A Mathematical Model for Instability in Snow Gliding Motion

Abstract

In this paper a fundamental model is proposed to describe the time-dependent behaviour of uniform snow glide on an infinite slope. This model is composed both of a mechanical balance equation relating a driving force and a resistant force, and of a rate equation for a real contact area at the boundary. In the model, a steady motion of glide is described as a stable equilibrium of glide motion, and a non-steady motion is considered as a transient one not in equilibrium. Finally, the model is applied to a full-depth avalanche release caused by acceleration of snow glide. By comparing the model predictions with glide-velocity field data, a proper model of acceleration prior to full-depth avalanche release is determined. As a result, we can obtain the safety standards to be applied in the event of full-depth avalanches in terms of a glide velocity.