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The Nonlinear Cusp-Catastrophe Model of Incipient Motion for Non-Uniform Sediment

Author(s): Jurui Yang; Xiaoxia Hou; Hui Li; Shuyou Cao; Xingnian Liu

Linked Author(s): Hui Li, Xingnian Liu

Keywords: Nonlinear; Catastrophe theory; Cusp-catastrophe; Sediment incipient motion; Model

Abstract: The cusp-catastrophe theory of nonlinear science is applied for studying sediment incipient motion in this paper. The state variables and the bound variables in cusp -catastrophe model have been found by analyzing the factors of sediment incipient motion, and the cusp-catastrophe model which used to reflect the sediment incipient motion has been built. Based on the standard equation of the cusp -catastrophe, the relation formula between Shields number and Reynolds number of sediment has been derived by using coordinate transform and topology transform. The Shields number is regarded as the state variable, and negative 0. 3 power Reynolds number of sediment and zero dimension number mdm/d0 are regarded as the bound variable in the cusp -catastrophe model. Sink experimental data verified the function relationship between flow shear stress t0 and particle size d0 of incipient motion. The verification results show that the calculated value agrees well with the sink experimental result. When d0 is larger, the error is between 1% 30% , which is small. While the particle size d0 is smaller, the error is larger; the maximum error is 76. 2% . This indicates that the cusp-catastrophe formula is reasonable, and the results fully reflect the characteristics of threshold motion of non-uniform sediment. The purpose of this paper is to explore the incipient motion laws of non-uniform sediment from the viewpoint of nonlinear science.


Year: 2013

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