FRACTAL GEOMETRY OF ISOCONCENTRATION SURFACES IN A SMOKE PLUME

The fractal properties of isoconcentration surfaces in a smoke plume a re studied in an atmospheric boundary layer wind tunnel. Instantaneous high-resolution two-dimensional images of the fine particle concentra tion at Schmidt number Sc --> infinity were obtained in three plume cr oss sections with a video imaging technique, The fractal dimension D o f isoconcentration contours is estimated with box-counting and area-pe rimeter methods; the range of thresholds is 0.5 less than or equal to c/(c) over bar less than or equal to 1.5, where cis the mean particle concentration for a particular image and c is the threshold. Using t he box-counting method, the local values of D = -d(log N-epsilon)/d(lo g epsilon) are found to be constant over variations in epsilon that ar e more than a decade, where N, is the number of boxes with size epsilo n required to cover an isoconcentration curve. Using the area-perimete r method, the fractal dimension is estimated with the relation P simil ar to A(D/2), where P and A denote the perimeter and area of the indiv idual closed isoconcentration curves. The noise influence on the measu red values of D is evaluated with a newly developed method based on sy nthetically generated noise. A new technique of noise filtering is pro posed, based on the area threshold. The effect of spatial resolution i s studied using video image smoothing in physical space. The present i nvestigation demonstrates that isoconcentration surfaces in a smoke pl ume are self-similar fractals over the range of thresholds 0.5 less th an or equal to c/(c) over bar less than or equal to 1.5 and that thei r 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.