Lagrangian Stochastic Particle Research Articles

Modeling wind-driven seed dispersal using a coupled Lagrangian particle tracking and 1-D [formula omitted]-[formula omitted] turbulence model

We present a one-dimensional k-ɛ model and a Markov chain stochastic Lagrangian particle tracking model to study wind-driven dispersal of forest and grassland seeds. The turbulence model within and above the canopy is implemented for transient winds so that time series of profiles of mean velocity, turbulence kinetic energy, dissipation rate, and the root-mean-square of fluctuating velocity components can be modeled. We validate the model for steady state conditions using observations in a wide range of canopies, and apply the model for predicting time series of seed dispersal of Andropogon gerardii in a tall grass prairie in Missouri, United States. The stochastic seed dispersal model is validated against experimental data from a Quercus-Carya (oak-hickory) forest where seeds were released from different heights for a range of wind speeds. Using the model, we explore the detailed seed movement trajectories, instantaneous velocities, and investigate the relationship between dispersal distance and the seed falling duration and the mean fluctuating velocity during the falling. Moreover, examining the role of individual turbulent velocity components, we elucidate the different roles of horizontal and vertical velocity fluctuations, i.e., the horizontal component mainly contributes to the seed spreading in the wind direction, while the vertical component enhances the long tail of the distribution in the downstream direction, i.e., promoting long-distance-dispersal of seeds by wind.

Developing a Lagrangian sediment transport model for open channel flows

A three-dimensional stochastic Lagrangian particle tracking sediment transport model is developed to solve the discrete advection–dispersion equation using a combination of empirical dispersion equations. The performance of three widely-used longitudinal dispersion coefficient equations was examined to select one of them as the primary dispersion equation term in the developed model. Also, a conditional empirical equation was used to consider the effect of vertical dispersion term in top layers near the water surface. The performance of particle tracking model (PTM) to calculate the sediment concentration was evaluated for various sediment classes (very fine sand, fine sand, and medium sand) using available laboratory dataset. Multiple statistical measures were calculated using the Taylor diagram for each dispersion equation. Based on the result, the developed particle tracking model estimated the suspended sediment concentration in a rectangular open channel with a correlation coefficient (R) of 0.96, standard deviation (STD) of 0.262, and root mean square deviation (RMSD) of 0.06 for three different sediment classes proving the acceptable accuracy of the developed model for different range of sediment gradations. In addition, the accuracy of PTM was compared to recently developed models. Comparison between the particle tracking model and the analytical solution of the advection–dispersion equation showed that the developed model predicted the maximum concentration of suspended sediment 6% and 9.4% lower than the analytical solution result for 30 and 50 s simulation time in the straight channel, respectively. However, there was a good agreement between the longitudinal and transverse sediment concentration distribution from the model and the analytical solution approach. The result of the sensitivity analysis and validation process showed that the model could be used to simulate sediment transport in open channel flows.

A 3D Lagrangian stochastic particle model for the concentration variance dispersion

A new scheme for the concentration variance calculation is assessed using field experiment data. The scheme is introduced in a Lagrangian stochastic particle model. The model provides run-time mean concentrations and concentrations’ variance 3D fields; thus, it does not need any off-line post-processing. The model is tested against the FFT-07 field experiment which involves a series of tracer releases. It is a short-range (500 m) highly instrumented experiment. In this work, measurement of tracer concentrations, emitted from a ground level point source is used to assess the ability of the new model in predicting the mean concentration, concentration variance, and the concentration fluctuation intensity at the ground level with a high spatial resolution. The results of the intercomparison are shown and discussed in terms of statistical plots and indices.

Employing Spectral Analysis to Obtain Dispersion Parameters in an Atmospheric Environment Driven by a Mesoscale Downslope Windstorm

Considering the influence of the downslope windstorm called “Vento Norte” (VNOR; Portuguese for “North Wind”) in planetary boundary layer turbulent features, a new set of turbulent parameterizations, which are to be used in atmospheric dispersion models, has been derived. Taylor’s statistical diffusion theory, velocity spectra obtained at four levels (3, 6, 14, and 30 m) in a micrometeorological tower, and the energy-containing eddy scales are used to calculate neutral planetary boundary layer turbulent parameters. Vertical profile formulations of the wind velocity variances and Lagrangian decorrelation time scales are proposed, and to validate this new parameterization, it is applied in a Lagrangian Stochastic Particle Dispersion Model to simulate the Prairie Grass concentration experiments. The simulated concentration results were shown to agree with those observed.

Unique stochastic Lagrangian particle dispersion models for inhomogeneous turbulent flows

It is well established that Lagrangian particle dispersion models, for inhomogeneous turbulent flows, must satisfy the ‘well-mixed condition’ of Thomson (J. Fluid Mech., vol. 180, 1987, pp. 529–556) in order to produce physically reasonable results. In more than one dimension, however, the well-mixed condition is not sufficient to define the dispersion model uniquely. The non-uniqueness, which is related to the rotational degrees of freedom of particle trajectories, permits models with trajectory curvatures and velocity autocorrelation functions which are clearly unphysical. A spin condition is therefore introduced to constrain the models. It requires an ensemble of particles with fixed initial position and velocity to have, at short times, expected angular momentum, measured relative to the mean position and velocity of an ensemble of fluid particles with initially random velocity, equal to the relative angular momentum of the mean flow at the ensemble mean location. The resulting unique model is found explicitly for the canonical example of inhomogeneous Gaussian turbulence and is characterised by accelerations which are exponential in the particle velocity. A simpler unique model with a quadratic acceleration is obtained using a weaker version of the spin condition. Unlike previous models, the unique models defined by the spin condition lead to particles having the correct (ensemble mean) angular speed in a turbulent flow in solid-body rotation. The properties of the new models are discussed in the settings of a turbulent channel flow and an idealised turbulent atmospheric boundary-layer flow.

Development of a Backward–Forward Stochastic Particle Tracking Model for Identification of Probable Sedimentation Sources in Open Channel Flow

As reservoirs subject to sedimentation, the dam gradually loses its ability to store water. The identification of the sources of deposited sediments is an effective and efficient means of tackling sedimentation problems. A state-of-the-art Lagrangian stochastic particle tracking model with backward–forward tracking methods is applied to identify the probable source regions of deposited sediments. An influence function is introduced into the models to represent the influence of a particular upstream area on the sediment deposition area. One can then verify if a specific area might be a probable source by cross-checking the values of influence functions calculated backward and forward, respectively. In these models, the probable sources of the deposited sediments are considered to be in a grid instead of at a point for derivation of the values of influence functions. The sediment concentrations in upstream regions must be known a priori to determine the influence functions. In addition, the accuracy of the different types of diffusivity at the water surface is discussed in the study. According to the results of the case study of source identification, the regions with higher sediment concentrations computed by only backward simulations do not necessarily imply a higher likelihood of sources. It is also shown that from the ensemble results when the ensemble mean of the concentration is higher, the ensemble standard deviation of the concentration is also increased.

An Interpolation Method to Reduce the Computational Time in the Stochastic Lagrangian Particle Dispersion Modeling of Spatially Dense XCO2 Retrievals.

A growing constellation of satellites is providing near‐global coverage of column‐averaged CO2 observations. Launched in 2019, NASA’s OCO‐3 instrument is set to provide XCO2 observations at a high spatial and temporal resolution for regional domains (100 × 100 km). The atmospheric column version of the Stochastic Time‐Inverted Lagrangian Transport (X‐STILT) model is an established method of determining the influence of upwind sources on column measurements of the atmosphere, providing a means of analysis for current OCO‐3 observations and future space‐based column‐observing missions. However, OCO‐3 is expected to provide hundreds of soundings per targeted observation, straining this already computationally intensive technique. This work proposes a novel scheme to be used with the X‐STILT model to generate upwind influence footprints with less computational expense. The method uses X‐STILT generated influence footprints from a key subset of OCO‐3 soundings. A nonlinear weighted averaging is applied to these footprints to construct additional footprints for the remaining soundings. The effects of subset selection, meteorological data, and topography are investigated for two test sites: Los Angeles, California, and Salt Lake City, Utah. The computational time required to model the source sensitivities for OCO‐3 interpretation was reduced by 62% and 78% with errors smaller than other previously acknowledged uncertainties in the modeling system (OCO‐3 retrieval error, atmospheric transport error, prior emissions error, etc.). Limitations and future applications for future CO2 missions are also discussed.

Stochastic Lagrangian Path for Leray’s Solutions of 3D Navier–Stokes Equations

In this paper we show the existence of stochastic Lagrangian particle trajectory for Leray's solution of 3D Navier-Stokes equations. More precisely, for any Leray's solution ${\mathbf u}$ of 3D-NSE and each $(s,x)\in\mathbb{R}_+\times\mathbb{R}^3$, we show the existence of weak solutions to the following SDE, which has a density $\rho_{s,x}(t,y)$ belonging to $\mathbb{H}^{1,p}_q$ provided $p,q\in[1,2)$ with $\frac{3}{p}+\frac{2}{q}>4$: $$ \mathrm{d} X_{s,t}={\mathbf u} (s,X_{s,t})\mathrm{d} t+\sqrt{2\nu}\mathrm{d} W_t,\ \ X_{s,s}=x,\ \ t\geq s, $$ where $W$ is a three dimensional standard Brownian motion, $\nu>0$ is the viscosity constant. Moreover, we also show that for Lebesgue almost all $(s,x)$, the solution $X^n_{s,\cdot}(x)$ of the above SDE associated with the mollifying velocity field ${\mathbf u}_n$ weakly converges to $X_{s,\cdot}(x)$ so that $X$ is a Markov process in almost sure sense.

Simulation of a dense gas chlorine release with a Lagrangian particle dispersion model (LPDM)

In 2015, 2016, nine chlorine releases experiments took place at Dugway Proving Ground (Utah, USA). Five trials conducted in 2015 featured a grid of CONEX shipping containers around the release tank to simulate an idealized urban area. The trials were a great occasion to collect data describing the dynamics of “high molecular weight” species in an idealized urban environment.This paper proposes a comparison of the PMSS (Parallel Micro-Swift Micro-Spray) suite against the experimental data from four of the trials, following the choice made by an international model inter-comparison team. PMSS combines two MPI parallelized urban modelling subsystems: (1) PSWIFT phenomenologically accounts for 3D wind flow and turbulence around buildings, and (2) PSPRAY simulates air-based contaminant dispersion in urban areas using a stochastic Lagrangian Particle Dispersion Model.For this comparison, PMSS is deployed first on a hypothetic configuration and compared to the Code_Saturne CFD model, and then using the data of the trials 1, 5, 6 and 7 performed during JRII (Jack Rabbit II) 2015 and 2016. The initial momentum due to the tank discharge and the dense gas and droplet effects of the pressurized chlorine release are modelled using a dedicated radial source term jet and the Glendening equations. In trials 1 and 5, the influence of the CONEX shipping containers on the wind flow and the dispersion is explicitly considered. While spread through a large interval, the chlorine concentrations are computed both in the near field and in the far field (up to 11 km) using PMSS nesting capabilities. The results of the model are compared with the experimental data and sensitivity tests are also presented.

Methane emissions from a waste treatment site: Numerical analysis of aircraft-based data

Methane (CH4) is an important greenhouse gas. Emissions from landfills and waste treatment sites are regarded as the third largest anthropogenic source in the world. Precise estimates of CH4 emissions depend on a well-designed sampling procedure and detailed analyses. This study estimates CH4 emissions from a waste treatment site by analyzing the data from a flight, which was carried out in Eastern Ontario, Canada, on May 6, 2011. The CH4 dispersion plume at about 140 m above ground level downwind of the source is analyzed with data from 14 flight tracks. The observation period of about 72 min is characterized by unstable boundary layer conditions, strong wind, and shifting wind direction. To replicate the boundary layer turbulence and the CH4 dispersion during the measurement period, a combined large-eddy simulation (LES) and Lagrangian stochastic (LS) particle dispersion modeling method is used. A preliminary simulation run with mean meteorological variables during the experiment's duration is carried out. The results reproduced the shifts in wind direction well, in addition to the dispersion plume, but in a smaller magnitude in comparison to the measured data. Therefore, two sets of LES runs are carried out to represent the boundary layer turbulence before and after the wind shift. Another deficiency in the LES runs is that the simulated turbulent velocity variances are systematically smaller than the observed counterparts. In response to this discrepancy, additional terms are incorporated into the LS dispersion model so as to represent the turbulence dispersion process better. With these treatments, the LES-LS modeling results replicated the dispersion plume both in lateral width and in concentration distribution shape. Then, by using the simulated relationship between source and concentrations/vertical fluxes in space, the CH4 emission rate of the site is estimated as 2393 (kg CH4 hr−1) / 2088 (kg CH4 hr−1) respectively.

A fast forecasting method for PM2.5 concentrations based on footprint modeling and emission optimization

We propose a method for fast forecasting of PM2.5 concentrations in the North China Plain based on footprint (source–receptor relationship) modeling and emission inventory inversion. A backward Lagrangian stochastic particle dispersion model was employed to derive the footprint, using meteorological fields and boundary layer parameters provided by the WRF model. An analytical Bayesian inversion model was used to optimize existing emission inventories using long-term, multi-site PM2.5 monitoring data. The fast simulation of PM2.5 concentrations was based on the optimized inventory and the footprint results. Two-year simulations were carried out for six cities (Baoding, Beijing, Dezhou, Shijiazhuang, Tianjin, and Tangshan), with model establishment and emission inversion in the first year (2015) and test forecasting in the second year (2016). Promising simulation results were obtained even when using the primary emission inventory. For all six cities, the fractions of simulations of measurements within a factor of two ranged from 0.49 to 0.68, and the correlation coefficients ranged from 0.40 to 0.56 in 2015. The model also well reproduced temporal variations in PM2.5 concentrations in Beijing during severe haze episodes in the winter of 2015. Great improvement was achieved for the simulations by using the optimized emission inventory. The proportion of samples that met the PM model criteria increased from 88% to 97%, and the proportion that achieved the modeling goal increased from 25% to 44%. This method maintained its high forecasting skill in 2016, with 92% and 46% of samples meeting the PM model criteria and achieving the modeling goal, respectively. However, the corresponding values were86% and 39% if emission optimization was not applied.

A very-high resolution (20m) measurement-based dust emissions and dispersion modeling approach for the Oceano Dunes, California

This study shows the results from very high-resolution (20 m) dust emissions and transport simulations for the Oceano Dunes State Vehicular Recreation Area (ODSVRA), a coastal sand dune complex located in San Luis Obispo County, California. Field data from an enhanced observation period carried out in May–July 2013 helped estimate the emissions and flow conditions over the dune field. Emissions are based on a comprehensive emissions grid developed from in-situ measurements using the Portable In-Situ Wind ERosion Lab (PI-SWERL). PI-SWERL estimates the potential for a soil surface to produce PM10 dust emissions for a range of wind speeds. This approach provided a well-determined PM10 emissions field as a function of time and space. Wind and turbulence fields were estimated using the CALMET diagnostic meteorological model constrained with surface stations, upper air soundings, buoys, and the North American Reanalysis data. Hourly, three-dimensional wind flow and instability objective analysis fields were developed at 20 m resolution in order to consider the complex flow over realistic dune morphology, land use/land cover and terrain characteristics over and around the Oceano Dunes. The dust dispersion simulations were performed using a computationally efficient and vectorized Lagrangian Stochastic Particle Dispersion Model driven by the CALMET output and the PI-SWERL time-space variable emissions. The dispersion model is based on the Langevin formulation and includes the turbulent diffusion and stochastic particle motion (of millions of particles) in the inertial sub-range, and assuming particles as discrete units neglecting deposition. The model estimates diffusion of particles from an initial particle releases that scale according to the PI-SWERL time-variable emissions estimates. Results were then tested at two independent-downwind locations, with positive correlations for flow conditions (R2 = 0.89) and similar receptor PM10 concentrations (R2 = 0.85). Evaluations against those observations during mean flow conditions as well as for elevated dust events suggest that the model framework can capture the spatial and temporal characteristics of mean day-to-day and diurnal PM10 variability. In this study we describe the details of the model framework and its performance as well as its implementation to locate the dust sources that have the strongest impact in the receptor sites and to evaluate the impact of different dust reduction strategies used at the ODSVRA to mitigate PM10 at downwind receptors.

Stochastic Lagrangian particle simulation of air pollution dynamic at mountain base and vicinity

In this work, we investigated the effect of horizontal turbulent diffusion coefficients on the pollution accumulation and distribution near the mountain. The diffusion coefficients, corresponding to variation of wind and particle flow, were considered in three different functions, which are constant, linear decay, and exponential decay function, in governing main simplified cases. In the calculation, the transport of pollution was performed using Lagrangian particle models. The results show that the characteristics of pollution distribution were given by how diffusion coefficients are functioned. Specifically, the non-variant of turbulent diffusion coefficient causes the pollution concentration to get highly accumulated close to the mountain boundary. However, the higher magnitude in non-variant diffusion coefficients allows more turbulences and reflect the highest pollution concentration to step away from the mountain base. Nevertheless, for diffusion coefficient in variant version, the pollution distribution characteristic lies between the low and high non-variant limits, caused by the decay of the diffusion coefficients away from the mountain. However, the exponential decay tends to spread the pollution further out than that of the linear decay due to the abrupt drop of the diffusion coefficients.

Numerical framework for the computation of urban flux footprints employing large-eddy simulation and Lagrangian stochastic modeling

Abstract. Conventional footprint models cannot account for the heterogeneity of the urban landscape imposing a pronounced uncertainty on the spatial interpretation of eddy-covariance (EC) flux measurements in urban studies. This work introduces a computational methodology that enables the generation of detailed footprints in arbitrarily complex urban flux measurements sites. The methodology is based on conducting high-resolution large-eddy simulation (LES) and Lagrangian stochastic (LS) particle analysis on a model that features a detailed topographic description of a real urban environment. The approach utilizes an arbitrarily sized target volume set around the sensor in the LES domain, to collect a dataset of LS particles which are seeded from the potential source area of the measurement and captured at the sensor site. The urban footprint is generated from this dataset through a piecewise postprocessing procedure, which divides the footprint evaluation into multiple independent processes that each yield an intermediate result. These results are ultimately selectively combined to produce the final footprint. The strategy reduces the computational cost of the LES–LS simulation and incorporates techniques to account for the complications that arise when the EC sensor is mounted on a building instead of a conventional flux tower. The presented computational framework also introduces a result assessment strategy which utilizes the obtained urban footprint together with a detailed land cover type dataset to estimate the potential error that may arise if analytically derived footprint models were employed instead. The methodology is demonstrated with a case study that concentrates on generating the footprint for a building-mounted EC measurement station in downtown Helsinki, Finland, under the neutrally stratified atmospheric boundary layer.

Impact Assessment of Pollutant Emissions in the Atmosphere from a Power Plant over a Complex Terrain and under Unsteady Winds

The development of a natural gas-fired tri-generation power plant (520 MW Combined Cycle Gas Turbines + 58 MW Tri-generation) in the Republic of San Marino, a small independent country in Northern Italy, is under assessment. This work investigates the impact of atmospheric emissions of NOx by the plant, under the Italian and European regulatory framework. The impact assessment was performed by the means of the Aria Industry package, including the 3D Lagrangian stochastic particle dispersion model SPRAY, the diagnostic meteorological model SWIFT, and the turbulence model SURFPRO (Aria Technologies, France, and Arianet, Italy). The Republic of San Marino is almost completely mountainous, 10 km west of the Adriatic Sea and affected by land-sea breeze circulation. SPRAY is suitable for simulations under non-homogenous and non-stationary conditions, over a complex topography. The emission scenario included both a worst-case meteorological condition and three 10-day periods representative of typical atmospheric conditions for 2014. The simulated NOx concentrations were compared with the regulatory air quality limits. Notwithstanding the high emission rate, the simulation showed a spatially confined environmental impact, with only a single NOx peak at ground where the plume hits the hillside of the Mount Titano (749 m a.s.l.), 5 km west of the future power plant.

A Lagrangian fluctuation–dissipation relation for scalar turbulence. Part I. Flows with no bounding walls

An exact relation is derived between scalar dissipation due to molecular diffusivity and the randomness of stochastic Lagrangian trajectories for flows without bounding walls. This ‘Lagrangian fluctuation–dissipation relation’ equates the scalar dissipation for either passive or active scalars to the variance of scalar inputs associated with initial scalar values and internal scalar sources, as these are sampled backward in time by the stochastic Lagrangian trajectories. As an important application, we reconsider the phenomenon of ‘Lagrangian spontaneous stochasticity’ or persistent non-determinism of Lagrangian particle trajectories in the limit of vanishing viscosity and diffusivity. Previous work on the Kraichnan (Phys. Fluids, 1968, vol. 11, pp. 945–953) model of turbulent scalar advection has shown that anomalous scalar dissipation is associated in that model with Lagrangian spontaneous stochasticity. There has been controversy, however, regarding the validity of this mechanism for scalars advected by an actual turbulent flow. We here completely resolve this controversy by exploiting the fluctuation–dissipation relation. For either a passive or an active scalar advected by any divergence-free velocity field, including solutions of the incompressible Navier–Stokes equation, and away from walls, we prove that anomalous scalar dissipation requires Lagrangian spontaneous stochasticity. For passive scalars, we prove furthermore that spontaneous stochasticity yields anomalous dissipation for suitable initial scalar fields, so that the two phenomena are there completely equivalent. These points are illustrated by numerical results from a database of homogeneous isotropic turbulence, which provide both additional support to the results and physical insight into the representation of diffusive effects by stochastic Lagrangian particle trajectories.

Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics.

In Holm (Holm 2015 Proc. R. Soc. A 471, 20140963. (doi:10.1098/rspa.2014.0963)), stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics naturally arises in a multi-scale decomposition of the deterministic Lagrangian flow map into a slow large-scale mean and a rapidly fluctuating small-scale map. We employ homogenization theory to derive effective slow stochastic particle dynamics for the resolved mean part, thereby obtaining stochastic fluid partial equations in the Eulerian formulation. To justify the application of rigorous homogenization theory, we assume mildly chaotic fast small-scale dynamics, as well as a centring condition. The latter requires that the mean of the fluctuating deviations is small, when pulled back to the mean flow.

Experimental evaluation of flux footprint models

In this study we experimentally evaluate analytical flux footprint models, as well as models based on Lagrangian stochastic particle dispersion. For this purpose, we conducted tracer experiments at a grassland site in southern Germany. An artificial tracer was released continuously over a number of flux-averaging intervals from a surface source. The flux contributions from the tracer source were measured by eddy covariance and compared to those predicted by footprint models. Furthermore, an additional eddy covariance measurement tower was used to evaluate the along-wind distribution of footprint models, as well as to analyze to what extent a forest edge upwind of the measurement tower affects model performance. Additionally, we quantify footprint model uncertainty resulting from the random error of input parameters.Our measurements show that all evaluated models match observations roughly, but tend to underestimate the value of the footprint maximum, and overestimate its distance. The analysis of stability dependence of model performances indicates that one model, based on simulation outputs of a Lagrangian stochastic model, clearly underestimates observations for near neutral to stable conditions, while no clear stability dependence could be identified for the performance of the other models.As expected, model performance is sensitive to an abrupt change in surface roughness and sensible heat flux at a forest edge in the near upwind fetch of the measurement tower. Using the local apparent roughness length (derived from measured wind speed and friction velocity) only slightly or negligibly improved model performance compared to the use of a constant local roughness length (determined from local surface characteristics). Thus we confirm experimentally that footprint estimates and related data quality assessments should be handled with care at sites with inhomogeneities in surface roughness.

The role of inter-particle collisions on elbow erosion

Erosion due to particle impingement, which can occur in a variety of practical cases, is often the key factor in pipeline failure. Parts such as elbows, for instance, are particularly prone to erosion issues. In this work, the Unsteady Reynolds Averaged Navier–Stokes (URANS) equations are combined with a stochastic Lagrangian particle tracking scheme considering all relevant elementary processes (drag and lift forces, particle rotation, inter-particle collisions, particle-wall interactions, coupling between phases) to numerically predict the erosion phenomenon on a 90° elbow pipe. After a detailed validation of the erosion model based on the experimental data of Solnordal et al. (2015), several cases regarding the wall roughness and static and dynamic coefficients of friction are analysed to elucidate the nature of the erosive process. For such analysis, more fundamental variables related to particle-wall interactions (impact velocity, impact angle, impact frequency) were used to scrutinize the basic erosion mechanisms. Finally, to prove the importance of inter-particle collision on elbow erosion, different mass loadings are additionally simulated. Especially for the high mass loading cases, interesting results about the role of the inter-particle collisions on elbow erosion are enlightened.

Target Lagrangian kinematic simulation for particle-laden flows.

The target Lagrangian kinematic simulation method was motivated as a stochastic Lagrangian particle model that better synthesizes turbulence structure, relative to stochastic separated flow models. By this method, the trajectories of particles are constructed according to synthetic turbulent-like fields, which conform to a target Lagrangian integral timescale. In addition to recovering the expected Lagrangian properties of fluid tracers, this method is shown to reproduce the crossing trajectories and continuity effects, in agreement with an experimental benchmark.