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Fractal derivative model for the transport of the suspended sediment in unsteady flows

Nie Shiqian (Hohai University, College of Water Conservancy and Hydropower Engineering, Nanjing, Jiangsu, China + Hohai University, College of Mechanics and Materials, Institute of Hydraulics and Fluid Mechanics, Department of Engineering Mechanic, Nanjing, Jiangsu, C)
Sun Hong Guang (Hohai University, College of Mechanics and Materials, Institute of Hydraulics and Fluid Mechanics, Department of Engineering Mechanic, Nanjing, Jiangsu, China)
Liu Xiaoting (Hohai University, College of Mechanics and Materials, Institute of Hydraulics and Fluid Mechanics, Department of Engineering Mechanic, Nanjing, Jiangsu, China)
Ze Wang (Hohai University, College of Mechanics and Materials, Institute of Hydraulics and Fluid Mechanics, Department of Engineering Mechanic, Nanjing, Jiangsu, China)
Xie Mingzhao (Hohai University, College of Environment, Nanjing, Jiangsu, China)

This paper makes an attempt to develop a Hausdorff fractal derivative model for describing the vertical distribution of suspended sediment in unsteady flow. The index of Hausdorff fractal derivative depends on the spatial location and the temporal moment in sediment transport. We also derive the approximate solution of the Hausdorff fractal derivative advection-dispersion equation model for the suspended sediment concentration distribution, to simulate the dynamics procedure of suspended concentration. Numerical simulation results verify that the Hausdorff fractal derivative model provides a good agreement with the experimental data, which implies that the Hausdorff fractal derivative model can serve as a candidate to describe the vertical distribution of suspended sediment concentration in unsteady flow.

Keywords: Hausdorff fractal derivative, suspended sediment, scaling transformation, advection-dispersion