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Asymptotic analysis for the propagation and arresting process of a finite dry granular mass down a rough incline

Published online by Cambridge University Press:  30 September 2016

K.-L. Lee  and
F.-L. Yang
K.-L. Lee
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan
F.-L. Yang*
Affiliation:
Department of Mechanical Engineering, National Taiwan University, Taipei 10617, Taiwan
*
†Email address for correspondence: [email protected]
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Abstract

This work presents an asymptotic analysis for the propagation and arresting process of a two-dimensional finite granular mass down a rough incline in a shallow configuration. Bulk shear stress and arresting mechanism are formulated according to the coherence length model that considers momentum transport at a length scale over which grains are spatially correlated. A Bagnold-like streamwise velocity and a non-zero transverse velocity are solved and integrated into a surface kinematic condition to give an advection–diffusion equation for the bulk surface profile, $h(x,t)$, that is solved using the matched asymptotic method. These flow solutions are further employed to determine composite solutions for a flow-front trajectory and a local coherence length, $l(x,t)$, which reveals smooth growth of $h(x,t)$ and $l(x,t)$ from zero at the propagating front with $l(x,t)\ll h(x,t)$. At the rear, $h(x,t)$ vanishes but $l(x,t)$ asymptotes to a constant that depends on inclination angle. According to the arresting mechanism, the location where $l(x,t)\sim h(x,t)$ is solved to the leading order to locate the deposition front so that its propagation dynamics can be derived. A finite flow arrest time, $T_{d}$, and the corresponding finite run-out distance, $L_{d}$, are evaluated when all the flowing mass has passed the deposition front and are employed to construct a modified front trajectory with the deposition effect. The predicted run-out distance and front trajectory profile compare reasonably well with experimental data in the literature on inclinations at angles higher than the material repose angle.

JFM classification

Geophysical and Geological Flows: Geophysical and Geological Flows Granular media: Granular media Geophysical and Geological Flows: Shallow water flows
Type
Papers
Information
Journal of Fluid Mechanics , Volume 806 , 10 November 2016 , pp. 234 - 253
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Copyright
© 2016 Cambridge University Press 

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