Shallow granular flows down flat frictional channels: steady flows and longitudinal vortices.

Granular flows down inclined channels with smooth boundaries are common in nature and industry. Nevertheless, flat boundaries have been much less investigated than bumpy ones, which are used by most experimental and numerical studies to avoid sliding effects. Using numerical simulations of each grain and of the side walls we recover quantitatively experimental results. At larger angles we predict a rich behavior, including granular convection and inverted density profiles suggesting a Rayleigh-Bénard type of instability. In many aspects flows on a flat base can be seen as flows over an effective bumpy base made of the basal rolling layer, giving Bagnold-type profiles in the overburden. We have tested a simple viscoplastic rheological model [Nature (London) 441, 727 (2006)] in average form. The transition between the unidirectional and the convective flows is then clearly apparent as a discontinuity in the constitutive relation.