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Entrainment and suspension of sand and gravel

de Leeuw, Jan and Lamb, Michael P. and Parker, Gary and Moodie, Andrew J. and Haught, Daniel and Venditti, Jeremy G. and Nittrouer, Jeffrey A. (2020) Entrainment and suspension of sand and gravel. Earth Surface Dynamics, 8 (2). pp. 485-504. ISSN 2196-632X. doi:10.5194/esurf-8-485-2020.

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The entrainment and suspension of sand and gravel are important for the evolution of rivers, deltas, coastal areas, and submarine fans. The prediction of a vertical profile of suspended sediment concentration typically consists of assessing (1) the concentration near the bed using an entrainment relation and (2) the upward vertical distribution of sediment in the water column. Considerable uncertainty exists in regard to both of these steps, especially the near-bed concentration. Most entrainment relations have been tested against limited grain-size-specific data, and no relations have been evaluated for gravel suspension, which can be important in bedrock and mountain rivers. To address these issues, we compiled a database with suspended sediment data from natural rivers and flume experiments, taking advantage of the increasing availability of high-resolution grain size measurements. We evaluated 12 dimensionless parameters that may determine entrainment and suspension relations and applied multivariate regression analysis. A best-fit two-parameter equation (r² = 0.79) shows that near-bed entrainment, evaluated at 10 % of the flow depth, decreases with the ratio of settling velocity to skin-friction shear velocity (w_(si)/u_(∗ skin)), as in previous relations, and increases with Froude number (Fr), possibly due to its role in determining bedload-layer concentrations. We used the Rouse equation to predict concentration upward from the reference level and evaluated the coefficient β_i, which accounts for differences in the turbulent diffusivity of sediment from the parabolic eddy viscosity model used in the Rouse derivation. The best-fit relation for β_i (r² = 0.40) indicates greater relative sediment diffusivities for rivers with greater flow resistance, possibly due to bedform-induced turbulence, and larger w_(si)/u_(∗ skin); the latter dependence is nonlinear and therefore different from standard Rouse theory. In addition, we used empirical relations for gravel saltation to show that our relation for near-bed concentration also provides good predictions for coarse-grained sediment. The new relations extend the calibrated parameter space over a wider range in sediment sizes and flow conditions compared to previous work and result in 95 % of concentration data throughout the water column predicted within a factor of 9.

Item Type:Article
Related URLs:
URLURL TypeDescription Information
de Leeuw, Jan0000-0002-2005-4351
Lamb, Michael P.0000-0002-5701-0504
Parker, Gary0000-0001-5973-5296
Moodie, Andrew J.0000-0002-6745-036X
Venditti, Jeremy G.0000-0002-2876-4251
Nittrouer, Jeffrey A.0000-0002-4762-0157
Additional Information:© Author(s) 2020. This work is distributed under the Creative Commons Attribution 4.0 License. Received: 20 November 2019 – Discussion started: 17 December 2019. Revised: 11 April 2020 – Accepted: 27 April 2020 – Published: 3 June 2020. We thank everyone involved in the suspended sediment data collection in the Yellow River (Brandee Carlson, Hongbo Ma) and the Fraser River (Nicola Rammell, Kate Donkers, Jacqui Brown, Michael Wong, Michelle Linde, and Alex Gitto). We thank the reviewers and editor Eric Lajeunesse for their helpful comments. This research has been supported by the US National Science Foundation (grant no. EAR 1427262), the Caltech Discovery Fund, and the NSF Graduate Research Fellowship (grant no. EAR 1842494). Author contributions. MPL and GP conceived the study. JdL compiled data and led data analysis with input from MPL. MPL and JdL wrote the initial paper. AJM, DH, JGV, and JAN supplied suspended sediment data and contributed to the final paper. Data availability. All data used in the analysis are provided in Table S1 of the Supplement. Model results for all possible variable combinations are given in Table S2. Supplement. Table S1 contains all the suspended sediment data that were used to find the empirical relations. Table S2 contains all entrainment and Rouse number models ranked according to goodness of fit as indicated by r². The supplement related to this article is available online at: The authors declare that they have no conflict of interest. This paper was edited by Eric Lajeunesse and reviewed by two anonymous referees.
Funding AgencyGrant Number
Caltech Discovery FundUNSPECIFIED
NSF Graduate Research FellowshipEAR-1842494
Issue or Number:2
Record Number:CaltechAUTHORS:20200624-104211458
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Official Citation:de Leeuw, J., Lamb, M. P., Parker, G., Moodie, A. J., Haught, D., Venditti, J. G., and Nittrouer, J. A.: Entrainment and suspension of sand and gravel, Earth Surf. Dynam., 8, 485–504,, 2020.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103997
Deposited By: George Porter
Deposited On:24 Jun 2020 21:18
Last Modified:16 Nov 2021 18:27

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