Fractal research of transverse sections of a long river channel below a dam

Abstract

Research on the propagation law of unsteady flow from dam discharge has significance for the engineering problems of shipping and urban flood control. Due to the problem of many factors influencing the process of unsteady flow, we propose using fractal dimensions to replace various hydraulic factors. In this paper, we choose a navigation-obstructing beach section in a river as the research object, establish a two-dimensional unsteady fractal mathematical model to obtain statistics on the channel width at the minimum maintenance water depth and then calculate the fractal dimension of the river cross section. The results show the first-order feature, and it is also shown that the fractal dimension of the river width has a strong relationship with the depth at the beach section and the shape of the cross section. In general, the shoal’s fractal dimension increases with the depth. The fractal dimension of the transverse sections has the trend of gradually reducing as a whole with the velocity. Compared to the fractal dimension of the beach in the same river section, the river cross-section topography is smoother and the section fractal dimension is smaller when the upstream flow is the same.