First-Order Inconsistencies Caused by Rogue Trajectories

Postma, John V.; Yee, Eugene; Wilson, John D.

doi:10.1007/s10546-012-9732-7

Cited by 10 publications

(5 citation statements)

References 16 publications

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“…This was needed here since the numerical formulation of the steady and horizontally homogenous drift for the skewed PDF was found to be more sensitive than the standard Gaussian formulation to the time varying turbulence statistics and this, occasionally, introduced the possibility of a serious numerical degradation for the simulated particle trajectories. The bi-Gaussian drift formulation is intrinsically less stable than the Gaussian, as first noted by Luhar and Britter (1989) and discussed in Yee and Wilson (2007), and the instability phenomenon noted here is similar to the phenomenon of "rogue trajectories" discussed in detail in Yee and Wilson (2007) and Postma et al (2012). However, here the main cause of instability appears to be the inconsistency between the formulation of the model (i.e.…”

Section: Introductionsupporting

confidence: 69%

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

Cassiani

Stohl

Brioude

2014

Boundary-Layer Meteorol

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A correction for the vertical gradient of air density has been incorporated into a skewed probability density function formulation for turbulence in the convective boundary layer. The related drift term for Lagrangian stochastic dispersion modelling has been derived based on the well-mixed condition. Furthermore, the formulation has been extended to include unsteady turbulence statistics and the related additional component of the drift term obtained. These formulations are an extension of the drift formulation reported by Luhar et al. (Atmos Environ 30:1407-1418, 1996 following the well-mixed condition proposed by Thomson (J Fluid Mech 180:529-556, 1987). Comprehensive tests were carried out to validate the formulations including consistency between forward and backward simulations and preservation of a well-mixed state with unsteady conditions. The stationary state CBL drift term with density correction was incorporated into the FLEXPART and FLEXPART-WRF Lagrangian models, and included the use of an ad hoc transition function that modulates the third moment of the vertical velocity based on stability parameters. Due to the current implementation of the FLEXPART models, only a steady-state horizontally homogeneous drift term could be included. To avoid numerical instability, in the presence of non-stationary and horizontally inhomogeneous conditions, a re-initialization procedure for particle velocity was used. The criteria for re-initialization and resulting errors were assessed for the case of non-stationary conditions by comparing a reference numerical solution in simplified unsteady conditions, obtained using the non-stationary drift term, and a solution based on the steady drift with re-initialization. Two examples of "real-world" numerical simulations were performed under different convective conditions to demonstrate the effect of the vertical gradient in density on the particle dispersion in the CBL.

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Section: Introductionsupporting

confidence: 69%

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

Cassiani

Stohl

Brioude

2014

Boundary-Layer Meteorol

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“…However, they present a serious difficulty for LS micromixing models computing higher moments of concentration [e.g., Postma et al, 2012]. However, they present a serious difficulty for LS micromixing models computing higher moments of concentration [e.g., Postma et al, 2012].…”

Section: Resultsmentioning

confidence: 99%

“Rogue Velocities” in a Lagrangian Stochastic Model for Idealized Inhomogeneous Turbulence

Wilson

2013

Lagrangian Modeling of the Atmosphere

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A Lagrangian stochastic model may sometimes generate velocities of unrealistic magnitude, and several authors have taken ad hoc steps to control their impact. The occurrence of these "rogue velocities" would, on first sight, appear to contradict the model's being well mixed; however, the problem is typically experienced in the context of a complex (and in some cases, discontinuous, i.e., gridded) regime of turbulence, corresponding to which there may (implicitly) be limitations on the allowable size of the time step that had not been respected. This article seeks to observe rogue velocities in an artificial regime of 1-D turbulence, in which two regions of differing constant velocity variance are joined by a ramp such that the gradient in velocity variance is discontinuous. The evolution of an initially well-mixed distribution of tracer is computed by integrating the Chapman-Kolmogorov equation (the resulting calculation is compared with the corresponding stochastic solution). It is found that unless the time step is small relative to an inhomogeneity time scale implied by the field of Eulerian velocity statistics, the well-mixed condition is violated: large velocities occur with greater probability than they ought.

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“…To do so, for each cell of the fine grid we keep the particle number between a minimal value and a maximal value which is given at the beginning of the simulation. By displacing particles, this method of particle management limits trajectory length and prevents rogue trajectories as described by Yee and Wilson (2007), Postma et al (2012) and Wilson (2013).…”

Section: Meso-nh Simulationmentioning

confidence: 99%

A new downscaling method for sub-grid turbulence modeling

et al. 2017

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Abstract. In this study we explore a new way to model subgrid turbulence using particle systems. The ability of particle systems to model small-scale turbulence is evaluated using high-resolution numerical simulations. These highresolution data are averaged to produce a coarse-grid velocity field, which is then used to drive a complete particle-systembased downscaling. Wind fluctuations and turbulent kinetic energy are compared between the particle simulations and the high-resolution simulation. Despite the simplicity of the physical model used to drive the particles, the results show that the particle system is able to represent the average field. It is shown that this system is able to reproduce much finer turbulent structures than the numerical high-resolution simulations. In addition, this study provides an estimate of the effective spatial and temporal resolution of the numerical models. This highlights the need for higher-resolution simulations in order to evaluate the very fine turbulent structures predicted by the particle systems. Finally, a study of the influence of the forcing scale on the particle system is presented.

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First-Order Inconsistencies Caused by Rogue Trajectories

Cited by 10 publications

References 16 publications

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

Lagrangian Stochastic Modelling of Dispersion in the Convective Boundary Layer with Skewed Turbulence Conditions and a Vertical Density Gradient: Formulation and Implementation in the FLEXPART Model

“Rogue Velocities” in a Lagrangian Stochastic Model for Idealized Inhomogeneous Turbulence

A new downscaling method for sub-grid turbulence modeling

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