Summary:
Granular avalanches on an open slope form channels, where a flowing region is bounded by quasistatic levees. Current
theories are inaccurate for these flows because they contain static and flowing regions at depths close to hstop.
The dimensions of the unconfined channels and the relations between the flowing and static regions provide insight
on the rheology of the flow. Previous work highlighted laboratory experiments of unconfined shallow granular flows
featuring a curved free surface in the flowing regions, bounded by static margins exerting lateral stresses on the
flow. As the velocity profile and the height of the margins are self-similar, the rheological parameters cannot be
uniquely determined, since the lateral stresses and flow depth both effect the velocity.
This study investigate the characteristics of a flowing granular material down a low-angle V-shaped inclined plane
under the action of gravity. The long-wave (shallow water) approximation relates the geometry of the flow directly
to the slight V-shaped angle and therefore the depth dependence of the velocity can be decoupled from the lateral
stresses. A combination of laboratory experiments and numerical simulations show that the surface of the flow,
steady both in time and down the slope, has significant curvature caused by second normal-stress differences,
similar to those observed in non-Newtonian fluids such as granular suspensions.
Experiments and numerical simulations validate the new theoretical model relating the height and velocity of the flow
directly to the V-shape angle.
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