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Steady inclined flows of granular-fluid mixtures

Published online by Cambridge University Press:  16 November 2009

D. BERZI  and
J. T. JENKINS
D. BERZI*
Affiliation:
Department of Environmental, Hydraulic, Infrastructures and Surveying Engineering, Politecnico di Milano, Milan 20133, Italy
J. T. JENKINS
Affiliation:
Department of Theoretical and Applied Mechanics, Cornell University, Ithaca, NY 14853, USA
*
†Email address for correspondence: [email protected]
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Abstract

We extend a recent theory for steady uniform gravity-driven flow of a highly concentrated granular-fluid mixture over an erodible bed between frictional sidewalls. We first include angles of inclination greater than the angle of repose of the particles; then, we introduce a boundary condition for flow over a rigid bumpy bed. We compare the predictions of the resulting theory with the volume flow rates, depths and angles of inclination measured in the experiments on dry and variously saturated flows over rigid and erodible boundaries. Finally, we employ the resulting theory, with the assumption that the flow is shallow, to solve, in an approximate way, for the variation of height and average velocities along a steady non-uniform inclined flow of a granular-fluid mixture that moves over a rigid bumpy bed. The solutions exhibit features of the flow seen in the experiments – for example, a dry bulbous snout in advance of the fluid, whose length increases with increasing number of the particles and that disappears with increasing velocity – for which satisfactory explanations were lacking.

JFM classification

Granular media: Granular media Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 641 , 25 December 2009 , pp. 359 - 387
Copyright
Copyright © Cambridge University Press 2009

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