Internal avalanche in a granular media
Résumé
The flow shape of a layer of granular material entrained by the motion of a bottom plate is studied. The flow is assumed steady, unidirectional and iso-volume, and is modeled by the Navier-Stokes equation, along with a simple constitutive law based on a constant friction coefficient. Under these assumptions, the problem can be tackled with the characteristics method, which yields an analytical expressions of the iso-velocity curves in the plane perpendicular to the flow. The flow shape is found to depend on the plate friction coefficient and the plate width, and the results can be summarized in a phase diagram. The possible extension of the study to a shear rate dependent friction coefficient is discussed.