Experimental Investigation and Dynamic Fractal and Multi-fractal Analysis of the Density Current Patterns
Subject Areas : Article frome a thesismohammad hosseini 1 , mohammad hadi fattahi 2 * , saied eslamian 3
1 - Department of Civil Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2 - Department of Civil Engineering, Marvdasht Branch, Islamic Azad University, Marvdasht, Iran
3 - Department of Water Engineering, Isfahan University of Technology, Isfahan, Iran.
Keywords: Entrainment ratio, Fractal geometry, Richardson number, Singularity spectrum, Scaling exponent,
Abstract :
Density current is caused by a slight density difference with the environmental fluid. These currents are of two-phase current type. These currents are non-linear in nature, which are complex and sensitive to initial conditions. Fractal geometry is used as a powerful tool to investigate geophysical phenomena including density current and many complex natural phenomena. This study aimed to conduct a comprehensive study on the fractal and multi-fractal properties of density current and established a significant relation between the Richardson number evolution and the entrainment of ratio density current through fractal analysis. For this purpose, three experimental models in 28 different states were performed by changing the bed slope, density and inlet discharge. The developed codes in MATLAB were used to calculate the multi-fractal generalized dimension indices D(q), singularity spectrum f(α), singularity angle α, the scaling exponent T(q) and fractal dimension Df. The results and various investigations indicated that the fractal dimension decreased a little with the increase of flume bed slope. Further, the fractal dimension increases with increasing the concentration and current discharge. As the Richardson number increases, the scaling exponent has a linear pattern. Furthermore, the fractal dimension changes are monotonic than q in these experiments, and the singularity angles are larger with less range. A significant relationship with 92% coefficient was made between Richardson number and entrainment ratio by fractal analysis.
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