TY - JOUR
T1 - A velocity-variation-based formulation for bedload particle hops in rivers
AU - Wu, Zi
AU - Singh, Arvind
AU - Foufoula-Georgiou, Efi
AU - Guala, Michele
AU - Fu, Xudong
AU - Wang, Guangqian
N1 - Publisher Copyright:
©
PY - 2021
Y1 - 2021
N2 - 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, 1.5 for the initial regime and 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.
AB - 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, 1.5 for the initial regime and 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.
KW - Mixing and dispersion
KW - Sediment transport
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U2 - 10.1017/jfm.2020.1126
DO - 10.1017/jfm.2020.1126
M3 - Article
AN - SCOPUS:85101434944
SN - 0022-1120
VL - 912
JO - Journal of Fluid Mechanics
JF - Journal of Fluid Mechanics
ER -