  Considering recent results revealing the existence of multi-scale rigid
clusters of grains embedded in granular surface flows, i.e. flows down an
erodible bed, we describe here the surface flows rheology through a non-local
constitutive law. The predictions of the resulting model are compared
quantitatively to experimental results: The model succeeds to account for the
counter-intuitive shape of the velocity profile observed in experiments, i.e. a
velocity profile decreasing exponentially with depth in the static phase and
remaining linear in the flowing layer with a velocity gradient independent of
both the flowing layer thickness, the angle between the flow and the
horizontal, and the coefficient of restitution of the grains. Moreover, the
scalings observed in rotating drums are recovered, at least for small rotating
speed.
