Abstract
This paper makes an attempt to develop a fractional model for describing the distribution of suspended sediment in unsteady flows and study nonlinear dynamic phenomenon of fluids. This model shows the dynamic process of suspended sediment transport. The continuous-time random walk (CTRW) framework provides reasonable physical meaning for fractional order. By solving the equations with different orders and analyzing the results, we get the changing laws of concentration of suspended sediment and find some interesting phenomenon. The above results prove that fractional derivative can well describe the non-local properties of suspended sediment transport, including the non-local properties of time and space. Thus, the fractional derivative model can be serve as a candidate to describe the distribution of suspended sediment in unsteady flows.
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