Smoothing of sandpile surfaces after intermittent and continuous avalanches: Three models in search of an experiment

We present and analyze in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the "bare" interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the "bare'' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.