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A velocity-variation-based formulation for bedload particle hops in rivers

Published online by Cambridge University Press:  16 February 2021

Zi Wu Open the ORCID record for Zi Wu [Opens in a new window] ,
Arvind Singh Open the ORCID record for Arvind Singh [Opens in a new window] ,
Efi Foufoula-Georgiou Open the ORCID record for Efi Foufoula-Georgiou [Opens in a new window] ,
Michele Guala Open the ORCID record for Michele Guala [Opens in a new window] ,
Xudong Fu Open the ORCID record for Xudong Fu [Opens in a new window]  and
Guangqian Wang
Zi Wu*
Affiliation:
State Key Laboratory of Hydroscience and Engineering; Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL 32816, USA Department of Civil and Environmental Engineering, University of California Irvine, Irvine, CA 92697, USA
Arvind Singh
Affiliation:
Department of Civil, Environmental and Construction Engineering, University of Central Florida, Orlando, FL 32816, USA
Efi Foufoula-Georgiou
Affiliation:
Department of Civil and Environmental Engineering, University of California Irvine, Irvine, CA 92697, USA Department of Earth System Science, University of California Irvine, Irvine, CA 92697, USA
Michele Guala
Affiliation:
St. Anthony Falls Laboratory, Department of Civil, Environmental and Geo-Engineering, University of Minnesota, Minneapolis, MN 55414, USA
Xudong Fu
Affiliation:
State Key Laboratory of Hydroscience and Engineering; Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China
Guangqian Wang
Affiliation:
State Key Laboratory of Hydroscience and Engineering; Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China
*
†Email addresses for correspondence: wuzi@tsinghua.edu.cn, wuzi@pku.edu.cn
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Abstract

Bedload particle hops are defined as successive motions of a particle from start to stop, characterizing one of the most fundamental processes of bedload sediment transport in rivers. Although two transport regimes have been recently identified for short and long hops, respectively, there is still the lack of a theory explaining the mean hop distance–travel time scaling for particles performing short hops, which dominate the transport and may cover over 80 % of the total hop events. In this paper, we propose a velocity-variation-based formulation, the governing equation of which is intrinsically identical to that of Taylor dispersion for solute transport within shear flows. The key parameter, namely the diffusion coefficient, can be determined by hop distances and travel times, which are easier to measure and more accurate than particle accelerations. For the first time, we obtain an analytical solution for the mean hop distance–travel time relation valid for the entire range of travel times, which agrees well with the measured data. Regarding travel times, we identify three distinct regimes in terms of different scaling exponents: respectively, $\sim$1.5 for the initial regime and $\sim$5/3 for the transition regime, which define the short hops, and 1 for the Taylor dispersion regime defining long hops. The corresponding distribution of the hop distance is analytically obtained and experimentally verified. We also show that the conventionally used exponential distribution, as proposed by Einstein, is solely for long hops. Further validation of the present formulation is provided by comparing the simulated accelerations with measurements.

JFM classification

Geophysical and Geological Flows: Sediment transport

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Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A33
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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