Response of Flood to the Fractal Dimension of River Length

Although the phenomenon that strictly meet the constant dimension fractal form in the nature does not exist, fractal theory provides a new way and means for the study of complex natural phenomena. Therefore, a large number of complex phenomena are described by application of variable dimension fractal, and the river fractal features is no exception. By using of the fractal theory to calibrate the fractal, to calculate the overall fractal dimension and partial fractal dimension, and to explore their relationships between overall fractal dimension and partial dimension of river length in section of Chongqing city of Yangtze River. The research results show that: (1) It does express a second-order accumulated variable-dimensional fractal phenomenon. (2) The fractal dimension can reflects the degree of bending in the river, the larger the fractal dimension, the more bent for the river. (3) The mathematical relation between overall fractal dimension and partial dimension of river length to meet the unite principle of fractal topography. (4) It has different dimensions at a different location in the same river. In the same river, the larger dimension, the worse flood carrying capacity of the river, and the more obvious of the flood will be on the performance.