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Discrete Dynamics in Nature and Society
Volume 2017, Article ID 5481531, 11 pages
Research Article

Vertical Distribution of Suspended Sediment under Steady Flow: Existing Theories and Fractional Derivative Model

1College of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing, Jiangsu 210098, China
2State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering, Institute of Soft Matter Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, Jiangsu 210098, China
3Department of Geological Sciences, University of Alabama, Tuscaloosa, AL 35487, USA
4Key Laboratory of Water Cycle and Related Land Surface Processes, Institute of Geographic Sciences and Natural Resources Research, Chinese Academy of Sciences, Beijing 100101, China
5Division of Hydrologic Sciences, Desert Research Institute, Las Vegas, NV 89119, USA

Correspondence should be addressed to HongGuang Sun; nc.ude.uhh@ghs

Received 28 March 2017; Revised 10 May 2017; Accepted 24 May 2017; Published 28 June 2017

Academic Editor: Hengfei Ding

Copyright © 2017 Shiqian Nie et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The fractional advection-diffusion equation (fADE) model is a new approach to describe the vertical distribution of suspended sediment concentration in steady turbulent flow. However, the advantages and parameter definition of the fADE model in describing the sediment suspension distribution are still unclear. To address this knowledge gap, this study first reviews seven models, including the fADE model, for the vertical distribution of suspended sediment concentration in steady turbulent flow. The fADE model, among others, describes both Fickian and non-Fickian diffusive characteristics of suspended sediment, while the other six models assume that the vertical diffusion of suspended sediment follows Fick’s first law. Second, this study explores the sensitivity of the fractional index of the fADE model to the variation of particle sizes and sediment settling velocities, based on experimental data collected from the literatures. Finally, empirical formulas are developed to relate the fractional derivative order to particle size and sediment settling velocity. These formulas offer river engineers a substitutive way to estimate the fractional derivative order in the fADE model.