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Collisionless kinetic theory for saltation over a rigid, bumpy bed

Published online by Cambridge University Press:  22 August 2024

Diego Berzi Open the ORCID record for Diego Berzi [Opens in a new window] ,
Alexandre Valance Open the ORCID record for Alexandre Valance [Opens in a new window]  and
James T. Jenkins Open the ORCID record for James T. Jenkins [Opens in a new window]
Diego Berzi*
Affiliation:
Department of Civil and Environmental Engineering, Politecnico di Milano, 20133 Milano, Italy
Alexandre Valance
Affiliation:
Institut de Physique de Rennes, CNRS UMR 6251, Université de Rennes I, 35042 Rennes, France
James T. Jenkins
Affiliation:
School of Civil and Environmental Engineering, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

We employ the methods of statistical mechanics to obtain closures for the balance equations of momentum and fluctuation kinetic energy that govern the ballistic motion of grains rebounding at a rigid, bumpy bed that are driven by turbulent or non-turbulent shearing fluids, in the absence of mid-trajectory collisions and fluid velocity fluctuations. We obtain semi-analytical solutions for steady and fully developed saltation over horizontal beds for the vertical profiles of particle concentration and stresses and fluid and particle velocities. These compare favourably with measurements in discrete-element numerical simulations in the wide range of conditions of Earth and other planetary environments. The predictions of the particle horizontal mass flux and its scaling with the amount of particles in the system, the properties of the carrier fluid and the intensity of the shearing also agree with numerical simulations and wind-tunnel experiments.

JFM classification

Rarefied Gas Flow: Kinetic theory Multiphase and Particle-laden Flows: Particle/fluid flow Geophysical and Geological Flows: Sediment transport
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 991 , 25 July 2024 , A15
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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