity variances are overestimated. A streamwise fetch of 14 km is needed following each domain transition in order for the solution to reach quasi-stationary results and for the velocity spectra to generate proper energy content at high wavelengths, however, a pile-up of energy is observed at the low-wavelength portion of the spectrum on the first nested domain. The inclusion of a second nest with higher resolution allows the solution to reach effective grid spacing well within the Kolmogorov inertial subrange of turbulence and develop an appropriate energy cascade that eliminates most of the pile-up of energy at low wavelengths. Consequently, the overestimation of velocity variances is substantially reduced and a considerably better agreement with respect to the stand-alone domain results is achieved.     

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.     

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.     

Lagrangian Stochastic Modeling of Dispersion in the Stable Boundary Layer

Lagrangian stochastic models are well-suited for modeling dispersion in the stable boundary layer, especially in complex terrain. This note briefly describes the formulations and application of a Lagrangian stochastic model to predict dispersion of tracers released within nocturnal drainage flows.     

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.     

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.     

Modelling Small-Scale Drifting Snow with a Lagrangian Stochastic Model Based on Large-Eddy Simulations

Observations of drifting snow on small scales have shown that, in spite of nearly steady winds, the snow mass flux can strongly fluctuate in time and space. Most drifting snow models, however, are not able to describe drifting snow accurately over short time periods or on small spatial scales as they rely on mean flow fields and assume equilibrium saltation. In an attempt to gain understanding of the temporal and spatial variability of drifting snow on small scales, we propose to use a model combination of flow fields from large-eddy simulations (LES) and a Lagrangian stochastic model to calculate snow particle trajectories and so infer snow mass fluxes. Model results show that, if particle aerodynamic entrainment is driven by the shear stress retrieved from the LES, we can obtain a snow mass flux varying in space and time. The obtained fluctuating snow mass flux is qualitatively compared to field and wind-tunnel measurements. The comparison shows that the model results capture the intermittent behaviour of observed drifting snow mass flux yet differences between modelled turbulent structures and those likely to be found in the field complicate quantitative comparisons. Results of a model experiment show that the surface shear-stress distribution and its influence on aerodynamic entrainment appear to be key factors in explaining the intermittency of drifting snow.     

Simulated Airborne Flux Measurements in a LES generated Convective Boundary Layer

One aim of past boundary-layer experiments with aircraft was the determination of areally averaged heat fluxes. In spite ofsophisticated instrumentation the measured fluxes extrapolated to the ground differed significantly from fluxes measured directly at ground stations. This studypresents simulated sensible heat flux measurements with aircraft flightsthrough a synthetic convective boundary layer created by a401 × 401 × 42 cubic-grid large eddy simulation (LES) with agrid spacing of 50 m. After some considerations with respect to necessary measurement lengths using results ofLenschow and Stankov (1986 – J. Atmos. Sci. 43, 1198–1209), simulated measurementcampaigns were carried out in three modelruns. During each model run five sets ofmeasurement runs were carried out successively.During each set of runs 10 aircraftflew at 10 altitudes with a ground speedof 100 m s^-1 simultaneously throughtime and space. In total, 150 legs were carried out, 15 at each flight level. The resulting`measured' heat fluxes were compared withthose of the `true' flux profiles obtaineddirectly from the ensemble-averagedLES-generated data. No significant systematic error between `measured' and `true' profiles was observed. Furthermore, the comparison of the resulting relative error with the theory ofLenschow and Stankov showed a good agreement at allmeasurement levels.     

A Comparison of Higher-Order Vertical Velocity Moments in the Convective Boundary Layer from Lidar with In Situ Measurements and Large-Eddy Simulation

We have analyzed measurements of vertical velocity w statistics with the NOAA high resolution Doppler lidar (HRDL) from about 390 m above the surface to the top of the convective boundary layer (CBL) over a relatively flat and uniform agricultural surface during the Lidars-in-Flat-Terrain (LIFT) experiment in 1996. The temporal resolution of the zenith-pointing lidar was about 1 s, and the range-gate resolution about 30 m. Vertical cross-sections of w were used to calculate second- to fourth-moment statistics of w as a function of height throughout most of the CBL. We compare the results with large-eddy simulations (LES) of the CBL and with in situ aircraft measurements. A major cause of the observed case-to-case variability in the vertical profiles of the higher moments is differences in stability. For example, for the most convective cases, the skewness from both LES and observations changes more with height than for cases with more shear, with the observations changing more with stability than the LES. We also found a decrease in skewness, particularly in the upper part of the CBL, with an increase in LES grid resolution.     

Numerical Simulation of Roll Vortices in the Convective Boundary Layer

Roll vortices,which often appear when cold air outbreaks over warm ocean surfaces,are an important system for energy and substance exchange between the land surface and atmosphere.Numerical simulations were carried out in the study to simulate roll vortices in the convective boundary layer(CBL).The results indicate,that with proper atmospheric conditions,such as thermal instability in the CBL,stable stratification in the overlying layer and suitable wind shear,and a temperature jump between the two layers in a two-layer atmosphere,convective bands appear after adding initial pulses in the atmosphere.The simulated flow and temperature fields presented convective bands in the horizontal and roll vortices in the crosswind section. The structure of the roll vortices were similar to those observed in the cloud streets,as well as those from analytical solutions.Simulations also showed the influence of depth and instability strength of the CBL, as well as the stratification above the top of the CBL,on the orientation spacing and strength of the roll vortices.The fluxes caused by the convective rolls were also investigated,and should perhaps be taken into account when explaining the surface energy closure gap in the CBL.     

Fluid Modelling Of Atmospheric Dispersion In The Convective Boundary Layer

A laboratory convection tank has been established following thepioneering work of Willis and Deardorff, but with many improvements and enhancements thattake advantage of modern technology. The main emphasis in the current design was toprovide the ability to conduct a virtually unlimited number of realizations under essentiallyidentical conditions in order to obtain reliable statistics on the dispersion of plumes and puffsreleased within the simulated atmospheric convective boundary layer. Described herein is the tankitself and its auxiliary systems, including a laser-induced-fluorescence and video-imaging system for makingnon-intrusive, full-field measurements of concentrations, and the interfacing of varioussubsystems with a master controller that automates essentially all operation and measurement functions.The current system provides unprecedented resolution, control, and data volumes. Exampleresults are presented from two types of releases: continuous plumes and instantaneous puffs.These data sets clearly show penetration of the highly buoyant plumes and puffs into theinversion above the convective boundary layer, gravity spreading within the inversion, andrapid diffusion within the mixed layer. They also show extreme `spottiness' in the instantaneousconcentration cross-sections.