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

TL;DR

This study analytically models the shape of a granular front on a rough incline, incorporating inertia and velocity profile effects, and validates predictions with experimental data, highlighting the importance of the velocity profile in granular flow modeling.

Contribution

It introduces a free shape factor in the Savage-Hutter model to account for velocity profiles, improving the understanding of granular front shapes on inclined planes.

Findings

Analytical model matches experimental data with shape factor α=5/4

Inertia influences the granular front profile through the Froude number

Bagnold-like velocity profile best fits experimental observations

Abstract

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 $\mu(I)$. Unlike previous studies where a "plug flow" is assumed, a free shape factor $\alpha$ 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 $\alpha$ 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 $\alpha$ = 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 $\mu(I)$ and its calibration from experimental data.