Empirical Model for Shields Diagram and Its Applications
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Volume 146, Issue 6
Abstract
The Shields diagram is a classic method for quantifying sand incipient motion in sediment transport. It is often expressed by empirical or semiempirical equations. This research applies the Padé approximant to the data in the extended Shields diagram and presents a simple generalized empirical model for the critical shear stress. The resulting dimensionless critical Shields parameter is a fractional function of the critical grain Reynolds number, which reproduces the extended Shields diagram by tending to two constants for lower and higher critical grain Reynolds numbers, respectively, and having a minimum value in the transitional regime. The proposed function results in an explicit Shields diagram in terms of grain Reynolds number and has an analytical solution for critical sediment diameter given a bed shear stress.
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Data Availability Statement
All data, models, and code generated or used during the study are available when requested.
Acknowledgments
The author thanks reviewers, associate editor, and the editor Professor A. T. Papaniclaou for their constructive comments that greatly improved the quality of the manuscript.
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Journal of Hydraulic Engineering
Volume 146 • Issue 6 • June 2020
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©2020 American Society of Civil Engineers.
History
Received: Jul 12, 2018
Accepted: Oct 28, 2019
Published online: Mar 23, 2020
Published in print: Jun 1, 2020
Discussion open until: Aug 23, 2020
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