Granular front for flow down a rough incline: about the value of the shape factor in depths averaged models
1 Sorbonne Universités, UPMC Univ Paris 06, CNRS, UMR 7190, Institut Jean Le Rond d’Alembert, F-75005 Paris, France
2 SVI (Saint-Gobain/CNRS UMR 125), Aubervilliers, France
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Published online: 30 June 2017
The thin layer (or Boundary Layer scaling) approximation of the Navier Stokes equation with μ(I) rheology for dry granular flows over an inclined plate is presented. It is called “Granular RNS/P” (Reduced Navier Stokes/ Prandtl). Integrated over the depth, it gives the classical depth averaged equations (Shallow Water type equations, popularized by Savage Hutter). But the process of depth averaging needs hypothesis on the velocity shape profile trough a “shape factor coefficient”. In the case of the displacement of the front of an avalanche down a rough incline, we present comparisons of “Granular RNS/P” simulations versus depth averaged model (which compares well with experimental data). One conclusion is that the shape factor goes from 5/4, the Bagnold value, to a unit value, corresponding to a flat velocity profile, in a region very close to the front of the avalanche.
© The Authors, published by EDP Sciences, 2017
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