Experimental Analytical Study on Fractal Behaviors of the Density Current

Abstract

Density current is caused by the difference in density with the ambient fluid, believed to hold fractal features. A comprehensive laboratorial study on fractal properties of density current is conducted. Variations of the bed slope, fluid concentration, discharge and channel narrowing are studied along with the fractal analysis of the density current. Experiments were performed in 28 different modes in a flume with 8 m length, 35 cm width and 60 cm depth and 1–3% longitudinal slope. All the experiments are recorded by the high-resolution cameras, and the pictures of the density current evolution are transformed into several snapshots. MATLAB codes are also developed for image processing and calculating the fractal indices of the images. Results indicated that as the flume bed slope increases, the fractal dimension of the density current decreases. Conversely, discharge and concentration of the density current depict a negative correlation with the fractal dimension. Moreover, when the vertex angle has a minimum value of 155° in non-narrowed channel, the angle escalated to 176.34° and 180° for local and protracted narrowing, respectively, a sign of transmuting from mono- to multi-fractality. Unlike discharge boosts, α range decreases 11.4% and α angle grows 7.8%, a sign of mono-fractality. However, when bed slope increases, α range increases 6.4% and the density current turns multi-fractal. Besides, current concentration shows a significant fractal-based correlation with the Reynolds numbers, R2 = 0.9. Finally, the correlation between the Richardson number and entrainment ratio enhances significantly from R2 = 0.81 to R2 = 0.92 when a fractal-based approach is applied.