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Raining into shallow water as a description of the collapse of a column of grains

Published online by Cambridge University Press:  24 April 2006

E. LARRIEU
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR CNRS/INPT/UPS 5502, 2, Allée du Professeur Camille Soula, 31400 Toulouse, France
L. STARON
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
E. J. HINCH
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

Abstract

A modified shallow-water model is presented for the collapse of tall columns of grains. The flow is divided in two parts. Depth-averaged shallow-water equations are applied to a thin horizontally spreading layer which is subjected to Coulombic friction. The falling mass of grains is gradually added to the zone of the initial column during the free-fall time of the column. This ‘rain’ is assumed to have no horizontal momentum. The results obtained here are in agreement with both planar and axisymmetric experiments over a range of aspect ratio $a$. In particular, the runout distance is found to vary as $a^{0.65}$ (planar) and $a^{0.52}$ (axisymmetric). The flow dynamics compares well with discrete simulations which have been successfully compared with experiments.

Type
Papers
Copyright
© 2006 Cambridge University Press

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