Fractal characteristics of isoconcentration surfaces in plumes dispersing in the atmospheric surface layer

Abstract

The geometrical properties of isoconcentration surfaces in a plume dispersing in the atmospheric surface layer are studied using a generalized box-counting method applied to a limited random point set. This method yields the hierarchy of generalized dimensions Dq that can be used to characterize the fractal nature of the plume concentration level sets. The dimension spectra for the concentration level sets are computed from one-dimensional cuts of the concentration field. The concentration level sets are found to be monofractals that can be characterized by one scaling exponent or fractal dimension. The fractal dimension of the level sets is independent of the concentration threshold over a wide range of threshold values. The evolution of the fractal dimension of plume concentration level sets with distance x downwind from the source, cross-wind distance y from the lateral mean-plume centerline, and vertical height z above the ground is examined. At a fixed plume height, the fractal dimension is essentially independent of either x or y. The fractal dimension of the plume isoconcentration surface decreases roughly linearly from a value of 0.7±0.05 near the surface (z≲1 m) to 0.45±0.05 higher up in the plume (z≳8 m). The increased wrinkling of the plume isoconcentration surface near the ground is most likely the result of the increased mean velocity shear and blocking by the surface.