Exact Solutions of a Model for Granular Avalanches

TL;DR

This paper provides exact analytical solutions for a non-linear model of granular avalanches, predicting shock behavior, slope relaxation, and velocities in sandpile profiles, aiding experimental understanding.

Contribution

It introduces exact solutions to the non-linear BCRE model for granular avalanches without diffusion, offering new analytical insights into avalanche dynamics.

Findings

Analytical shock conditions and coordinates derived.

Universal quantities at the shock identified.

Predictions for slope relaxation and velocities in sandpiles.

Abstract

We present exact solutions of the non-linear {\sc bcre} model for granular avalanches without diffusion. We assume a generic sandpile profile consisting of two regions of constant but different slope. Our solution is constructed in terms of characteristic curves from which several novel predictions for experiments on avalanches are deduced: Analytical results are given for the shock condition, shock coordinates, universal quantities at the shock, slope relaxation at large times, velocities of the active region and of the sandpile profile.