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.