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Einstein conjecture and resting-time statistics in the bed-load transport of monodispersed particles

Published online by Cambridge University Press:  14 August 2019

Luigi Fraccarollo Open the ORCID record for Luigi Fraccarollo [Opens in a new window]  and
Marwan A. Hassan Open the ORCID record for Marwan A. Hassan [Opens in a new window]
Luigi Fraccarollo*
Affiliation:
Department of Civil, Environmental and Mechanical Engineering, University of Trento, via Mesiano, 77, 38123, Trento, Italy
Marwan A. Hassan
Affiliation:
Department of Geography, The University of British Columbia, Vancouver, BC V6T 1Z2, Canada
*
†Email address for correspondence: luigi.fraccarollo@unitn.it
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Abstract

Sediment transport in rivers consists, at moderate discharge stage, of individual grains that undergo a series of step movements and rest periods (bed-load). Following a large number of grain trajectories in time and space is difficult and the results are affected by bias due to censorship of the time-spatial window. Therefore, the data sets available for the description of the statistics of resting-times, travel-time and lengths of the steps, are still insufficient. In this paper, an innovative experimental methodology has been designed and applied to get data representing the evolution of a bed surface and to support a robust statistical analysis of sediment transport. The methodology is based on image sequences taken of a flat bed made of well-sorted (mono-dispersed) particles. The acquired data are interpreted analytically through equations that describe the effects of grain entrainment and deposition. We show that grains’ displacement have a mean value independent of bed-load rate under low to moderate transport intensity for a given sediment type and bed-slope. Hence, we provide a strong validation of the seminal conjecture of Einstein in his theoretical statistical description of sediment transport. Finally, we describe the probability density functions of the resting-time for a few values of the sediment discharge.

JFM classification

Geophysical and Geological Flows: Sediment transport Geophysical and Geological Flows: River dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 1077 - 1089
Copyright
© 2019 Cambridge University Press 

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