A model for the dynamics of sandpile surfaces

Abstract

We propose a new continuum description of the dynamics of sandpile surfaces, which recognizes the existence of two populations of grains: immobile and rolling. The rolling grains are carried down the slope with a constant drift velocity and have a certain dispersion constant. We introduce a simple bilinear approximation for the interconversion process, which represents both the random sticking of rolling grains (below the angle of repose), and the dislodgement of immobile grains by rolling ones (for greater slopes). We predict that the mean downhill motion of rolling grains causes surface features to move uphill; shocks can arise at large amplitudes