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1.
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  相似文献   

2.
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.  相似文献   

3.
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.  相似文献   

4.
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.  相似文献   

5.
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.  相似文献   

6.
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.  相似文献   

7.
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.  相似文献   

8.
In a turbulent fluid, the time a particle needs to travel from a point source to the observation point, can be considered as a random variable. It is shown that the probability density function (pdf) for this random variable is determined by the Lagrangian particle position pdf. The characteristics of the transport time pdf are discussed for the simple case of a turbulent fluid moving with a constant mean velocity.  相似文献   

9.
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.  相似文献   

10.
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 > zruf)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 zruf 2.3hc, where hc iscanopy height. A single length scale hc, was usedfor the stability parameter 3 = hc/L in the height range 0.25 < z/hc < 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 = hc/L, were used to calculate the stabilitydependence of w(z) and L(z) in the roughness sublayer. For z/hc < 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.  相似文献   

11.
A new solution is presented to the problem ofrelating source strength and concentration profiles within a plant canopy. The solution is based on the Lagrangian dispersion theory developed by G. I. Taylor in 1921. A dispersion matrix is derived that relates the source and concentration profiles based on profiles of the turbulent length and velocity scales. The matrix translates the effects of persistence (a temporal effect) into spatialcoordinates and represents the change from near-field to far-field in acontinuous fashion, successfully accounting for both regimes. A test ofthe new model using wind-tunnel data showed excellent quantitative agreement between model and measurements. A comparison was also made withM. R. Raupach's localized near-field theory, which underestimated the near-field effect in the wind-tunnel data and relative to the new model.  相似文献   

12.
A number of authors have reported the problem of unrealistic velocities (“rogue trajectories”) when computing the paths of particles in a turbulent flow using modern Lagrangian stochastic (LS) models, and have resorted to ad hoc interventions. We suggest that this problem stems from two causes: (1) unstable modes that are intrinsic to the dynamical system constituted by the generalized Langevin equations, and whose actual triggering (expression) is conditional on the fields of the mean velocity and Reynolds stress tensor and is liable to occur in complex, disturbed flows (which, if computational, will also be imperfect and discontinuous); and, (2) the “stiffness” of the generalized Langevin equations, which implies that the simple stochastic generalization of the Euler scheme usually used to integrate these equations is not sufficient to keep round-off errors under control. These two causes are connected, with the first cause (dynamical instability) exacerbating the second (numerical instability); removing the first cause does not necessarily correct the second, and vice versa. To overcome this problem, we introduce a fractional-step integration scheme that splits the velocity increment into contributions that are linear (U i ) and nonlinear (U i U j ) in the Lagrangian velocity fluctuation vector U, the nonlinear contribution being further split into its diagonal and off-diagonal parts. The linear contribution and the diagonal part of the nonlinear contribution to the solution are computed exactly (analytically) over a finite timestep Δt, allowing any dynamical instabilities in the system to be diagnosed and removed, and circumventing the numerical instability that can potentially result in integrating stiff equations using the commonly applied explicit Euler scheme. We contrast results using this and the primitive Euler integration scheme for computed trajectories in a drastically inhomogeneous urban canopy flow.  相似文献   

13.
This work re-examines and further develops an analytical solution for the deposition swath of heavy particles released in the atmosphere from an elevated source over uniform terrain, correcting the particle diffusivity for the crossing trajectory effect. The revised (approximate) analytical solution proves to be accurate within 20% over a wide range of micrometeorological conditions and particle size, despite its neglect of the turbulence component of the deposition flux. It compares very satisfactorily with experimental data and with the simulations of a Lagrangian stochastic model, provided the variable U(H)/w g ≤7 (ratio of the mean horizontal wind speed at source height to the particle settling velocity). In this domain of validity, simple formulae relating the statistics of the deposition swath to U(H)/w g are derived.  相似文献   

14.
Atmospheric turbulence was measured within a black spruce forest, a jack pine forest, and a trembling aspen forest, located in southeastern Manitoba, Canada. Drag coefficients (C d ) varied little with height within the pine and aspen canopies, but showed some height dependence within the dense spruce canopy. A constant C d of 0.15, with the measured momentum flux and velocity profiles, gave good estimates of leaf-area-index (LAI) profiles for the pine and aspen canopies, but underestimated LAI for the spruce canopy.Velocity spectra were scaled using the Eulerian integral time scales and showed a substantial inertial subrange above the canopies. In the bottom part of the canopies, the streamwise and cross-stream spectra showed rapid energy loss whereas the vertical spectra showed an apparent energy gain, in the region where the inertial subrange is expected. The temperature spectra showed an inertial subrange with the expected -2/3 slope at all heights. Cospectra of momentum and heat flux had slopes of about -1 in much of the inertial subrange. Possible mechanisms to explain some of the spectral features are discussed.  相似文献   

15.
When modelling the turbulent dispersion of a passive tracer using Reynolds-averaged Navier–Stokes (RANS) simulations, two different approaches can be used. The first consists of solving a transport equation for a scalar, where the governing parameters are the mean velocity field and the turbulent diffusion coefficient, given by the ratio of the turbulent viscosity and the turbulent Schmidt number Sc t . The second approach uses a Lagrangian particle tracking algorithm, where the governing parameters are the mean velocity and the fluctuating velocity field, which is determined from the turbulence kinetic energy and the Lagrangian time T L . A comparison between the two approaches and wind-tunnel data for the dispersion in the wake of a rectangular building immersed in a neutral atmospheric boundary layer (ABL) is presented. Particular attention was paid to the influence of turbulence model parameters on the flow and concentration field. In addition, an approach to estimate Sc t and T L based on the calculated flow field is proposed. The results show that applying modified turbulence model constants to enable correct modelling of the ABL improves the prediction for the velocity and concentration fields when the modification is restricted to the region for which it was derived. The difference between simulated and measured concentrations is smaller than 25% or the uncertainty of the data on 76% of the points when solving the transport equation for a scalar with the proposed formulation for Sc t , and on 69% of the points when using the Lagrangian particle tracking with the proposed formulation for T L .  相似文献   

16.
Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of large-eddy simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turn out to be compatible with the Richardson t3 law for the average of square particle separation, where t is time. This emerges from the application of non-standard methods of analysis through which a precise measure of the Richardson constant was also possible. Its value is estimated as C2 0.5, in close agreement with recent experiments and three-dimensional direct numerical simulations.  相似文献   

17.
A new method for obtaining instantaneous vertical profiles of two components of velocity and temperature in thermally stratified turbulent shear flows is presented. In this report, the design and construction of the traversing system will be discussed and results to date will be presented. The method is based on rapid vertical sampling whereby probe sensors are moved vertically at a high speed such that the measurement is approximately instantaneous. The system is designed to collect many measurements for the calculation of statistics such as vertical wave number spectra, mean square vertical gradients, and Thorpe scales. Results are presented for vertical profiles of temperature and compared to vertical profiles measured by single-point Eulerian time averages. The quality of the vertical profiles is found to be good over many profiles. Some comparisons are made between vertical measurements and standard single-point Eulerian measurements for three cases of stably stratified turbulent shear flow in which the initial microscale Reynolds number, Reλ≈30. In case 1, the mean conditions are characterized by a gradient Richardson number, Rig=0.015, for which the flow is “unstable”, meaning the spatially evolving turbulent kinetic energy (Ek) grows. In case 2, Rig=0.095, for which the evolving turbulent kinetic energy is almost constant. In case 3, the flow is highly stable, where Rig=0.25 and Ek decays with spatial evolution. The measurements indicate anisotropy in the small scales for all cases. In particular, it is found that the ratio grows initially to a maximum and then decays with further evolution. Maximum Thorpe displacements are measured and compared to single-point measures of the vertical scales. It is found that vertical length scales derived from single-point measurements, such as the Ozmidov scale, LO=(ε/N3)1/2 and the overturn scale, Lt=θ′/(dT/dz), do not represent well the wide range of overturning scales which are actually present in the turbulence.  相似文献   

18.
Well-mixed, first-order Lagrangian stochastic (LS) particle trajectory models are derived from several idealized (“toy”) turbulent velocity distributions, and their performance is compared against the observations of Project Prairie Grass, i.e., the case of a continuous point source of tracer near the ground, in the horizontally homogeneous and neutrally stratified surface layer. Although in a context of limited information a Gaussian distribution is the preferred choice, and although the Gaussian corresponds to the simplest of this set of LS models (namely, the Langevin equation), models stemming from other velocity distributions give similar, albeit distinguishable, predictions.  相似文献   

19.
Two simple analytical Lagrangian and a Lagrangian random walk model,together with three options for the parameterisation of the Lagrangian timescale, are compared in their ability to predict fluxes and scalar concentrationsof CO2, H2O and sensible heat within and above a mountain meadowin the eastern Alps. Results indicate that both scalar concentrations and ecosystemfluxes exhibit little sensitivity to the differences between the investigated modelsand may be predicted satisfactorily by one of the simpler models so long as thesource/sink strength is parameterised correctly. Model results also show littlesensitivity to the parameterisation of the vertical variation of the Lagrangiantime scale, yet the increase of the Lagrangian time scale towards the groundpredicted by one of the three investigated parameterisation options resulted inless agreement with measurements as compared to the other two, which assumedthe Lagrangian time scale to be either constant with height or to decay towardszero at the ground surface. Correspondence between simulated and measuredfluxes and scalar concentrations of CO2, H2O and sensible heat weregenerally satisfactory, except for shortly after the meadow was cut, when thesignificant increase of respiratory carbon losses could not be captured by themodel.  相似文献   

20.
Statistics of atmospheric turbulence within and above a corn canopy   总被引：1，自引：2，他引：1  
Two three-dimensional split-film anemometers were used to measure turbulence statistics within and above a corn canopy. Normalised profiles of mean windspeed, root-mean-square velocity, momentum flux, and heat flux were constructed from half-hourly averages by dividing within-canopy measurements by the simultaneous canopy-top measurement. With the exception of the heat flux, these profiles showed consistent shape from day to day. Time series of the three velocity components were recorded on magnetic tape and subsequently analysed to obtain Eulerian time and length scales and the power spectrum of each component at several heights. The timescale was found to have a local minimum value at the top of the canopy. However the length scale L wformed from the timescale and the root-mean-square vertical velocity varied with height as L w 0.1 z. The power-spectra were non-dimensionalised to facilitate comparison of spectra at different heights and times. All spectra had -5/3 regions spanning at least two decades in frequency.  相似文献   

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