On the front shape of an inertial granular flow down a rough incline

G Saingier (1) , S Deboeuf (1) , Pierre-Yves Lagrée (1)

1 DALEMBERT - Institut Jean Le Rond d'Alembert

Granular material flowing on complex topographies are ubiquitous in industrial and geophysical situations. In this paper, we study the small-scale model of a granular layer flowing on a rough incline. The shape of a granular front is solved analytically by using a 1D Savage-Hutter's model based on depth-averaged mass and momentum equations with the fractional expression for the frictional rheology µ(I). Unlike previous studies where a "plug flow" is assumed, a free shape factor α describing the vertical velocity profile, is taken into account to determine the solution. Such a way, we put in evidence an effect of inertia through the Froude number Fr and the shape factor α on the front profile. The analytical predictions are compared with experimental results published by [O. Pouliquen, Phys. Fluids 11, 1956 (1999)] and with our new experimental data obtained at higher Froude numbers. A good agreement between theory and experiments is found when α = 5/4 is used in our model, corresponding to a Bagnold-like velocity profile. However, open questions are raised about the vertical velocity profile in granular flows and about the expression of the rheological function µ(I) and its calibration from experimental data.

Mots clés: inclined plane; front morphology; granular flow; frictional rheology; Saint-Venant equations; Bagnold-like velocity profile

Domaines: Autre [cond-mat.other]

G Saingier, S Deboeuf, Pierre-Yves Lagrée. On the front shape of an inertial granular flow down a rough incline. 2015. ⟨hal-01226495⟩