Interplay of entrainment and rheology in snow avalanches: a numerical study

A one-dimensional evolution equation for the slope-normal velocity profile of a streamwise uniform avalanche over an entrainable bed is derived. The boundary conditions are no slip at the bed, a stress-free surface and constant bed shear stress equal to the shear strength of the snow cover. The resulting equation is solved numerically by means of finite differences on a regular grid with a superposed fine grid near the erosion front that is adjusted at each time-step. The first exploratory simulations yield realistic entrainment rates and show that the entrainment rate tends towards a constant value while the flow depth and the velocity increase linearly with time for all investigated rheologies. It is shown that there indeed exists a rheology-independent asymptotic solution to the equation of motion of an entraining slab if the bottom friction is equal to the bed shear strength; the asymptotic acceleration is found to be half the downslope gravitational acceleration. The model can easily be extended to general path profiles, non-uniform flows and variable snow properties.