B. L. Sawford

Review of Lagrangian Stochastic Models for Trajectories in the Turbulent Atmosphere

We review the theoretical basis for, and the advantages of, random flight models for the trajectories of tracer particles in turbulence. We then survey their application to calculate dispersion in the principal types of atmospheric turbulence (stratified, vertically-inhomogeneous, Gaussian or non-Gaussian turbulence in the surface layer and above), and show that they are especially suitable for some problems (e.g., quantifying ground emissions).

Reynolds number effects in Lagrangian stochastic models of turbulent dispersion

A second‐order autoregressive equation is used to model the acceleration of fluid particles in turbulence in order to study the effect of Reynolds number on Lagrangian turbulence statistics. It is shown that this approach provides a good representation of dissipation subrange structure of Lagrangian velocity and acceleration statistics. The parameters of the model, two time scales representing the energy‐containing and dissipation scales, are determined by matching the model velocity autocorrelation function to Kolmogorov similarity forms in the inertial subrange and the dissipation subrange. The model is tested against the Lagrangian statistics obtained by Yeung and Pope [J. Fluid Mech. 207, 531 (1989)] from direct numerical simulations of turbulence. Agreement between the model predictions and simulation data for second‐order Lagrangian statistics such as the velocity structure function, the acceleration correlation function, and the dispersion of fluid particles is excellent, indicating that the main d...

Structure of the temperature field downwind of a line source in grid turbulence

A Lagrangian stochastic model is used in conjunction with detailed wind-tunnel measurements to examine the structure and development of the temperature field behind a line source in grid turbulence. It is shown that on the scale of these experiments molecular diffusion and viscosity have an important influence on temperature fluctuations (particularly on the intensity of these fluctuations) and must be explicitly modelled. The model accounts for a wide range of the measured properties of the temperature field and provides a unified treatment of temperature fluctuations through all stages of the development of the temperature field. This development is discussed in terms of a simple physical picture in which the hot plume is initially smooth and is moved about bodily by the turbulence, but gradually develops increasing internal structure or patchiness as it grows with distance downstream until a self-similar state is reached in which this internal structure maintains the temperature fluctuations.

A family of stochastic models for two-particle dispersion in isotropic homogeneous stationary turbulence

A family of Lagrangian stochastic models for the joint motion of particle pairs in isotropic homogeneous stationary turbulence is considered. The Markov assumption and well-mixed criterion of Thomson (1990) are used, and the models have quadratic-form functions of velocity for the particle accelerations. Two constraints are derived which formally require that the correct one-particle statistics are obtained by the models. These constraints involve the Eulerian expectation of the ‘acceleration’ of a fluid particle with conditioned instantaneous velocity, given either at the particle, or at some other particles position. The Navier-Stokes equations, with Gaussian Eulerian probability distributions, are shown to give quadratic-form conditional accelerations, and models which satisfy these two constraints are found. Dispersion calculations show that the constraints do not always guarantee good one-particle statistics, but it is possible to select a constrained model that does. Thomsons model has good one-particle statistics, but is shown to have unphysical conditional accelerations. Comparisons of relative dispersion for the models are made.

Effects of turbulence structure, molecular diffusion and source size on scalar fluctuations in homogeneous turbulence

A Lagrangian stochastic model of two-point displacements which includes explicitly the effects of molecular diffusion and viscosity is developed from the marked-particle model of Durbin (1980) and used to study the influence of these molecular processes on scalar fluctuations in stationary homogeneous turbulence. It is shown that for the homogeneous scalar field resulting from a uniform-gradient source distribution or for a cloud produced by a source large compared with the Kolmogorov microscale, the variance of scalar fluctuations

Lagrangian statistical simulation of the turbulent motion of heavy particles

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Estimation of the Kolmogorov constant (C0) for the Lagrangian structure function, using a second‐order Lagrangian model of grid turbulence

is independent of the molecular diffusivity for large Reynolds number Re provided that the Prandtl number Pr is finite. In these circumstances

Conditional concentration statistics for surface plumes in the atmospheric boundary layer

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Generalized random forcing in random-walk turbulent dispersion models

can be calculated from marked-particle-pair statistics. For source sizes that are not large compared with the Kolmogorov microscale,

Atmospheric boundary-layer measurements of concentration statistics from isolated and multiple sources

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