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Journal ArticleDOI

Criteria for the selection of stochastic models of particle trajectories in turbulent flows

David J. Thomson1
01 Jul 1987-Journal of Fluid Mechanics (Cambridge University Press)-Vol. 180, Iss: -1, pp 529-556
TL;DR: In this paper, the relationships between the various criteria are examined for a very general class of models and it is shown that most of the criteria are equivalent and also how a model can be designed to satisfy these criteria exactly and to be consistent with inertial-subrange theory.
Abstract: Many different random-walk models of dispersion in inhomogeneous or unsteady turbulence have been proposed and several criteria have emerged to distinguish good models from bad. In this paper the relationships between the various criteria are examined for a very general class of models and it is shown that most of the criteria are equivalent. It is also shown how a model can be designed to satisfy these criteria exactly and to be consistent with inertial-subrange theory. Some examples of models that obey the criteria are described. As an illustration some calculations of dispersion in free-convective conditions are presented.
Citations
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Journal ArticleDOI
TL;DR: The Lagrangian particle dispersion model FLEXPART was originally designed for calculating the long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant.
Abstract: The Lagrangian particle dispersion model FLEXPART was originally (about 8 years ago) designed for calculating the long-range and mesoscale dispersion of air pollutants from point sources, such as after an accident in a nuclear power plant In the meantime FLEXPART has evolved into a comprehensive tool for atmospheric transport modeling and analysis Its application fields were extended from air pollution studies to other topics where atmospheric transport plays a role (eg, exchange between the stratosphere and troposphere, or the global water cycle) It has evolved into a true community model that is now being used by at least 25 groups from 14 different countries and is seeing both operational and research applications A user manual has been kept actual over the years and was distributed over an internet page along with the model's source code In this note we provide a citeable technical description of FLEXPART's latest version (62)

1,656 citations


Cites methods from "Criteria for the selection of stoch..."

  • ...5 (32) Lacking suitable turbulence parameterizations above the ABL (z>h), a constant vertical diffusivity Dz=0.1 m 2s−1 is used in the stratosphere, following recent work of Legras 5 et al. (2003), whereas a horizontal diffusivity Dh=50 m 2s−1 is used in the free troposphere....

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Journal ArticleDOI
TL;DR: In this article, the authors summarized the current knowledge on the calculation and application of trajectories and their different techniques that can be used to compute trajectories, and their error sources are described.

969 citations


Cites background or methods from "Criteria for the selection of stoch..."

  • ...This is written as the ̧angevin equation (Thomson, 1987)...

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  • ...tracer are initially mixed uniformly in a turbulent flow, they will remain so (Thomson, 1987)....

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  • ...See Thomson (1984, 1987), Wilson and Sawford (1996) and Rodean (1996) for detailed treatments of the mathematical and physical background of LPDM, and Uliasz (1994) and Zannetti (1992) for discussions of more practical aspects of LPDM simulations....

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  • ...Using sufficiently small time steps, equation (16) fulfills the most important criterion for an LPDM, the ‘‘well-mixed’’ criterion, which states that if the particles of a passive tracer are initially mixed uniformly in a turbulent flow, they will remain so (Thomson, 1987)....

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  • ...This is written as the ¸angevin equation (Thomson, 1987) dv@ i "a i (X, v@, t)dt#b ij (X, v@, t) d¼ j (t) (15) where a and b are functions of X, v@ and t and the d¼ j are the increments of a vector-valued ¼iener process with independent components....

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Journal ArticleDOI
TL;DR: In this paper, a comprehensive validation of FLEXPART, a recently developed Lagrangian particle dispersion model based on meteorological data from the European Centre for Medium-Range Weather Forecasts, is described.

781 citations


Cites background or methods from "Criteria for the selection of stoch..."

  • ...The turbulent fluctuations are calculated according to the Langevin equation (Thomson, 1987) dv 5i "a i (x, v 5 , t) dt#b ij (x, v 5 , t) d¼ j (4) where a and b are functions of the position, the turbulent velocity and time....

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  • ...The turbulent fluctuations are calculated according to the Langevin equation (Thomson, 1987)...

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  • ...This form was shown by Thomson (1987) to fulfill the well-mixed criterion which states that ‘‘if a species of passive marked particles is initially mixed uniformly in position and velocity space in a turbulent flow, it will stay that way’’ (Rodean, 1996)....

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Journal ArticleDOI
TL;DR: In this article, the Lagrangian particle dispersion model FLEXPART was used to construct a global data set of 1.4 million continuous trajectories and a climatology of transport in and to the Arctic was developed.
Abstract: [1] The Lagrangian particle dispersion model FLEXPART was used to construct a global data set of 1.4 million continuous trajectories. At the model start, particles were distributed homogeneously in the atmosphere and were then transported for 5.5 years using both resolved winds from European Centre for Medium-Range Weather Forecasts analyses and parameterized turbulent and convective transport. On the basis of this data set, a climatology of transport in and to the Arctic was developed. It was found that the time air resides continuously north of 70°N, called its Arctic age, is highest near the surface in the North American sector of the Arctic. North of 80°N and near the surface, the mean Arctic age of air is about 1 week in winter and 2 weeks in summer. It decreases rapidly with altitude to about 3 days in the upper troposphere. In the most isolated regions of the Arctic, air is exposed to continuous darkness for, on average, 10–14 days in December. Transport from the stratosphere to the lower troposphere is much slower in the Arctic than in the middle latitudes. In the central Arctic, for instance, the probability that air near the surface was transported from the stratosphere within 10 days is only about 1% in winter and 0.3% in summer. Air pollution can be transported into the Arctic along three different pathways: low-level transport followed by ascent in the Arctic, low-level transport alone, and uplift outside the Arctic, followed by descent in the Arctic. Only this last pathway is frequent for pollution originating from North America and Asia, whereas European pollution can follow all three pathways in winter, and pathways one and three in summer. Sensitivities of Arctic air masses to emissions of air pollutants, based on transport alone, were calculated for times of up to 30 days before the air masses reached the Arctic. They were highest over Siberia and Europe in winter and over the oceans in summer. Using an inventory for anthropogenic black carbon (BC) emissions, it was found that near the surface and for transport timescales of 5 and 10 days, BC source contributions from south Asia are only 1.6% and 10%, respectively, of the corresponding European values, despite much higher emissions in south Asia. Using an inventory for BC emissions from forest fires, BC source contributions to the Arctic, particularly from fires in Siberia, were larger than anthropogenic BC source contributions in summer in years of average burning.

709 citations


Cites methods from "Criteria for the selection of stoch..."

  • ...simulation, the model must not violate the so-called wellmixed criterion [Thomson, 1987], i....

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  • ...As particles were not repositioned during the simulation, the model must not violate the so-called well-mixed criterion [Thomson, 1987], i.e., accumulate particles or leave voids in certain regions....

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Journal ArticleDOI
TL;DR: In this article, the authors propose a method for calculating the statistics of inhomogeneous turbulent flows of practical importance, and are particularly attractive if chemical reactions are involved, where the information contained at this level of closure is considerably more than that provided by moment closures.
Abstract: Lagrangian Probability Density Function (PDF) methods have arisen the past 10 years as a union between PDF methods and stochastic Lagrangian models, similar to those that have long been used to study turbulent dispersion. The methods provide a computationally-tractable way of calculating the statistics, of inhomogeneous turbulent flows of practical importance, and are particularly attractive if chemical reactions are involved. The information contained at this level of closure--equivalent to a multi-time Lagrangian joint pdf--is considerably more than that provided by moment closures. The computational implementation is conceptually simple and natural. At a given time, the turbulent flow is represented by a large number of particles, each having its own set of properties--position, velocity, composition etc. These properties evolve in time according to stochastic model equations, so that the computational particles simulate fluid particles. The particle-property time series contain information equivalent to the multi-time Lagrangian joint pdf. But, at a fixed time, the ensemble of particle properties contains no multi-point information: Each particle can be considered to be sampled from a different realization of the flow. (Hence two particles can have the same position, but different velocities and compositions.) It is generally acknowledged (e.g. Reynolds 1990) that many different approaches have important roles to play in tackling the problems posed by turbulent flows. Each approach has its own strengths and weaknesses.

610 citations

References
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Journal ArticleDOI
TL;DR: In this paper, a boundary layer experiment conducted over a flat site in northwestern Minnesota is discussed, where wind and temperature fluctuations near the ground were measured with AFCRL's fast-response instrumentation on a 32 m tower with MRU probes attached at five different heights to the tethering cable of a 1300 m2 kite balloon.
Abstract: Results from a boundary layer experiment conducted over a flat site in northwestern Minnesota are discussed Wind and temperature fluctuations near the ground were measured with AFCRL's fast-response instrumentation on a 32 m tower Measurements between 32 m and the inversion base zi were made with MRU probes attached at five different heights to the tethering cable of a 1300 m2 kite balloon The daytime convective boundary layer appears to be well-mixed with evidence of significant heat and momentum entrainment through the capping inversion The spectra of velocity components are generalized within the framework of mixed-layer similarity The characteristic wavelength for w increases linearly with height up to z = 0l zi following free convection prediction, but approaches a limiting value of 15 zi, in the upper half of the boundary layer The characteristic wavelengths for u and v are maintained at approximately 15 zi down to heights very close to the ground This limiting wavelength correspo

889 citations

Book
26 Nov 1980
TL;DR: Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise; and the role of partial differential equations in this context.
Abstract: Presents theory, sources, and applications of stochastic differential equations of Ito's type; those containing white noise. Closely studies first passage problems by modern singular perturbation methods and their role in various fields of science. Introduces analytical methods to obtain information on probabilistic quantities. Demonstrates the role of partial differential equations in this context. Clarifies the relationship between the complex mathematical theories involved and sources of the problem for physicists, chemists, engineers, and other non-mathematical specialists.

592 citations