Numerical Simulation of Powder-Snow Avalanches

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Abstract
Appropriate expressions describing the motion of powder-snow avalanches are derived. The model consists of four equations, i.e. the conservation equations of fluid mass, snow-particle mass, momentum of the cloud, and kinetic energy of the turbulence. Insofar as the density difference between the avalanche and the ambient air becomes rather large compared with the density of the ambient air, the Boussinesq approximation, which is typically used to analyze density currents, cannot be adopted in the present case. As opposed to previous models, the total buoyancy of a powder-snow avalanche is allowed to change freely via erosion from and deposition on to a static snow layer on a slope. In the model, the snow-particle entrainment rate from the slope is directly linked to the level of turbulence. A discontinuous, large-scale powder-snow avalanche occurred on 26 January 1986 near Maseguchi, Niigata Prefecture, Japan. The avalanche appears to have had a dense core at its base. The present model is employed to simulate that part of the avalanche above any dense core. The depth of the layer of fresh snow is considered to be an important parameter in the model. The larger the depth of fresh snow, the larger is the concentration of snow attained in the avalanche, and the faster its speed. It is seen that the model provides a reasonable description of the powder-snow avalanche generated near Maseguchi. In particular, the model prediction that a powder-snow avalanche strong enough to reach Maseguchi requires a depth of fresh snow of at least 2 m is in agreement with the observed depth just before the event.