Analytical solution to one-dimensional mathematical model of flow and morphological evolution in open channels
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alytical solution to one-dimensional mathematical model of flow and morphological evolution in open channels 1,2
3,4*
DING Yun , LI ZuiSen 1
, SHI YongZhong
3,4
& ZHONG DeYu
5,6*
State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Hohai University, Nanjing 210098, China; 2 College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, China; 3 Zhejiang Institute of Hydraulics and Estuary, Hangzhou 310008, China; 4 Zhejiang Provincial Key Laboratory of Hydraulic Disaster Prevention and Mitigation, Hangzhou 310008, China; 5 Joint-Sponsored State Key Laboratory of Plateau Ecology and Agriculture, Qinghai University, Xining 810016, China; 6 State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, China Received July 27, 2020; accepted September 7, 2020; published online October 23, 2020
The evolution of open-channel flow and morphology can be simulated by one-dimensional (1D) mathematical models. These models are typically solved by numerical or analytical methods. Because the behavior of variables can be explained by explicit mathematical determinations, compared to numerical solutions, analytical solutions provide fundamental and physical insights into flow and sediment transport mechanisms. The singular perturbation technique derives a hierarchical equation of waves and describes the evolutionary nature of disturbances in hyperbolic systems. The wave hierarchy consists of dynamic, diffusion, and kinetic waves. These three types of waves interact with each other in the process of propagation. Moreover, the Laplace transform is implemented to transform partial differential equations into ordinary differential equations. Analytical expressions in the wave front are subtracted by the approximation of kinetic and diffusion models. Moreover, an analytical solution consists of a linear combination of the kinetic wave front and the diffusion wave front expressions, pursuing to describe the physical mechanism of motion in open channels as completely as possible. Analytical solutions are presented as a combination of exponential functions, hyperbolic functions, and infinite series. The obtained analytical solution was further applied to the simulation of flood path and morphological evolution in the Lower Yellow River. The phenomenon of increased peak discharge in the downstream reach was successfully simulated. It was encouraging that the results were in good agreement with the observed data. open channel, mathematical model, analytical solution, Laplace transform, morphological evolution Citation:
Ding Y, Li Z S, Shi Y Z, et al. Analytical solution to one-dimensional mathematical model of flow and morphological evolution in open channels. Sci China Tech Sci, 2020, 60, https://doi.org/10.1007/s11431-020-1721-6
1 Introduction Understanding the flow mechanism and morphological evolution is crucial for river training, flood control, water resources management, and environmental improvements. Physically, the flow and sedimentation proc
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