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R. I. Sykes and R. S. Gabruk

Abstract

Fractal analysis techniques have been applied to the concentration fields from large-eddy simulations of plume dispersion in a turbulent boundary layer. Fractal dimensions between 1.3 and 1.35 are obtained from area-perimeter and box-counting analyses for neutral and convective conditions. These values are close to previous estimates from atmospheric data. Methods for generating fractal fields with given statistical moments are examined and the simplest of these, the recursive refinement technique, is shown to be inadequate. The problem is shown to be the interpolation step of the procedure, which intrinsically reduces the variance with each refinement. Accurate statistical representation is obtained by replacing the interpolation step of the refinement technique with a sum of random pulses of appropriate width and random location. The pulse technique can easily he adapted to generate either clipped-normal or lognormal one-point probability distributions. Results from the fractal generation technique using simulated mean statistics are compared with realizations of instantaneous plume cross sections from the large-eddy simulations. The simulated probability distributions lie between the clipped normal and the lognormal, so the fractal fields cannot match the realizations precisely. Larger-scale features of the plumes are generally well represented by the fractal method, however.

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R. I. Sykes and R. S. Gabruk

Abstract

A practical model for the effect of averaging time on the turbulent dispersion of a continuous plume is presented. The model is based on a second-order turbulence closure scheme, but is applied to the integrated spatial moments of the plume to provide a Gaussian spread prediction. Velocity fluctuation variances are used directly by the closure model to predict the dispersion, and are partitioned into meandering and diffusive scales based on the instantaneous spread of the plume. Finite time averaging is represented by a simple estimate of the turbulent energy spectrum. The model is compared with short-duration atmospheric measurements for dispersing clouds.

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R. I. Sykes, R. S. Gabruk, and D. S. Henn

Abstract

An improved method for representing the small-scale structure of a turbulent scalar field using fractal recursion techniques is described. The model generalizes the fractal successive refinement method described by Sykes and Gabruk to include a more realistic description of the pseudodissipation field. that is, the square of the scalar gradient. Turbulent dissipation fields are known to be multifractal, so a multifractal generation technique has been incorporated into the fractal refinement model to yield a scalar field with isosurfaces but with a multifractal pseudodissipation field.

The model fields are compared with realizations from large-eddy simulations of turbulent scalar dispersion and shown to provide improved agreement with the small-scale structure. The simple combination of fractal and multifractal properties employed in the model also provides insight into the structure of the random scalar field. Finally, the generation technique is completely localized in physical space and is therefore applicable to inhomogeneous fields.

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