Fractal Representation of Turbulent Dispersing Plumes

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.