Selection of velocity profile and flow depth in granular flows.
The dynamics of a two-dimensional pile constituted by spherical grains organized in parallel layers is investigated theoretically. Only three effects are taken into account in the model: driving by gravity, nonlocal dissipation due to shocks, and trapping of grains by the bumps of the underneath layer. This is sufficient to recover the basic properties of granular avalanches: the transition between static and flowing state is hysteretic; the pile does not flow on the whole height but only in a layer at the surface; the velocity profile inside the flowing layer is approximately linear and is followed by a creep motion in the (quasi) static part. The flow height increases as a function of the pile angle and tends to infinity for a critical angle straight phi(infinity). The dependence of this critical angle with the static angle straight phi(s), the restitution coefficient rho, and the moment of inertia J, is investigated.
Andreotti
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Laboratoire de Physique Statistique de l'Ecole Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France.
Douady
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