Fractal Geometry of Isoconcentration Surfaces in a Smoke Plume

Abstract

The fractal properties of isoconcentration surfaces in a smoke plume are studied in an atmospheric boundary layer wind tunnel. Instantaneous high-resolution two-dimensional images of the fine particle concentration at Schmidt number Sc → ∞ were obtained in three plume cross sections with a video imaging technique. The fractal dimension D of isoconcentration contours is estimated with box-counting and area-perimeter methods; the range of thresholds is 0.5 ≤ c*/c̄ ≤ 1.5, where c̄ is the mean particle concentration for a particular image and c* is the threshold. Using the box-counting method, the local values of D = −d(log Nε)/d(log ε) are found to be constant over variations in ε that are more than a decade, where Nε, is the number of boxes with size ε required to cover an isoconcentration curve. Using the area-perimeter method, the fractal dimension is estimated with the relation P ∼ AD/2, where P and A denote the perimeter and area of the individual closed isoconcentration curves. The noise influence on the measured values of D is evaluated with a newly developed method based on synthetically generated noise. A new technique of noise filtering is proposed, based on the area threshold. The effect of spatial resolution is studied using video image smoothing in physical space. The present investigation demonstrates that isoconcentration surfaces in a smoke plume are self-similar fractals over the range of thresholds 0.5 ≤ c*/c̄ ≤ 1.5 and that their fractal dimension D for all images analyzed is found to be 1.41 ± 0.06 and 1.45 ± 0.08 for the box-counting and area-perimeter methods, respectively.