Thick surface flows of granular materials: The effect of the velocity profile on the avalanche amplitude

TL;DR

This paper investigates how different velocity profiles within granular surface flows influence avalanche behavior, extending existing models by incorporating non-uniform velocity distributions and analyzing their effects analytically.

Contribution

It introduces a modified model with velocity profiles in granular flows, providing analytical solutions and demonstrating the impact on avalanche amplitude.

Findings

Avalanche amplitude is significantly affected by the velocity profile.

Analytical solutions are derived for linear and power-law velocity profiles.

Modifying the velocity assumption alters the physical predictions of granular flow models.

Abstract

A few years ago, Bouchaud al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. Fr. I, 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion/accretion mechanism. Boutreux et al. [Phys. Rev. E, 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. In this article, we therefore modify the above models by introducing a velocity profile in the flow, and study the physical consequences of this modification in the simple situation of an avalanche in an open cell. We present a complete analytical description of the avalanche in the case of a linear velocity profile, and generalize the results for a power-law dependency. We show, in particular, that the amplitude of the avalanche is strongly affected by the velocity profile.