Numerical Simulation of Dry-Snow Avalanche Flow over Natural Terrain

Abstract

A physical model for dry snow avalanche flow is presented. The well established model for dense granular flow proposed by Savage and Hutter [21] is adapted to describe the dense, lower part of a snow avalanche. In order to account for the high velocities of snow avalanches, a velocity dependent bed shear stress in addition to the Coulomb law for dry friction is introduced. Since the model has to be applied to arbitrarily shaped topographies, certain simplifying assumptions of geometrical nature must be introduced. In contrast to former numerical implementations of the Savage-Hutter model based on Finite Difference schemes, a Lagrangian Finite Volume method is formulated using integral balance laws. For the powder snow avalanche forming on top of the denser part a mixture model with a constant slip velocity between ice particles and air is introduced. The k-є turbulence model modified in order to account for buoyancy effects caused by the suspended particles is implemented. The resulting system of equations is solved by applying a Finite Volume scheme on a fixed grid. The transfer of snow mass from the dense flow into the powder snow avalanche is modelled by an analogy to turbulent momentum transfer.