Comments on the 'Universality of the Lagrangian Velocity Structure Function Constant (C0) ACROSS DIFFERENT KINDS OF TURBULENCE’

Recently Du ( Boundary-Layer Meteorology 83, 207–219, 1997) estimated the value of the Lagrangian velocity structure constant, C0, in the inertial subrange by comparing experimental diffusion data and simulation results obtained with the one-dimensional form of Thomson's model ( J. Fluid Mech. 180, 529–556, 1987). Du reported that for several different flows (grid turbulence, a wind-tunnel boundary layer and the atmospheric surface layer under neutral stratification) the value of C0 is 3.0±0.5. Here, it is shown that optimal model agreement with experimental diffusion data for the wind-tunnel boundary layer is, in fact, obtained when C0=5.0 ± 0.5. It is also shown that accounting for the skewness of velocity statistics and finite Reynolds number effects does not significantly change this estimate for the value of C0. It is suggested that one-dimensional Lagrangian stochastic models are inconsistent with the supposed universality of C0.     

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.     

Estimation of the Lagrangian Velocity Structure Function Constant C0 by Large-Eddy Simulation

The inertial subrange Kolmogorov constant C ₀, which determines the effective turbulent diffusion in velocity space, plays an important role in the Lagrangian modelling of pollutants. A wide range of values of the constant are found in the literature, most of them determined at low Reynolds number and/or under different assumptions. Here we estimate the constant C ₀ by tracking an ensemble of Lagrangian particles in a planetary boundary layer simulated with a large-eddy simulation model and analysing the Lagrangian velocity structure function in the inertial subrange. The advantage of this technique is that it easily allows Reynolds numbers to be achieved typical of convective turbulent flows. Our estimates of C ₀ is C ₀=4.3±0.3 consistent with values found in the literature     

Rotation Of Trajectories In Lagrangian Stochastic Models Of Turbulent Dispersion

We present a new measure for the rotation of Lagrangian trajectories in turbulence that simplifies and generalises that suggested by Wilson and Flesch ( Boundary-Layer Meteorol. 84, 411–426). The new measure is the cross product of the velocity and acceleration and is directly related to the area, rather than the angle, swept out by the velocity vector. It makes it possible to derive a simple but exact kinematic expression for the mean rotation of the velocity vector and to partition this expression into terms that are closed in terms of Eulerian velocity moments up to second order and unclosed terms. The unclosed terms arise from the interaction of the fluctuating part of the velocity and the rate of change of the fluctuating velocity.We examine the mean rotation of a class of Lagrangian stochastic models that are quadratic in velocity for Gaussian inhomogeneous turbulence. For some of these models, including that of Thomson ( J. Fluid Mech. 180, 113–153), the unclosed part of the mean rotation vanishes identically, while for other models it is non-zero. Thus the mean rotation criterion clearly separates the class of models into two sets, but still does not provide a criterion for choosing a single model.We also show that models for which = 0 are independent of whether the model is derived on the assumption that total Lagrangian velocity is Markovian or whether the fluctuating part is Markovian.     

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.     

APPLICATION OF HYSPLIT MODEL IN DEFINITION OF THE ONSET OF SOUTH CHINA SEA SUMMER MONSOON

Using NCEP reanalysis data and an airflow trajectory model based on the Lagrangian method, the Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model, the daily backward trajectories on the height of 850 hPa above the South China Sea (SCS) area are simulated from April to June. The onset date of the SCS summer monsoon from 1948 to 2009 is determined according to the simulated source of airflow in the monitored area of the SCS. By analyzing the SCS monsoon onset dates over the 62 years, we found that the number of years in which the SCS monsoon onset is earlier accounts for 13%, and the later years 14%, the normal years 73%, of all the 62 years. Analyses with the Lagrangian method, done in comparison with the other two methods which combine wind and potential pseudo-equivalent temperature, were performed to determine the onset dates of the SCS summer monsoon. In some years, the source of the southwest airflow in the monitored area of the SCS is in the subtropical region before the onset of the SCS monsoon, so the airflow from the subtropics can be distinguished with the airflow from the tropics by using the Lagrangian method. The simulation by the trajectory model indicated that in some years, after the onset of SCS summer monsoon, the SCS will be controlled by the southeast wind instead of the southwesterly usually expected.     

THE CHARACTERISTICS OF SUMMER MONSOON AND TRANSPORT OF MOISTURE IN A HEAVY RAIN OVER SOUTH CHINA IN 1994

The trajectory of atmospheric particles and material lines on an isentropic surface are computed using the Lagrangian method. It is shown that the 1994 heavy rain in South China was closely linked to the summer monsoon, especially the tropical monsoon in East Asia. which plays a decisive role. The method is useful in tracking the source area and evolution of water moisture and analyzing the transporting part of airflow for water moisture.     

On Trajectory Curvature as a Selection Criterion for Valid Lagrangian Stochastic Dispersion Models

Recently Wilson and Flesch (Boundary-Layer Meteorology, 84, 411-426, 1997) suggested that the average increment d z to the orientation = arctan(w/u) of the Lagrangian velocity-fluctuation vector can be used to distinguish the better Lagrangian stochastic models within the well-mixed class. Here it is demonstrated that the specification of d z constitutes neither a sufficient or universally applicable criterion to distinguish the better Lagrangian stochastic models within the well-mixed class. The hypothesis made by Wilson and Flesch that Lagrangian stochastic models with /P_E irrotational are zero-spin models, having d z=0, is proven     

A Lagrangian Solution to the Relationship between Source Strength and Concentration Profile Under Conditions of Local Advection

We propose a two-dimensional Lagrangian analytical solution for relating source strength and concentration profiles within and above a plant canopy. The new solution describes passive scalar dispersion under conditions of local advection through a fetch correction function in a one-dimensional Lagrangian analytical dispersion model. The model is capable of predicting absolute concentration profiles of passive scalars for different fetches for situations in which the reference concentration is known or the background concentration is available. Tests of the model showed good agreement with measurements from field and wind-tunnel experiments.     

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.     

半拉格朗日方法在全球原始方程模式中的实现

简单介绍了半拉格朗日平流方案的基本概念,并详细总结了基估全球原始方程模式,特别是在ＩＦＳ的具体实现过程,拉格朗日平流的观点是着流体质点看流体运动,基贩关键是流体轨迹的计算。轨迹中点和起始点水平坐标的示得可以利用球面三角,直接在球极坐标中进行,并采用一些较高的近似。为了充分获得半拉格朗日方案析益处,在起始点的内插能工巧匠春阶数至少应在四阶以上,为避免昂贵的三维三次内插,可以采用三维“准三次”内插 。     

A Three-Dimensional Backward Lagrangian Footprint Model For A Wide Range Of Boundary-Layer Stratifications

We present a three-dimensional Lagrangian footprint model with the ability to predict the area of influence (footprint) of a measurement within a wide range of boundary-layer stratifications and receptor heights. The model approach uses stochastic backward trajectories of particles and satisfies the well-mixed condition in inhomogeneous turbulence for continuous transitions from stable to convective stratification. We introduce a spin-up procedure of the model and a statistical treatment of particle touchdowns which leads to a significant reduction of CPU time compared to conventional footprint modelling approaches. A comparison with other footprint models (of the analytical and Lagrangian type) suggests that the present backward Lagrangian model provides valid footprint predictions under any stratification and, moreover, for applications that reach across different similarity scaling domains (e.g., surface layer to mixed layer, for use in connection with aircraft measurements or with observations on high towers).     

一次梅雨锋暴雨过程的中尺度特征分析

利用中尺度非静力平衡模式WRF-V2.1对2007年7月7-8日江淮地区一次梅雨锋暴雨过程进行数值模拟,分析其中的中尺度重力波(MGW)特征,并运用拉格朗日Rossby数(Ro)来诊断非平衡流特征.研究表明:这次暴雨过程中的中尺度重力波波长约为56～75 km,相速约12～19 m·s~(-1);在有利的大尺度环流形势下,地转调整机制是MGW产生的首要机制,Wave-CISK和地转调整为波动传播提供了充足的能量,使MGW在具有波导结构的大气中维持了相当长的时间;满足舶指标的不平衡运动区与重力波活动区十分接近,它对波动产生的时间和区域方面有一定的指示作用.     

Estimation of Scalar Source/Sink Distributions in Plant Canopies Using Lagrangian Dispersion Analysis: Corrections for Atmospheric Stability and Comparison with a Multilayer Canopy Model

Source/sink distributions of heat, water vapour andCO₂ within a rice canopy were inferred using aninverse Lagrangian dispersion analysis and measuredmean profiles of temperature, specific humidity andCO₂ mixing ratio. Monin–Obukhov similarity theorywas used to account for the effects of atmosphericstability on _w(z), the standard deviation ofvertical velocity and _L(z), the Lagrangian timescale of the turbulence. Classical surface layer scaling was applied in the inertial sublayer (z > z_ruf)using the similarity parameter = (z - d)/L, where z is height above ground, d is the zero plane displacementheight for momentum, L is the Obukhov length,and z_ruf 2.3h_c, where h_c iscanopy height. A single length scale h_c, was usedfor the stability parameter 3 = h_c/L in the height range 0.25 < z/h_c < 2.5. This choice is justified by mixing layer theory, which shows that within the roughness sublayer there is one dominant turbulence length scaledetermined by the degree of inflection in the windprofile at the canopy top. In the absence of theoretical or experimental evidence for guidance,standard Monin–Obukhov similarity functions, with = h_c/L, were used to calculate the stabilitydependence of _w(z) and _L(z) in the roughness sublayer. For z/h_c < 0.25 the turbulence length and time scales are influenced by the presence of the lowersurface, and stability effects are minimal. With theseassumptions there was excellent agreement between eddycovariance flux measurements and deductions from theinverse Lagrangian analysis. Stability correctionswere particularly necessary for night time fluxes whenthe atmosphere was stably stratified.The inverse Lagrangian analysis provides a useful toolfor testing and refining multilayer canopy models usedto predict radiation absorption, energy partitioningand CO₂ exchanges within the canopy and at thesoil surface. Comparison of model predictions withsource strengths deduced from the inverse analysisgave good results. Observed discrepancies may be dueto incorrect specification of the turbulent timescales and vertical velocity fluctuations close to theground. Further investigation of turbulencecharacteristics within plant canopies is required toresolve these issues.     

周边地区对北京地面SO2影响的初步研究

采用Lagrangian传输、扩散、沉降模式计算了1994年9、10月份(非采暖期)、1995年1月和2000年1月(采暖期)北京地区SO2的变化规律,并分别计算了北京市不同类型的排放源以及周边地区污染源对平均地面SO2浓度的贡献.计算结果与实际观测资料对比表明,模式能够较好地模拟北京地区SO2的浓度量级和逐日变化趋势.北京地区地面SO2浓度受天气条件的影响较大.采暖期,北京当地排放源的影响相对较大;但在大气条件有利输送的背景下,来自周边地区污染排放源的影响不容忽视.     

An Analytical one-Dimensional Second-Order Closure Model of Turbulence Statistics and the Lagrangian Time Scale Within and Above Plant Canopies of Arbitrary Structure

An analytical one-dimensional second-order closure model is developed to describe the within canopy velocity variances, turbulent intensities, dissipation rates, Lagrangian time scale and Lagrangian far field diffusivities for vegetation canopies of arbitrary structure and density. The model incorporates and extends the model of momentum transfer developed by Massman (1997) and the model of within canopy velocity variances developed by Weil (unpublished) from the second-order closure model of Wilson and Shaw (1977). Model predictions of within and above canopy velocity variances, turbulent intensities, dissipation rates and the Lagrangian time scale are in reasonable agreement with previously measured or estimated values for these parameters. The present model suggests that the Lagrangian time scale and the far field diffusivity could be strongly dependent upon foliage structure and density through the foliage effects on the velocity variances. A simple formulation for the Lagrangian time scale at canopy height is derived from model results. Taken as a whole, the present model may provide a relatively simple way to incorporate turbulence parameters into models of soil/canopy/atmosphere mass transfer.     

The Turbulent Lagrangian Time Scale in Forest Canopies Constrained by Fluxes,Concentrations and Source Distributions

One-dimensional Lagrangian dispersion models, frequently used to relate in-canopy source/sink distributions of energy, water and trace gases to vertical concentration profiles, require estimates of the standard deviation of the vertical wind speed, which can be measured, and the Lagrangian time scale, T _L , which cannot. In this work we use non-linear parameter estimation to determine the vertical profile of the Lagrangian time scale that simultaneously optimises agreement between modelled and measured vertical profiles of temperature, water vapour and carbon dioxide concentrations within a 40-m tall temperate Eucalyptus forest in south-eastern Australia. Modelled temperature and concentration profiles are generated using Lagrangian dispersion theory combined with source/sink distributions of sensible heat, water vapour and CO₂. These distributions are derived from a multilayer Soil-Vegetation-Atmospheric-Transfer model subject to multiple constraints: (1) daytime eddy flux measurements of sensible heat, latent heat, and CO₂ above the canopy, (2) in-canopy lidar measurements of leaf area density distribution, and (3) chamber measurements of CO₂ ground fluxes. The resulting estimate of Lagrangian time scale within the canopy under near-neutral conditions is about 1.7 times higher than previous estimates and decreases towards zero at the ground. It represents an advance over previous estimates of T _L , which are largely unconstrained by measurements.     

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.     

浅水波模式半拉格朗日方法的并行研究

该文研究的问题是分布式并行计算机消息传递方式下半拉格朗日并行算法, 重点研究二维浅水波并行模式中有关子区域过渡带(HALO)的问题和有关求解赫姆霍兹方程的并行算法。进行了一系列的对比试验, 研究在不同分辨率下模式的并行效率的问题。结果表明:采用分区域并行计算的方法, 可得到较好的并行效率。模式中使用半拉格朗日方法处理平流项是有利的, 在分辨率高时, 可有效地提高计算速度。