Has it really stopped? Interplay between rheology, topography and mesh resolution in numerical modelling of snow avalanches

Depth-averaged models of snow avalanches have hitherto lacked an objective arrest criterion. In this study, we investigate the stoppage mechanisms of simulated avalanches, considering the interplay between mesh resolution, simple/complex topographies, and cohesion. We use a second-order depth-averaged model including a modified Voellmy model with cohesion and a physical yielding criterion. Simulated results were found to be sensitive to the mesh resolution, until the cell width is less than 20 % of the characteristic flow depth. The yielding criterion is sufficient to unambiguously define flow arrest for highly cohesive avalanches, even on the complex topography with feature sizes comparable to the typical flow depth. In contrast, for weakly-cohesive avalanches on the complex topography, a fully static state is never reached, due to numerical diffusion enhanced by local non-zero slopes. We hence investigated different global and local arrest criteria applied during post-processing, complementing the yielding criterion. Most of these criteria require setting ad-hoc thresholds, the values of which depend on numerous factors. However, tracking the evolution to a static state of the highest point of the flow material in the runout zone appears to offer an objective and practical solution to indicate when the model enters a numerical-diffusion-dominated regime, whereupon simulations can reasonably be terminated.