Production and decay of random kinetic energy in granular snow avalanches

Any model of snow avalanches must be able to reproduce velocity profiles. This is a key problem in avalanche science because the profiles are the result of a multitude of snow/ice particle interactions that, in the end, define the rheology of flowing snow. Recent measurements on real-scale avalanches show that the velocity profiles change from a highly sheared profile at the avalanche front to a plug-like profile at the avalanche tail, preventing the application of a single, simple rheology to the avalanche problem. In this paper, we model not only the velocity profiles but also the evolution of the velocity profiles, by taking into account the production and decay of the kinetic energy of the random motion of the snow granules. We find that the generation of this random energy depends on the distribution of viscous shearing within the avalanche. Conversely, the viscous shearing depends on the magnitude of the random energy and therefore its collisional dissipation. Thus, there is a self-consistency problem that must be resolved in order to predict the amount of random energy and therefore the velocity profiles. We solve this problem by stating equations that describe the production and decay of random energy in avalanches. An important guide to the form of these equations is that the generation of random energy is irreversible. We show that our approach successfully accounts for measured profiles in natural avalanches.