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1.
It is shown how the correspondence between Lagrangian stochasticmodels and second-moment closures of the scalar-flux equation can be exploited to distinguishbetween Lagrangian stochastic models in the well-mixed class. It is found that physically realisticclosures of the scalar-flux equation correspond to Lagrangian stochastic models that have non-zero`spin' and so produce spiralling tracer-particle trajectories, whilst `zero-spin'models correspond to the isotropic-production model of scalar-fluxes.Lagrangian stochastic models consistent with rapid distortion theory and Speziale's transformation rule for the Reynolds stressequations in the extreme limit of two-dimensional turbulence are also shown to have non-zero spin.The residual non-uniqueness associated with satisfaction of thewell-mixed condition and the specification of mean spin is shown to be related to the helicity oftracer-particle trajectories. Investigations are also made of the influence upon turbulent dispersion oftime-dependent spin and of mean rotations of the fluctuating Lagrangian acceleration vector(i.e., second-order spin).  相似文献   

2.
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   

3.
The planetary boundary layer (PBL) differs from other simple boundary layers in that it forms on the earth's rotating surface. While the effect of the earth's rotation on the mean wind vector of the PBL is well known, the rotational influence on PBL turbulence is not yet established. In the present work, the latter effect is investigated using numerical models that account for the influence of the earth's rotation on the turbulence. It is found that the earth's rotational influence on PBL turbulence is negligible, and therefore does not need to be included in turbulence models used to simulate PBL flows.  相似文献   

4.
By integrating the Fokker-Planck equation corresponding to a Lagrangian stochastic trajectory model, which is consitent with the selection criterion of Thomson (1987), an analytical solution is given for the joint probability density functionp(xi, ui, t) for the position (x i) and velocity (u i) at timet of a neutral particle released into linearly-sheared, homogeneous turbulence. The solution is compared with dispersion experiments conforming to the restrictions of the model and with a shortrange experiment performed in highly inhomogeneous turbulence within and above a model crop canopy. When the turbulence intensity, wind shear and covariance are strong, the present solution is better than simpler solutions (Taylor, 1921; Durbin, 1983) and as good as any numerical Lagrangian stochastic model yet reported.  相似文献   

5.
A Lagrangian Decorrelation Time Scale in the Convective Boundary Layer   总被引：1，自引：1，他引：0  
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 Bi, 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.  相似文献   

6.
Abstract

We analyse the trajectories of 24 deep‐drogued, satellite‐tracked drifters launched between 50 and 52°N in the northeast Pacific during June and October 1987. Three aspects of the observed motions at the drogue depths of 100 to 120 m are studied: (i) the spatial structure of the mean and variance velocity fields; (ii) the dispersion and eddy diffusion characteristics of the fluctuating motions; and (iii) the properties of selected mesoscale eddies.

The mean Lagrangian velocity field is consistent with the mean flow pattern derived from the historical dynamic height topography. Fluctuating motions within the region are dominated by mesoscale eddies and meanders. Several instances of persistent O(100 days) westward flowing countercurrents were also observed. Based on the Lagrangian integral time‐ and length scales, drifter motions become decorrelated within a period of 10 days and a separation of 100 km. The mean zonal and meridional integral time‐scales of 4.5 and 3.6 days, respectively, are nearly identical with those obtained by Krauss and Böning (1987) from deep‐drogued drifter tracks in the North Atlantic. Because of the relatively small (<100 cm2 s?2) kinetic energy values in the northeast Pacific, the corresponding mean Lagrangian length scales of 29.4 and 29.9 km are roughly half those for the Atlantic.

The observed drifter dispersion is generally consistent with Taylor's (1921) theory for single‐particle dispersion in homogeneous isotropic turbulence. Estimates obtained using 476 pseudo‐drifter tracks generated from the original records indicate that the dispersion increases linearly with time, t, within the first 3 to 5 days of launch and subsequently increases as t1/2 (the random‐walk regime) within 10 days of launch. The respective peak zonal and meridional eddy diffusion coefficients of 4.1 × and 3.8 × 107 cm2 s?1 are reached within 30 days of deployment. Similar estimates for the peak eddy diffusivities are obtained using dispersion curves for sets of 4 drifters launched at the same location during the June and October deployments. The dispersion of these clusters followed an exponential rather than a t1/2 dependence over the first 70 days after release.

Eddies are predominantly clockwise rotary and are characterized by radii of 26 ± 16 km, periods of rotation of 16.0 ± 5.2 days, and azimuthal current speeds of 12.7 ± 8.6 cm s?1. One eddy was tracked for over 10 months. Oceanographic data collected during the October deployment period showed the eddies have vertical extents of 500 to 700 m and are linked to isotherm depressions of over 100 m in the main pycnocline. All eddies in the bifurcation zone propagate to the west at roughly 1.5 ± 0.4 cm s?1 counter to the prevailing mean flow and winds. These speeds are consistent with the westward phase speeds of first mode baroclinic planetary (Rossby) waves.  相似文献   

7.
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   

8.
Lagrangian stochastic models, quadratic in velocity and satisfying the well-mixed condition for two-dimensional Gaussian turbulence, are used to make predictions of scalar dispersion within a model plant canopy. The non-uniqueness associated with satisfaction of the well-mixed condition is shown to be non-trivial (i.e. different models produce different predictions for scalar dispersion). The best agreement between measured and predicted mean concentrations of scalars is shown to be obtained with a small sub-class of optimal models. This sub-class of optimal models includes Thomson's model (J. Fluid Mech. 180, 529–556, 1987), the simplest model that satisfies the well-mixed condition for Gaussian turbulence, but does not include two other models identified recently as being in optimal agreement with the measured spread of tracers in a neutral boundary layer. It is therefore demonstrated that such models are not universal, i.e. applicable to a wide range of flows without readjustment of model parameters. Predictions for scalar dispersion in the model plant canopy are also obtained using the model of Flesch and Wilson (Boundary-Layer Meteorol. 61, 349–374, 1992). It is shown that, when used with a Gaussian velocity distribution or a maximum-missing-information velocity distribution, which accounts for the measured skewness and kurtosis of velocity statistics, the agreement between predictions obtained using the model of Flesch and Wilson and measurements is as good as that obtained using Thomson's model.  相似文献   

9.
The problem of boundary conditions for the variances and covariances of scalar quantities (e.g., temperature and humidity) at the underlying surface is considered. If the surface is treated as horizontally homogeneous, Monin–Obukhov similarity suggests the Neumann boundary conditions that set the surface fluxes of scalar variances and covariances to zero. Over heterogeneous surfaces, these boundary conditions are not a viable choice since the spatial variability of various surface and soil characteristics, such as the ground fluxes of heat and moisture and the surface radiation balance, is not accounted for. Boundary conditions are developed that are consistent with the tile approach used to compute scalar (and momentum) fluxes over heterogeneous surfaces. To this end, the third-order transport terms (fluxes of variances) are examined analytically using a triple decomposition of fluctuating velocity and scalars into the grid-box mean, the fluctuation of tile-mean quantity about the grid-box mean, and the sub-tile fluctuation. The effect of the proposed boundary conditions on mixing in an archetypical stably-stratified boundary layer is illustrated with a single-column numerical experiment. The proposed boundary conditions should be applied in atmospheric models that utilize turbulence parametrization schemes with transport equations for scalar variances and covariances including the third-order turbulent transport (diffusion) terms.  相似文献   

10.
A three-dimensional Lagrangian stochastic (LS) model to evaluate pollutant dispersion in the atmospheric boundary layer has been developed. The model satisfies the well-mixed criterion of Thomson and allows for inhomogeneous, skew turbulence. Making use of the spherical reference frame, one of the possible solutions has been obtained. A skewed joint probability density function (PDF), which reproduces the given velocity moments (means, variances, skewness and covariances), has been built-up by a linear combination of eight Gaussian PDFs. In order to verify consistency with the well-mixed criterion, the long term results have been compared with the theoretical behaviour. A comparison between our model and Thomson's published algorithms was also carried out. By comparing wind-tunnel data and numerical predictions, a further validation of our LS model has been obtained. From an analysis of the numerical results, we can state that our model is able to evaluate dispersion in the case of complex flows where the application of previous models is unsuccessful.  相似文献   

11.
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   

12.
Thermal internal boundary layers in onshore air flows have a significant influence on pollutant diffusion in coastal areas. Although several models for this diffusion problem exist, measurements for model verification are scarce. In this paper, we present a set of wind tunnel observations and examine the performance of a Lagrangian stochastic model. The good agreement between the model simulation and the tunnel measurements confirms the usefulness of the Lagrangian stochastic model for practical purposes. Sensitivity tests of the model to turbulence statistics show that uncertainty in velocity skewness to the extent of observational scatter does not seem to have a significant influence on pollutant dispersion, while uncertainties in turbulence intensity (variance) significantly influence the dispersion pattern.  相似文献   

13.
A study of the neutrally-stratified flow within and over an array of three-dimensional buildings (cubes) was undertaken using simple Reynolds-averaged Navier—Stokes (RANS) flow models. These models consist of a general solution of the ensemble-averaged, steady-state, three-dimensional Navier—Stokes equations, where the k-ε turbulence model (k is turbulence kinetic energy and ε is viscous dissipation rate) has been used to close the system of equations. Two turbulence closure models were tested, namely, the standard and Kato—Launder k-ε models. The latter model is a modified k-ε model designed specifically to overcome the stagnation point anomaly in flows past a bluff body where the standard k-ε model overpredicts the production of turbulence kinetic energy near the stagnation point. Results of a detailed comparison between a wind-tunnel experiment and the RANS flow model predictions are presented. More specifically, vertical profiles of the predicted mean streamwise velocity, mean vertical velocity, and turbulence kinetic energy at a number of streamwise locations that extend from the impingement zone upstream of the array, through the array interior, to the exit region downstream of the array are presented and compared to those measured in the wind-tunnel experiment. Generally, the numerical predictions show good agreement for the mean flow velocities. The turbulence kinetic energy was underestimated by the two different closure models. After validation, the results of the high-resolution RANS flow model predictions were used to diagnose the dispersive stress, within and above the building array. The importance of dispersive stresses, which arise from point-to-point variations in the mean flow field, relative to the spatially-averaged Reynolds stresses are assessed for the building array.  相似文献   

14.
Large eddy simulation has encountered difficulties in handling turbulence in the atmospheric surface layer due to deficiencies in sub-grid scale models. This paper addresses the possibility of resolving the turbulence in the upper part of the surface layer by a low-aspect ratio of grid spacing. Results show that resolved-scale shear stresses dominate over the sub-grid scale components so that effects due to the sub-grid scale model can be ignored in this region. The effects of the lower boundary condition on the resolved-scale turbulence in the upper part of the surface layer are discussed. It is concluded that the normalized mean velocity shear and resolved turbulence in the upper part of the surface layer are not affected by the specification of the lower boundary condition. In addition, the present work proposes a new independent model parameter, the Smagorinsky Reynolds Number (ReSM), and demonstrates that this number determines the resolved turbulence in the upper part of the surface layer.  相似文献   

15.
A Random Displacement Model (RDM) and a Langevin Equation Model (LEM) are used to simulate point releases in a complex flow around a building. The flow field is generated by a three-dimensional finite element model that uses the standardk- model to parameterize the turbulence. The RDM- and LEM-calculated concentration fields are compared, with particular emphasis on the structure in regions with high turbulence and/or recirculation. RDM and LEM results are similar qualitatively, but RDM tends to predict lower concentration levels. In part this is due to the higher early-time diffusion. However, the expected convergence at later times is prevented by the interaction of the diffusion with the strongly inhomogeneous mean flow.Notation a i coefficient in the Langevin equation - b ij coefficient in the Langevin equation - C 0 the universal constant associated with the Lagrangian structure function - H building height (22.5 m) - K eddy viscosity - K k eddy viscosity used in the definition of the off-diagonal Reynolds stresses - k turbulent kinetic energy - LEM Langevin Equation Model - p 1 local unit vector in thexy-plane, orthogonal tos - p 2 local unit vector, orthogonal to boths andp 1 - RDM Random Displacement Model - s local unit vector in the streamline direction - T local decorrelation time (Lagrangian time scale) - U magnitude of the local Eulerian mean wind velocity - u s total velocity in the streamline direction - u 1 velocity component in thexy-plane, orthogonal to the streamline direction - u 2 velocity component orthogonal to bothu s andu 1 - i mean Eulerian wind velocity - W i stochastic vector-valued Wiener process - x unit vector inx-direction - y unit vector iny-direction - z unit vector inz-direction - angle between thexy-plane and the mean wind streamline - angle between the projection in thexy-plane of the streamline and thex-axis - ij the Kronecker delta function - rate of turbulence dissipation - i/ga the part ofa i that contains mean wind and turbulence gradients - ij inverse of a Reynolds stress tensor component - ij shorthand for a quantity that defines a part of i/ga - i shorthand for a quantity that defines a part of i/ga - ij Reynolds stress tensor component  相似文献   

16.
A large-eddy simulation (LES) with the dynamic Smagorinsky-Germano subgrid-scale (SGS) model is used to study the dispersion of solid particles in a turbulent boundary layer. Solid particles are tracked in a Lagrangian way. The instantaneous velocity of the surrounding fluid is considered to have a large-scale part (directly computed by the LES) and a small-scale part. The SGS velocity of the surrounding fluid is given by a three-dimensional Langevin model written in terms of SGS statistics at a mesh level. An appropriate Lagrangian correlation time scale is considered in order to include the influences of gravity and inertia of the solid particle. Inter-particle collisions and the influence of particles on the mean flow are also taken into account. The results of the LES are compared with the wind-tunnel experiments of Nalpanis et al. (1993 J Fluid Mech 251: 661–685) and of Tanière et al. (1997 Exp in Fluids 23:463–471) on sand particles in saltation and in modified saltation, respectively.  相似文献   

17.
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   

18.
The joint concentration probability density function of two reactive chemical species is modelled using a bivariate Gamma distribution coupled with a three-dimensional fluctuating plume model able to simulate the diffusion and mixing of turbulent plumes. A wind-tunnel experiment (Brown and Bilger, J Fluid Mech 312:373–407, 1996), carried out in homogeneous unbounded turbulence, in which nitrogen oxide is released from a point source in an ozone doped background and the chemical reactions take place in non-equilibrium conditions, is considered as a test case. The model is based on a stochastic Langevin equation reproducing the barycentre position distribution through a proper low-pass filter for the turbulence length scales. While the meandering large-scale motion of the plume is directly simulated, the internal mixing relative to the centroid is reproduced using a bivariate Gamma density function. The effect of turbulence on the chemical reaction (segregation), which in this case has not yet attained equilibrium, is directly evaluated through the covariance of the tracer concentration fields. The computed mean concentrations and the O3–NO concentration covariance are also compared with those obtained by the Alessandrini and Ferrero Lagrangian single particle model (Alessandrini and Ferrero, Physica A 388:1375–1387, 2009) that entails an ad hoc parametrization for the segregation coefficient.  相似文献   

19.
Large-Eddy Simulation of Stably-Stratified Flow Over a Steep Hill   总被引：1，自引：1，他引：0  
Large-eddy simulation (LES) is used to simulate stably-stratified turbulent boundary-layer flow over a steep two-dimensional hill. To parametrise the subgrid-scale (SGS) fluxes of heat and momentum, three different types of SGS models are tested: (a) the Smagorinsky model, (b) the Lagrangian dynamic model, and (c) the scale-dependent Lagrangian dynamic model (Stoll and Porté-Agel, Water Resour Res 2006, doi:). Simulation results obtained with the different models are compared with data from wind-tunnel experiments conducted at the Environmental Flow Research Laboratory (EnFlo), University of Surrey, U.K. (Ross et al., Boundary-Layer Meteorol 113:427–459, 2004). It is found that, in this stably-stratified boundary-layer flow simulation, the scale-dependent Lagrangian dynamic model is able to account for the scale dependence of the eddy-viscosity and eddy-diffusivity model coefficients associated with flow anisotropy in flow regions with large mean shear and/or strong flow stratification. As a result, simulations using this tuning-free model lead to turbulence statistics that are more realistic than those obtained with the other two models.  相似文献   

20.
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).  相似文献   

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