Journal of Fluid Mechanics


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

E. LARRIEU a1, L. STARON a2 and E. J. HINCH a2
a1 Institut de Mécanique des Fluides de Toulouse, UMR CNRS/INPT/UPS 5502, 2, Allée du Professeur Camille Soula, 31400 Toulouse, France
a2 Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

Article author query
larrieu e   [Google Scholar] 
staron l   [Google Scholar] 
hinch ej   [Google Scholar] 


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.

(Published Online April 24 2006)
(Received February 22 2005)
(Revised August 19 2005)