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

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