Volume 46, Number 5, June I 1999
|Page(s)||595 - 601|
|Section||Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics|
|Published online||01 September 2002|
Propagating fronts on sandpile surfaces
Laboratoire de Physique Statistique, Ecole Normale Supérieure 24 rue Lhomond, 75231
Paris Cedex 05, France
Accepted: 29 March 1999
The flow of granular matter such as sand is often characterized by the motion of a thin superficial layer near the free surface, while the bulk of the solid remains immobile. A pair of equations called the BCRE equations (Bouchaud J-P., Cates M. E., Ravi Prakash J. and Edwards S. F. J. Phys. 4 (1994) 1383) have been proposed to model these flows and account for the dynamic exchange of mass between moving and stationary grains using the simplest kinematic considerations. We uncover a new conservation law for the BCRE equations and its variants that unifies a variety of recent special solutions and show that these equations support simple waves, and are capable of finite time singularities that correspond to propagating erosion fronts.
PACS: 45.70.Ht – Avalanches / 83.70.Fn – Granular solids / 83.50.Tq – Wave propagation, shocks, fracture, and crack healing
© EDP Sciences, 1999
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