An alternative depth-integrated formulation for granular avalanches over temporally varying topography with small curvature

Abstract

An alternative formulation is proposed for deriving depth-integrated equations for gravity-driven granular avalanches over a non-trivial topography with small curvature. The coordinate system of Bouchut and Westdickenberg (2004 Bouchut, F and Westdickenberg, M. 2004. Gravity driven shallow water models for arbitrary topography. Commun. Math. Sci., 2: 359–389. [Crossref] , [Google Scholar]) is combined with the unified coordinate (UC) method, so that it can evolve in accordance with the entrainment–deposition processes at the basal surface. The resultant mass and momentum equations are formulated as a conservation system of the Cartesian components of the conservative physical variables. The motion of the flows is driven by the basal topography-induced pressure, pressure gradient, and resisted by the basal friction. The best benefit of this formulation is that it greatly simplifies the computation of the varying coordinate orientations. The features and advantages of this formulation are illustrated by the sliding-mass examples where we simulate the motion of a finite mass of granular material sliding down an inclined chute, running through a transition zone, and being deposited onto a horizontal plane.