Bed-load transport in natural rivers exhibits nonlinear dynamics with strong temporal memory (i.e., retention due to burial) and/or spatial memory (i.e., fast displacement driven by turbulence). Nonlinear bed-load transport is discrete in nature due to the discontinuity in the sediment mass density and the intermittent motion of sediment along river beds. To describe the discrete bed-load dynamics, we propose a discrete spatiotemporal fractional advection-dispersion equation (D-FADE) without relying on the debatable assumption of a continuous sediment distribution. The new model is then applied to explore nonlinear dynamics of bed-load transport in flumes. Results show that, first, the D-FADE model can capture the temporal memory and spatial dependency characteristics of bed-load transport for sediment with different sizes. Second, fine sediment particles exhibit stronger super-diffusive features, while coarse particles exhibit significant subdiffusive properties, likely due to the size-selective memory impact. Third, sediment transport with an instantaneous source exhibits stronger history memory and weaker spatial nonlocality, compared to that with a continuous source (since a smaller number of particles might be blocked or buried relatively easier). Hence, the D-FADE provides a strict computational model to quantify discrete bed-load transport, whose nonlinear dynamics can be sensitive to particle sizes and source injection modes, both common in applications.
Discrete Fractional Derivative Based Computational Model to Describe Dynamics of Bed-Load Transport
Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received November 30, 2017; final manuscript received March 25, 2018; published online April 18, 2018. Assoc. Editor: Zaihua Wang.
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Sun, H., Li, Z., Zhang, Y., and Liu, X. (April 18, 2018). "Discrete Fractional Derivative Based Computational Model to Describe Dynamics of Bed-Load Transport." ASME. J. Comput. Nonlinear Dynam. June 2018; 13(6): 061004. https://doi.org/10.1115/1.4039878
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