Snow avalanche flow-regime transitions induced by mass and random kinetic energy fluxes

We perform a linear-stability analysis of a system of ordinary differential equations describing the motion of dense flowing avalanches. The depth-averaged equations relate the mean translational velocity of the avalanche to the production of turbulent kinetic energy associated with the random motion of the snow granules. Flow friction is described by an extended Voellmy model, where both the Coulomb and turbulent resistance are related to the random kinetic energy. We identify two snow avalanche flow regimes: (1) an unstable frictional flow regime characterized by low random kinetic energy production and (2) a stable, collisional flow regime at the avalanche front. Flow-regime transitions are governed by the production of random kinetic energy, which is controlled by mass. The unstable regime is characterized by a saddle point which the avalanche encounters at the onset of motion and deposition. Depending on the release mass and/or mass growth, the avalanche head will either fluidize, leading to far-reaching avalanches, or starve and die out. At the tail of the avalanche this saddle point also controls the commencement of deposition and therefore the stopping behaviour of avalanches. We discuss the conditions for flow-regime transitions and the enhanced mobility of snow avalanches.