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.
Bibliographical noteFunding Information:
This work is partially supported by the National Science Foundation of China (51525901) and the National Key Research and Development Programme of China (2016YFE0201900). E.F.-G. acknowledges support by the National Science Foundation (NSF) under grants EAR-1811909, ECCS-1839441 and DMS-1839336. A.S. acknowledges partial support from NSF EAR-1854452.
- Mixing and dispersion
- Sediment transport