scholarly journals Adaptive stochastic trajectory modelling in the chaotic advection regime

2015 ◽  
Vol 769 ◽  
pp. 1-25 ◽  
Author(s):  
J. G. Esler
Keyword(s):  
Turbulent Flows ◽  
Numerical Estimate ◽  
Accurate Method ◽  
Particle Dispersion ◽  
Transport Problem ◽  
Chaotic Advection ◽  
Back Trajectory ◽  
Tracer Transport ◽  
Lagrangian Simulation ◽  
Main Challenge

Motivated by the goal of improving and augmenting stochastic Lagrangian models of particle dispersion in turbulent flows, techniques from the theory of stochastic processes are applied to a model transport problem. The aim is to find an efficient and accurate method to calculate the total tracer transport between a source and a receptor when the flow between the two locations is weak, rendering direct stochastic Lagrangian simulation prohibitively expensive. Importance sampling methods that combine information from stochastic forward and back trajectory calculations are proposed. The unifying feature of the new methods is that they are developed using the observation that a perfect strategy should distribute trajectories in proportion to the product of the forward and adjoint solutions of the transport problem, a quantity here termed the ‘density of trajectories’ $D(\boldsymbol{x},t)$. Two such methods are applied to a ‘hard’ model problem, in which the prescribed kinematic flow is in the large-Péclet-number chaotic advection regime, and the transport problem requires simulation of a complex distribution of well-separated trajectories. The first, Milstein’s measure transformation method, involves adding an artificial velocity to the trajectory equation and simultaneously correcting for the weighting given to each particle under the new flow. It is found that, although a ‘perfect’ artificial velocity $\boldsymbol{v}^{\ast }$ exists, which is shown to distribute the trajectories according to $D$, small errors in numerical estimates of $\boldsymbol{v}^{\ast }$ cumulatively lead to difficulties with the method. A second method is Grassberger’s ‘go-with-the-winners’ branching process, where trajectories found unlikely to contribute to the net transport (losers) are periodically removed, while those expected to contribute significantly (winners) are split. The main challenge of implementation, which is finding an algorithm to select the winners and losers, is solved by a choice that explicitly forces the distribution towards a numerical estimate of $D$ generated from a previous back trajectory calculation. The result is a robust and easily implemented algorithm with typical variance up to three orders of magnitude lower than the direct approach.

A Modeling Study on Particle Dispersion in Wall-Bounded Turbulent Flows

2014 ◽  
Vol 6 (06) ◽  
pp. 764-782 ◽  
Author(s):  
Jian-Hung Lin ◽  
Keh-Chin Chang
Keyword(s):  
Turbulent Flows ◽  
Particle Dispersion ◽  
Hard Sphere Model ◽  
Wall Roughness ◽  
Mass Loading ◽  
Particle Collisions ◽  
Physical Mechanisms ◽  
Parametric Studies ◽  
Low Mass ◽  
Bounded Particle

AbstractThree physical mechanisms which may affect dispersion of particle’s motion in wall-bounded turbulent flows, including the effects of turbulence, wall roughness in particle-wall collisions, and inter-particle collisions, are numerically investigated in this study. Parametric studies with different wall roughness extents and with different mass loading ratios of particles are performed in fully developed channel flows with the Eulerian-Lagrangian approach. A low-Reynolds-numberk–εturbulence model is applied for the solution of the carrier-flow field, while the deterministic Lagrangian method together with binary-collision hard-sphere model is applied for the solution of particle motion. It is shown that the mechanism of inter-particle collisions should be taken into account in the modeling except for the flows laden with sufficiently low mass loading ratios of particles. Influences of wall roughness on particle dispersion due to particle-wall collisions are found to be considerable in the bounded particle–laden flow. Since the investigated particles are associated with large Stokes numbers, i.e., larger thanO(1), in the test problem, the effects of turbulence on particle dispersion are much less considerable, as expected, in comparison with another two physical mechanisms investigated in the study.

scholarly journals Particle dispersion processes in two-dimensional turbulence: a comparison with 2-D kinematic simulation.

2007 ◽  
Vol 14 (2) ◽  
pp. 139-151 ◽  
Author(s):  
R. Castilla ◽  
J. M. Redondo ◽  
P. J. Gámez-Montero ◽  
A. Babiano
Keyword(s):  
Turbulent Flows ◽  
Particle Dispersion ◽  
Space Time ◽  
Relative Dispersion ◽  
Kinematic Simulation ◽  
Space Time Structure ◽  
Coherent Vortices ◽  
The One ◽  
Turbulent Particle Dispersion ◽  
Kinematic Simulations

Abstract. We study numerically the comparison between Lagrangian experiments on turbulent particle dispersion in 2-D turbulent flows performed, on the one hand, on the basis of direct numerical simulations (DNS) and, on the other hand, using kinematic simulations (KS). Eulerian space-time structure of both DNS and KS dynamics are not comparable, mostly due to the absence of strong coherent vortices and advection processes in the KS fields. The comparison allows to refine past studies about the contribution of non-homogeneous space-time 2-D Eulerian structure on the turbulent absolute and relative particle dispersion processes. We particularly focus our discussion on the Richardson's regime for relative dispersion.

scholarly journals Direct Lagrangian tracking simulation of droplet growth in vertically developing cloud

2018 ◽  
Vol 18 (22) ◽  
pp. 16619-16630 ◽  
Author(s):  
Yuichi Kunishima ◽  
Ryo Onishi
Keyword(s):  
Cloud Condensation Nuclei ◽  
Ground Surface ◽  
Droplet Growth ◽  
Back Trajectory ◽  
Lagrangian Statistics ◽  
Lagrangian Simulation ◽  
Comparison Results ◽  
Snow Crystals ◽  
Lagrangian Tracking ◽  
Condensational Growth

Abstract. We present a direct Lagrangian simulation that computes key warm-rain processes in a vertically developing cloud, including cloud condensation nuclei (CCN) activation, condensational growth, collisional growth, and droplet gravitational settling. This simulation, which tracks the motion and growth of individual particles, is applied to a kinematic simulation of an extremely vertically elongated quasi-one-dimensional domain, after which the results are compared with those obtained from a spectral-bin model, which adopts the conventional Eulerian framework. The comparison results, which confirm good bulk statistical agreement between the Lagrangian and conventional spectral-bin simulations, also show that the Lagrangian simulation is free from the numerical diffusion found in the spectral-bin simulation. After analyzing the Lagrangian statistics of the surface raindrops that reach the ground surface, back-trajectory scrutiny reveals that the Lagrangian statistics of surface raindrops contains the information about the sky where the raindrops grow like the shape does for snow crystals.

scholarly journals Impact of optimized mixing heights on simulated regional atmospheric transport of CO<sub>2</sub>

2014 ◽  
Vol 14 (14) ◽  
pp. 7149-7172 ◽  
Author(s):  
R. Kretschmer ◽  
C. Gerbig ◽  
U. Karstens ◽  
G. Biavati ◽  
A. Vermeulen ◽  
...  
Keyword(s):  
Dispersion Model ◽  
Synthetic Data ◽  
Wrf Model ◽  
Horizontal Resolution ◽  
Particle Dispersion ◽  
Random Errors ◽  
Tracer Transport ◽  
European Continent ◽  
Co2 Transport ◽  
The Impact

Abstract. The mixing height (MH) is a crucial parameter in commonly used transport models that proportionally affects air concentrations of trace gases with sources/sinks near the ground and on diurnal scales. Past synthetic data experiments indicated the possibility to improve tracer transport by minimizing errors of simulated MHs. In this paper we evaluate a method to constrain the Lagrangian particle dispersion model STILT (Stochastic Time-Inverted Lagrangian Transport) with MH diagnosed from radiosonde profiles using a bulk Richardson method. The same method was used to obtain hourly MHs for the period September/October 2009 from the Weather Research and Forecasting (WRF) model, which covers the European continent at 10 km horizontal resolution. Kriging with external drift (KED) was applied to estimate optimized MHs from observed and modelled MHs, which were used as input for STILT to assess the impact on CO2 transport. Special care has been taken to account for uncertainty in MH retrieval in this estimation process. MHs and CO2 concentrations were compared to vertical profiles from aircraft in situ data. We put an emphasis on testing the consistency of estimated MHs to observed vertical mixing of CO2. Modelled CO2 was also compared with continuous measurements made at Cabauw and Heidelberg stations. WRF MHs were significantly biased by ~10–20% during day and ~40–60% during night. Optimized MHs reduced this bias to ~5% with additional slight improvements in random errors. The KED MHs were generally more consistent with observed CO2 mixing. The use of optimized MHs had in general a favourable impact on CO2 transport, with bias reductions of 5–45% (day) and 60–90% (night). This indicates that a large part of the found CO2 model–data mismatch was indeed due to MH errors. Other causes for CO2 mismatch are discussed. Applicability of our method is discussed in the context of CO2 inversions at regional scales.

Two-Particle Dispersion in Isotropic Turbulent Flows

2009 ◽  
Vol 41 (1) ◽  
pp. 405-432 ◽  
Author(s):  
Juan P.L.C. Salazar ◽  
Lance R. Collins
Keyword(s):  
Turbulent Flows ◽  
Particle Dispersion

scholarly journals The backward Îto method for the Lagrangian simulation of transport processes with large space variations of the diffusivity

2007 ◽  
Vol 4 (4) ◽  
pp. 623-652 ◽  
Author(s):  
D. Spivakovskaya ◽  
A. W. Heemink ◽  
E. Deleersnijder
Keyword(s):  
Random Walk ◽  
Turbulent Flows ◽  
Transport Processes ◽  
Test Cases ◽  
Continuous Change ◽  
Smooth Functions ◽  
Large Space ◽  
Lagrangian Simulation ◽  
Itô Calculus ◽  
Ito Method

Abstract. Random walk models are a powerful tool for the investigation of transport processes in turbulent flows. However, standard random walk methods are applicable only when the flow velocities and diffusivity are sufficiently smooth functions. In practice there are some regions where the rapid but continuous change in diffusivity may be represented by a discontinuity. The random walk model based on backward Îto calculus can be used for these problems. This model was proposed by LaBolle et al. (2000). The latter is best suited to the problems under consideration. It is then applied for two test cases with discontinuous diffusivity, highlighting the advantages of this method.

Improved Discrete Random Walk Stochastic Model for Simulating Particle Dispersion and Deposition in Inhomogeneous Turbulent Flows

2020 ◽  
Vol 142 (10) ◽  
Author(s):  
Amir A. Mofakham ◽  
Goodarz Ahmadi
Keyword(s):  
Random Walk ◽  
Turbulent Flows ◽  
Particle Deposition ◽  
Finite Size ◽  
Particle Dispersion ◽  
Concentration Profiles ◽  
Velocity Fluctuations ◽  
Point Particles ◽  
Deposition Velocities ◽  
Gradient Drift

Abstract The performance of different versions of the discrete random walk models in turbulent flows with nonuniform normal root-mean-square (RMS) velocity fluctuations and turbulence time scales were carefully investigated. The OpenFOAM v2−f low Reynolds number turbulence model was used for evaluating the fully developed streamwise velocity and the wall-normal RMS velocity fluctuations profiles in a turbulent channel flow. The results were then used in an in-house matlab particle tracking code, including the drag and Brownian forces, and the trajectories of randomly injected point-particles with diameters ranging from 10 nm to 30 μm were evaluated under the one-way coupling assumption. The distributions and deposition velocities of fluid-tracer and finite-size particles were evaluated using the conventional-discrete random walk (DRW) model, the modified-DRW model including the velocity gradient drift correction, and the new improved-DRW model including the velocity and time gradient drift terms. It was shown that the conventional-DRW model leads to superfluous migration of fluid-point particles toward the wall and erroneous particle deposition rate. The concentration profiles of tracer particles obtained by using the modified-DRW model still are not uniform. However, it was shown that the new improved-DRW model with the velocity and time scale drift corrections leads to uniform distributions for fluid-point particles and reasonable concentration profiles for finite-size heavy particles. In addition, good agreement was found between the estimated deposition velocities of different size particles by the new improved-DRW model with the available data.

The Importance of Mineral Dust and Proteinaceous Ice Nucleating Particles in the Canadian High Artic During the Fall of 2018 

2021 ◽  
Author(s):  
Jingwei Yun ◽  
Erin Evoy ◽  
Soleil Worthy ◽  
Melody Fraser ◽  
Daniel Veber ◽  
...  
Keyword(s):  
Hydrological Cycle ◽  
Mineral Dust ◽  
Dispersion Model ◽  
High Arctic ◽  
Particle Dispersion ◽  
Early Spring ◽  
The Arctic ◽  
Ice Formation ◽  
Back Trajectory ◽  
Early Fall

&lt;p&gt;Ice nucleating particles (INPs) can initiate ice formation in clouds, which has a large impact on the hydrological cycle and radiative budget of the Earth. Constraints on the concentration and composition of INPs are needed to predict ice formation in clouds and hence the climate. Despite previous INP measurements in the Arctic, our understanding of the concentrations, composition, and sources of Arctic INPs is insufficient. Here we report daily concentrations of INPs at Alert, a ground site in the Canadian High Arctic, during October and November of 2018. The contributions of mineral dust and proteinaceous particles to the total INP population were evaluated by testing the responses of the samples to heat and ammonium treatments. Possible source locations of the most effective INPs were investigated using back-trajectory simulations with a Lagrangian particle dispersion model. The results show that the INP concentrations in October were higher than that in November. Combining our results with previous INP measurements at Alert, a seasonal trend was observed for the INP concentrations at -18 &amp;#176;C and -22 &amp;#176;C, with a higher concentration in the late spring, summer and early fall, and a lower concentration in the early spring, late fall, and winter. For the October samples, proteinaceous INPs were detected at T &gt; -21 &amp;#176;C with a fraction of 60% to 100% and mineral dust INPs were detected at T &lt; -21 &amp;#176;C. For the November samples, proteinaceous INPs were only detected at T &gt; -16 &amp;#176;C with a fraction of 88% to 100% and mineral dust INPs were detected at T &lt; -20 &amp;#176;C. The most effective INPs were possibly from South China and California based on 20-day backward simulations using the FLEXible PARTicle dispersion model and the correlations between INP concentrations and Al, , Na&lt;sup&gt;+&lt;/sup&gt;, and Cl&lt;sup&gt;-&lt;/sup&gt; measured at the site.&amp;#160;&amp;#160;&lt;/p&gt;

Unique stochastic Lagrangian particle dispersion models for inhomogeneous turbulent flows

2021 ◽  
Vol 927 ◽  
Author(s):  
J.G. Esler
Keyword(s):  
Angular Momentum ◽  
Turbulent Flows ◽  
Particle Dispersion ◽  
Mean Flow ◽  
Dispersion Models ◽  
Lagrangian Particle ◽  
Mixed Condition ◽  
Unique Model ◽  
Ensemble Mean ◽  
The Mean

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.

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