Gravity-Driven Rapid Shear Flows of Dry Granular Masses in Helically Curved and Twisted Channels

In this paper we present a two-dimensional depth-integrated theory for the gravity-driven free surface flow of a granular avalanche over a helicoidal topography which is an important extension of the original Savage & Hutter theory. In contrast to other previous extensions, this local coordinate system is based on a generating curve with curvature and torsion. Its derivation was necessary because real avalanches are often guided by rather strongly curved and twisted corries. The motion of the avalanche follows the helicoidal talweg. The theory that is based on the helicoidal metric and non-orthogonal basis allows relatively easy access to comparisons with laboratory experiments. The emerging theory is believed to be capable of predicting the flow of dense granular materials over moderately curved and twisted channels. The model equations are tested by constructing analytical similarity solutions. The qualitative behaviour of both the traditional theory and its present extension agree well through these similarity solutions.