Quasi-Wavelet Model of Von Kármán Spectrum of Turbulent Velocity Fluctuations

The von Kármán spectra of turbulent temperature andvelocity fluctuations have been widely used in the literature on turbulenceand electromagnetic, seismic, and acoustic wave propagation in random media.In this paper we provide a phenomenological motivation for the vonKármán velocity spectrum in terms of the quasi-wavelet model ofturbulence developed recently. In this model, turbulence is represented as asuperposition of self-similar localized eddies of many different scales. Wefind a functional form for these eddies that yields the von Kármán velocity spectrum exactly. We also show that other eddy functions producevelocity spectra that have the same general form as the von Kármán spectrum, and we consider possible quasi-wavelet representations of the`Kansas' spectrum and the `-1' spectrum. We also present asystematic determination, based on turbulence similarity theories, of theparameters of the von Kármán spectra of temperature and velocityfluctuations in an unstable atmospheric boundary layer.     

Doppler Lidar Measurements of Vertical Velocity Spectra in the Convective Planetary Boundary Layer

We utilized a Doppler lidar to measure spectra of vertical velocity w from 390m above the surface to the top of the daytime convective boundary layer (CBL). The high resolution 2μm wavelength Doppler lidar developed by the NOAA Environmental Technology Laboratory was used to detect the mean radial velocity of aerosol particles. It operated continuously during the daytime in the zenith-pointing mode for several days in summer 1996 during the Lidars-in-Flat-Terrain experiment over level farmland in central Illinois, U.S.A. The temporal resolution of the lidar was about 1 s, and the range-gate resolution was about 30m. The vertical cross-sections were used to calculate spectra as a function of height with unprecedented vertical resolution throughout much of the CBL, and, in general, we find continuity of the spectral peaks throughout the depth of the CBL. We compare the observed spectra with previous formulations based on both measurements and numerical simulations, and discuss the considerable differences, both on an averaged and a case-by-case basis. We fit the observed spectra to a model that takes into account the wavelength of the spectral peak and the curvature of the spectra across the transition from low wavenumbers to the inertial subrange. The curvature generally is as large or larger than the von Kármán spectra. There is large case-to-case variability, some of which can be linked to the mean structure of the CBL, especially the mean wind and the convective instability. We also find a large case-to-case variability in our estimates of normalized turbulent kinetic energy dissipation deduced from the spectra, likely due for the most part to a varying ratio of entrainment flux to surface flux. Finally, we find a relatively larger contribution to the low wavenumber region of the spectra in cases with smaller shear across the capping inversion, and suggest that this may be due partly to gravity waves in the inversion and overlying free atmosphere.     

Spectral Structure of Small-Scale Turbulent and Mesoscale Fluxes in the Atmospheric Boundary Layer over a Thermally Inhomogeneous Land Surface

Spectral analysis was performed on aircraft observations of a convective boundary layer (CBL) that developed over a thermally inhomogeneous, well-marked mesoscale land surface. The observations, part of the GAME-Siberia experiment, were recorded between April and June 2000 over the Lena River near Yakutsk City. A special integral parameter termed the ‘reduced depth of the CBL’ was used to scale the height of the mixed layer with variable depth. Analysis of wavelet cospectra and spectra facilitated the separation of fluxes and other variables into small-scale turbulent fluctuations (with scales less than the reduced depth of the CBL, approximately 2 km) and mesoscale fluctuations (up to 20 km). This separation approach allows for independent exploration of the scales. Analyses showed that vertical distributions obeyed different laws for small-scale fluxes and mesoscale fluxes (of sensible heat, water vapour, momentum and carbon dioxide) and for other variables (wind speed and air temperature fluctuations, coherence and degree of anisotropy). Vertical profiles of small-scale turbulent fluxes showed a strong decay that differed from generally accepted similarity models for the CBL. Vertical profiles of mesoscale fluxes and other variables clearly showed sharp inflections at the same relative (with respect to the reduced depth of the CBL) height of approximately 0.55 in the CBL. Conventional similarity models for sensible heat fluxes describe both small-scale turbulent and mesoscale flows. The present results suggest that mesoscale motions that reach up to the relative level of 0.55 could be initiated by thermal surface heterogeneity. Entrainment between the upper part of the CBL and the free atmosphere may cause mesoscale motions in that region of the CBL.     

Regional-Scale Heat and Water Vapour Fluxes in an Agricultural Landscape: An Evaluation of CBL Budget Methods at OASIS

This paper evaluates convective boundary layer (CBL) budget methods as a tool for estimating regionally averaged sensible and latent heat fluxes for the study region used in OASIS (Observations at Several Interacting Scales). This is an agricultural region of mixed cropping and grazing extending about 100 km west of the town of Wagga Wagga, NSW, Australia.The analysis proceeds in three stages: first, a simpleone-dimensional model of the well-mixed layer (the CBL slab model), forced with measurements of the surface heat and evaporation fluxes, is evaluated by comparing measured and modelled CBL temperature, humidity and depths. A comparison of several entrainment schemes shows that a simple model, where the entrainment kinetic energy is parameterised as a fraction (₃) of the surface sensible heat flux, works well if is set to 0.5. Second, the slab model is coupled to a Penman–Monteith model of surface evaporation to predict regional scale evaporation and thence heat fluxes. Finally, the integral CBL budget approach, which is an inverse method using theone-dimensional slab model, is used to infer regional heat and evaporation fluxes from measured time series of CBL temperature and humidity.We find that the simple CBL slab model works reasonably well for predicting CBL depth and very well for CBL temperature, especially if approximate estimates of subsidence velocity and warming due to advection are included. Regional sensible heat fluxes estimated from the integral CBL method match those measured, although the method is very sensitive to measurement errors. Measurement-model differences were larger for short integration times, because the well-mixed assumptions are violated at particular times of the day. The corollary is that `whole-day' (0530–1530 h) estimates are in reasonable agreement with measured values. Integral methods could not be used to infer the regional evaporation flux directly because CBL humidity profiles were complex and often not well mixed until mid-afternoon. We recommend that regional evaporation fluxes be predicted either from a coupled Penman–Monteith – CBL slab model, or inferred as a residual term from estimates of the regionally averaged available energy and sensible heat flux. Furthermore, we show that inferring fluxes via integral methods will always be difficult when the scalar concentrations have either a large surface source and free atmosphere sink (in the case of water vapour and methane), or a large surface sink and upper level source (in the case of CO₂).     

Dispersion of passive tracer in the atmospheric convective boundary layer with wind shears: a review of laboratory and numerical model studies

Summary Paper reviews recent laboratory and numerical model studies of passive gaseous tracer dispersion in the atmospheric convective boundary layer (CBL) with surface and elevated wind shears. Atmospheric measurement data used for validation of these two model techniques are briefly discussed as well. A historical overview is given of laboratory studies of dispersion in the atmospheric CBL. Model studies of tracer dispersion in two CBL types, the (i) non-steady, horizontally homogeneous CBL and (ii) quasi-stationary, horizontally heterogeneous CBL, are reviewed. The discussion is focused on the dispersion of non-buoyant plume emitted from a point source located at different elevations within the CBL. Approaches towards CBL modeling employed in different laboratory facilities (water tanks and wind tunnels) are described. The reviewed numerical techniques include Large Eddy Simulation (LES) and Lagrangian modeling. Numerical data on dispersion in the sheared CBL is analyzed in conjunction with experimental results from wind-tunnel CBLs.     

Scaling Properties of Temperature Spectra and Heat-Flux Cospectra in the Surface Friction Layer Beneath an Unstable Outer Layer

Temperature variance and temperature power spectra in the unstable surface layer have always presented a problem to the standard Monin-Obukhov similarity model. Recently that problem has intensified with the demonstration by Smedman et al. (2007, Q J Roy Meteorol Soc 133: 37–51) that temperature spectra and heat-flux cospectra can have two distinct peaks in slightly unstable conditions, and by McNaughton et al. (2007, Nonlinear Process Geophys 14: 257–271) who showed that the wavenumber of the peak of temperature spectra in a convective boundary layer (CBL), closely above the surface friction layer (SFL), can be sensitive to the CBL depth, z _i. Neither the two-peak form at slight instability nor the dependence of peak position on z _i at large instability is compatible with the Monin-Obukhov model. Here we examine the properties of temperature spectra and heat-flux cospectra from between these extremes, i.e. from within the unstable SFL, in two experiments. The analysis is based on McNaughton’s model of the turbulence structure in the SFL. According to this model, heat is transported through most of the SFL by sheet plumes, created by the action of impinging outer eddies. The smallest and most effective of these outer eddies have sizes that scale on SFL depth, z _s. The z _s-scale eddies and plumes are organised within the overall convection pattern in the CBL, and in turn they organise the motion of smaller eddies within the SFL, whose sizes scale on height, z. The main experimental results are: (1) the peak amplitudes of the temperature spectra in the SFL are collapsed with a scaling factor (z_sz)^1/3e_o^2/3{(z_{\rm s}z)^{1/3}\varepsilon_{\rm o}^{2/3}} divided by the square of the surface temperature flux, where e_o{\varepsilon_{\rm o}} is the dissipation rate of turbulent energy in the outer CBL (above the SFL); (2) the peak wavenumbers of the temperature spectra are collapsed with the mixed length scale (z _i z _s)^1/2; (3) the peak wavenumbers of the heat-flux cospectra are collapsed with the doubly-mixed length scale (z _i z _s)^1/4 z ^1/2; (4) for z/z _s < 0.03, the peak in the cospectrum is replaced by another peak at a wavenumber about a magnitude larger. This peak’s position scales on z; (5) all these findings are consistent with the observations of Smedman et al.     

Flux Footprints in the Convective Boundary Layer: Large-Eddy Simulation and Lagrangian Stochastic Modelling

We investigated the flux footprints of receptors at different heights in the convective boundary layer (CBL). The footprints were derived using a forward Lagrangian stochastic (LS) method coupled with the turbulent fields from a large-eddy simulation model. Crosswind-integrated flux footprints shown as a function of upstream distances and sensor heights in the CBL were derived and compared using two LS particle simulation methods: an instantaneous area release and a crosswind linear continuous release. We found that for almost all sensor heights in the CBL, a major positive flux footprint zone was located close to the sensor upstream, while a weak negative footprint zone was located further upstream, with the transition band in non-dimensional upwind distances −X between approximately 1.5 and 2.0. Two-dimensional (2D) flux footprints for a point sensor were also simulated. For a sensor height of 0.158 z _i, where z _i is the CBL depth, we found that a major positive flux footprint zone followed a weak negative zone in the upstream direction. Two even weaker positive zones were also present on either side of the footprint axis, where the latter was rotated slightly from the geostrophic wind direction. Using CBL scaling, the 2D footprint result was normalized to show the source areas and was applied to real parameters obtained using aircraft-based measurements. With a mean wind speed in the CBL of U = 5.1 m s⁻¹, convective velocity of w _* = 1.37 m s⁻¹, CBL depth of z _i = 1,000 m, and flight track height of 159 m above the surface, the total flux footprint contribution zone was estimated to range from about 0.1 to 4.5 km upstream, in the case where the wind was perpendicular to the flight track. When the wind was parallel to the flight track, the total footprint contribution zone covered approximately 0.5 km on one side and 0.8 km on the other side of the flight track.     

Observations of the Relation Between Upslope Flows and the Convective Boundary Layer in Steep Terrain

Slope flow mechanisms are crucial for the transport of air pollutants in complex terrain. Previous observations in sloping terrain showed upslope flows filling the entire convective boundary layer (CBL) and reducing air pollution concentrations by venting air pollutants out of the CBL into the free atmosphere. During the Pacific 2001 Air Quality Field Study in the Lower Fraser Valley, British Columbia, Canada, we observed slope flows during weak synoptic winds, clear skies, and strong daytime solar heating. With a Doppler sodar we measured the three wind components at the foot of a slope having an average angle of 19° and a ridge height of 780 m. We operated a scanning lidar system and a tethersonde at a nearby site on the adjacent plain to measure backscatter of particulate matter, temperature, wind speed, wind direction, and specific humidity. Strong daytime upslope flows of up to 6 m s⁻¹ through a depth of up to 500 m occurred in the lower CBL, but with often equally strong and deep return flows in the upper part of the CBL. The mass transport of upslope flow and return flow approximately balanced over a 4-h morning period, suggesting a closed slope-flow circulation within the CBL. These observations showed that air pollutants can remain trapped within a CBL rather than being vented from the CBL into the free atmosphere.     

城市建筑动力学效应对对流边界层影响的敏感性试验

本文将大涡模拟应用于城市对流边界层(CBL)湍流结构和流场特征的研究,在大涡模式中,拖曳系数取与建筑物高度及建筑物高度标准差有关的表达式以考虑次网格建筑物对风速和湍流动能(TKE)的面积平均影响.模拟结果表明,由于城市建筑物对气流的拖曳作用,使建筑物冠层及整个CBL内风速大幅度减小,城市冠层内部风速减小尤为明显,在夹卷层内,风速有一明显的跃变.在边界层中部对流运动已经发展成为较强的热泡,城市建筑物的动力学效应使热泡的水平尺度增大,CBL内平均上升气流速度和下沉气流速度减小,同时使CBL中上升气流所占比例比平坦地面增大.城市建筑物使CBL低层热通量、动量通量、速度方差和位温方差明显增大,但对近地层高度以上的湍流量影响不大.     

非均匀对流边界层的地转强迫流动和动量输送

用大涡模拟方法研究地转强迫下的对流边界层流动和地表热力非均匀性影响.模拟重现了典型对流边界层的平均风廓线和动量通量垂直分布.地表热力非均匀性对区域平均风速和动量通量分布无明显影响,但边界层内的局地流动性状和湍流动量输送情况有系统性的改变.下风较热区近地面风速增强而高空流动受到阻塞,上风较冷区之上情况则正好相反.对应于平均流动场的畸变,地表较热区之上边界层大部可以出现动量向上输送的情况,较冷区成为大气动量下传的主要通道.地面应力在较热区增强、较冷区减弱的趋势明显.     

On the existence of a relation between the Kolmogoroff and von Kármán constants

A model is described, in which the mean vertical wind profile and turbulence spectra at different heights are calculated for a turbulent boundary layer without thermal stratification. The model makes use of Heisenberg's formula for the transfer of turbulent energy and is based on the assumption of a constant shearing stress in that boundary layer. As a result, a logarithmic wind profile follows with 0.39 as the value of von Kármán's constant, which is — in this model — strongly related to the inertial subrange of the turbulent energy spectra and therefore to the Kolmogoroff constant.This paper is based on studies done by the author during a one-year visit to CSIRO Division of Meteorological Physics, Aspendale, Australia, and was presented at the AGARD Specialists Meeting on The Aerodynamics of Atmospheric Shear Flows sponsored by the Fluid Dynamics Panel at Munich, Germany, during 15–17 Sept. 1969.     

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.     

Structure of mean winds and turbulence in the planetary boundary layer over rural terrain

A detailed analysis has been carried out of the temporal and spatial structure of mean winds and turbulence in the neutrally-stable planetary boundary layer over typically rural terrain. The data were obtained from a horizontal array of tower-mounted propeller anemometers (z = 11 m) during a five-hour period for which the mean wind direction was virtually perpendicular to the main span of the array. Various turbulence characteristics have been obtained for all three components of velocity and have been compared with idealized models for such a flow and with some of the other available atmospheric results.Considerable tower-to-tower and block-to-block variability has been observed in many of the measured results, particularly in those for the horizontal-component integral scales. Surface shear stress, roughness length and turbulence intensities were in good agreement with expected values for such a site. Power spectra for all components displayed significantly more energy at middle and lower frequencies than that observed by Kaimal et al. (1972) over flat, relatively featureless terrain. This is felt to be a result of the generally rougher gross features of the terrain in the present case and has led to the development of a modified version of the Kaimal-spectral model which fits the observed data better than either the original Kaimal model or the von Kármán model. It is suggested that it may in future be possible to represent power spectra over a wide range of terrain types by using such a modified spectral model.Integral scales of turbulence were calculated by three different techniques and in most cases displayed a strong dependence on the technique used. Averaged values of scale showed reasonable agreement with most of the available atmospheric data and with the values suggested by ESDU (1975). The anticipated elongation of turbulent eddies in the longitudinal direction was confirmed for all three velocity components, although it was found to be not as large as some other observations.     

一种粒子——烟团扩散模型的应用研究

本文运用随机游动模拟方法改进建立一种粒子—烟团模式，成功地模拟了对流边界层条件下污染物扩散，粒子—烟团模式的模拟结果与水槽试验的结果吻合较好。数值模拟试验结果表明粒子—烟团模式能在施放粒子数较少，从而运行时间很短的情况下，得到优于一般随机游动模式的模拟性能。用KNRC的资料对模式的模拟性能作一验证，表明模式也能很好地模拟实际大气中不同稳定度情况下的扩散。     

Impacts of Aerosol Shortwave Radiation Absorption on the Dynamics of an Idealized Convective Atmospheric Boundary Layer

We investigated the impact of aerosol heat absorption on convective atmospheric boundary-layer (CBL) dynamics. Numerical experiments using a large-eddy simulation model enabled us to study the changes in the structure of a dry and shearless CBL in depth-equilibrium for different vertical profiles of aerosol heating rates. Our results indicated that aerosol heat absorption decreased the depth of the CBL due to a combination of factors: (i) surface shadowing, reducing the sensible heat flux at the surface and, (ii) the development of a deeper inversion layer, stabilizing the upper CBL depending on the vertical aerosol distribution. Steady-state analytical solutions for CBL depth and potential temperature jump, derived using zero-order mixed-layer theory, agreed well with the large-eddy simulations. An analysis of the entrainment zone heat budget showed that, although the entrainment flux was controlled by the reduction in surface flux, the entrainment zone became deeper and less stably stratified. Therefore, the vertical profile of the aerosol heating rate promoted changes in both the structure and evolution of the CBL. More specifically, when absorbing aerosols were present only at the top of the CBL, we found that stratification at lower levels was the mechanism responsible for a reduction in the vertical velocity and a steeper decay of the turbulent kinetic energy throughout the CBL. The increase in the depth of the inversion layer also modified the potential temperature variance. When aerosols were present we observed that the potential temperature variance became significant already around $0.7z_i$ (where $z_i$ is the CBL height) but less intense at the entrainment zone due to the smoother potential temperature vertical gradient.     

盆地环流型及冷湖的形成和消散的数值研究

本文建立了一个三维原始方程数值模式，模拟三维盆地中的环流，重点讨论在热力强迫环流型的转变过程中能量场的动量场的配置情况及环流演变过程。模拟结果表明，夜间地面强烈的辐射冷却过程引起盆地各坡面冷迳流的发展，盆地中成为冷空气湖，逆温层结建立。日出后对流边界层从大气低层向上发展，逆温从底部随之消蚀，仅在上层存在了夜间逆温残余，即所谓稳定核，上坡风在对流边界层发展，而稳定核内仍维持夜间下坡风环流。     

Modelling Regional Scale Surface Energy Exchanges And Cbl Growth In A Heterogeneous, Urban-Rural Landscape

Over the last decade, simple models of theconvective boundary layer (CBL) have beensuggested as an approach to inferring regionallyaveraged land-air exchanges of heat, water and tracegases, because the properties of the CBL respond toan average of the underlying small-scaleheterogeneity. This paper explores the use of anintegral CBL method to infer regionally averagedfluxes in a landscape that has at least three majorsources of heterogeneity – irrigated andnon-irrigated rural land use and a large urban area(Sacramento region, California).The first part of the paper assesses the validity ofthe simple slab model of the CBL – this isintegrated forwards in time using local-scalemeasured heat and water vapour fluxes, to predictmixed-layer depth, temperature and humidity. Of thefour different CBL growth schemes used, the Tennekesand Driedonks model is found to give the bestperformance. Evaluation of the model performancewith different weightings of heat and water vapourfluxes based on the land use characteristics in theregion suggest that the source area for theboundary-layer sonde measurements is larger thanphysically-based estimates would suggest.Finally, measured time series of potentialtemperature are used to infer regionally averagedsensible heat fluxes using an integral CBL (ICBL)method. These ICBL fluxes are compared with thosemeasured at the local scale over the three land usetypes that comprise the region of interest. They arefound to be closest to the heat fluxes calculated byappropriately weighting the measured heat fluxes inthe source area calculated for the ICBL. We concludethat the integral CBL budget method providesadequate estimates of regionally-averaged surfaceheat fluxes in a landscape that is characterised bysurface types with distinctly different surfaceenergy budgets.     

Performance of WRF Large Eddy Simulations in Modeling the Convective Boundary Layer over the Taklimakan Desert,China

The maximum height of the convective boundary layer (CBL) over the Taklimakan Desert can exceed 5000 m during summer and plays a crucial role in the regional circulation and weather. We combined the Weather Research and Forecasting Large Eddy Simulation (WRF-LES) with data from Global Positioning System (GPS) radiosondes and from eddy covariance stations to evaluate the performance of the WRF-LES in simulating the characteristics of the deep CBL over the central Taklimakan Desert. The model reproduced the evolution of the CBL processes reasonably well, but the simulations generated warmer and moister conditions than the observation as a result of the over-prediction of surface fluxes and large-scale advection. Further simulations were performed with multiple configurations and sensitivity tests. The sensitivity tests for the lateral boundary conditions (LBCs) showed that the model results are sensitive to changes in the time resolution and domain size of the specified LBCs. A larger domain size varies the distance of the area of interest from the LBCs and reduces the influence of large forecast errors near the LBCs. Comparing the model results using the original parameterization of sensible heat flux with the Noah land surface scheme and those of the sensitivity experiments showed that the desert CBL is sensitive to the sensible heat flux produced by the land surface scheme during daytime in summer. A reduction in the sensible heat flux can correct overestimates of the potential temperature profile. However, increasing the sensible heat flux significantly reduces the total time needed to increase the CBL to a relatively low altitude (< 3 km) in the middle and initial stages of the development of the CBL rather than producing a higher CBL in the later stages.     

Analytical Model of Roll Vortices in the Convective Boundary Layer

Analytical solutions of convective waves in the convective boundary layer (CBL) were obtained with two-layer linearized atmospheric equations including Rayleigh friction, which represents the turbulent viscosity in the lower CBL. The analytical model shows that the interaction between the convection in the lower layer and gravity waves in the upper layer is one of the causes for the formation of convective bands. The flow and temperature fields obtained by the analytical model present the main characteristics of convective bands found in field observations. We have also investigated the influences of atmospheric conditions on the characteristics of the bands. Results accord with previous knowledge about these phenomena.     

A Parameterization of Third-order Moments for the Dry Convective Boundary Layer

We describe one-dimensional (1D) simulations of the countergradient zone of mean potential temperature observed in the convective boundary layer (CBL). The method takes into account the third-order moments (TOMs) in a turbulent scheme of relatively low order, using the turbulent kinetic energy equation but without prognostic equations for other second-order moments. The countergradient term is formally linked to the third-order moments and , and a simple parameterization of these TOMs is proposed. It is validated for several cases of a dry CBL, using large-eddy simulations that have been realized from the MESO-NH model. The analysis of the simulations shows that TOMs are responsible for the inversion of the sign of in the higher part of the CBL, and budget analysis shows that the main terms responsible for turbulent fluxes and variances are now well reproduced.