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Particle saltation over rigid bumpy beds in viscous shearing flows

Published online by Cambridge University Press:  25 August 2022

Alexandre Valance Open the ORCID record for Alexandre Valance [Opens in a new window]  and
Diego Berzi Open the ORCID record for Diego Berzi [Opens in a new window]
Alexandre Valance*
Affiliation:
Institut de Physique de Rennes, Université de Rennes 1, Campus Beaulieu, 35 042 Rennes Cedex, France
Diego Berzi
Affiliation:
Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy
*
†Email address for correspondence: jfm@damtp.cam.ac.uk
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Abstract

We investigate the steady motion of solid particles through successive jumps over a horizontal, rigid, bumpy bed driven by the shearing of a viscous fluid in the absence of turbulence, lubrication forces and collisions above the bed. We employ a discrete element method for the particles coupled to a mean field continuum model for the fluid to run quasi-two-dimensional simulations that we compare with the predictions of a simple model which assumes that all the particles follow identical periodic trajectories determined by the intensity of the shearing and compatible with previously suggested laws relating the particle velocities before and after the impact with the bed. We solve the periodic model both numerically and analytically, and identify the solutions that are linearly stable to small perturbations. We show that the stable solutions of the periodic model are in qualitative and quantitative agreement with the discrete simulations, as long as the number of moving particles in the system is not too large. The discrete simulations further reveal that there are two distinct families of particle trajectories, and that the simple periodic model is actually a good representation of the more energetic particles, that spend most of their time in the upper flow layers where they can gain momentum from the flow.

JFM classification

Geophysical and Geological Flows: Sediment transport Low-Reynolds-number flows: Stokesian dynamics
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A28
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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