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Mandelbrot, B.B. (1977) Fractals: Form, Chance, and Dimension. W.H. Freeman & Company, New York.

has been cited by the following article:

  • TITLE: Inverse Source Locating Method Based on Graphical Analysis of Dye Plume Images in a Turbulent Flow

    AUTHORS: Qianqian Shao, Daichi Sekine, Takahiro Tsukahara, Yasuo Kawaguchi

    KEYWORDS: Graphical Analysis, Inverse Problem, Passive Scalar Diffusion, Source Estimation, Turbulent Flow

    JOURNAL NAME: Open Journal of Fluid Dynamics, Vol.6 No.4, December 8, 2016

    ABSTRACT: The inverse estimation of a source location of pollutant released into a turbulent flow is a probability problem instead of a deterministic one, as the turbulent flow is chaotic and irreversible. However, researches can be conducted to provide helpful instructions to the possible source location with corresponding uncertainty. This study aims to propose a method of inverse estimation of a passive-scalar source location. Experimental investigation of the dye plume characteristics released into a fully-developed turbulent flow is performed in a water channel. A planar laser-induced fluorescence (PLIF) technique is used to obtain two-dimensional images of spreading dye plumes at a bulk Reynolds number of 20,000. The distributions of high concentration areas in the PLIF images are chosen as features that characterize the traveling (diffusion) distance or time from the dye source. Graphical analysis is used to extract these high concentration areas. The procedure of graphical analysis has three steps: 1) binarization using a threshold to extract high concentration dye patches; 2) labeling individual high-concentration dye patches in the binarized images; and 3) pixel-counting to measure the area and perimeter of each dye patch. We examine the variations of fractal dimension of patches, and the fractal dimension is observed to be almost constant irrespective of the distance from the source. The kurtosis of the probability density function curve of the logarithm dimensionless dye patch areas is found to be related with the downstream diffusion distance, based on which an inverse estimation method to locate a passive-scalar point source is proposed and evaluated.