Erosion-deposition dynamics and long distance propagation of granular avalanches
The net erosion-deposition rate of a snow avalanche is fundamental to the dynamics of the flow and in determining its growth or decay. Small-scale experiments are performed in this paper that are analogous to a finite mass release on a marginally stable surface layer of snow. An avalanche is initiated by releasing a given volume of yellow sand onto a stationary erodible layer of the same material, but coloured red, which coats the rough bed of an inclined plane. Depending on the erodible layer depth and the slope angle, the resulting avalanche is found to either decay, grow, propagate steadily or rapidly shed grains to produce secondary avalanches. The use of different coloured sand with identical frictional properties shows that a particle exchange occurs during erosion from the substrate and deposition by the avalanche, which eventually results in a flow that is comprised entirely of particles from the stationary layer rather than the initial release. It is notoriously difficult to model the erosion and deposition processes in granular flows such as these. Nonetheless, it is shown in this paper that a two-dimensional shallow-water-like avalanche model, together with a basal friction rule that is responsible for handling the transition between stationary and moving regions of the flow, is able to qualitatively reproduce of all the observed avalanche behaviours. The model is solved numerically together with equations governing the three-dimensional motion of individual particles, which allows the positions of specific grains to be tracked. The results illustrate how a continuous exchange of particles with the substrate layer is fundamentally important to the propagation of such avalanches. An investigation into long distance propagation distance behaviour reveals that avalanches can reach a steady state, the size and speed of which are independent of the initially released volume but are set by the slope angle and basal layer thickness. In certain conditions, including an abundance of erodible material available, avalanches can sometimes grow to steady states that are significantly more massive than the flows from which they are originally formed. This paper therefore demonstrates the dominant effect that erosion and deposition may have, and the importance of including these effects correctly in operational forecast models of snow avalanches and geophysical mass flows.