Propagating fronts on sandpile surfaces

  • Mahadevan L
  • Pomeau Y
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Abstract

The how 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

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Authors

  • L. Mahadevan

  • Y. Pomeau

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