How does the flow rheology constrain the erosion rate of an avalanche?

What is it about?

The complicated problem of an avalanche flowing over an erodible snow cover is simplified by assuming that the flow is isotropic (but not constant in time) in the two slope-parallel directions (a.k.a. the infinite-slope approximation). This makes the problem effectively one-dimensional along the slope-normal direction. The second simplification is to assume that the particles at the top of the snow cover are instantly released when the shear stress from the avalanche reaches a critical value. As a consequence, the shear stress at the interface will be locked at this critical value even if the shear stress near the bottom of the avalanche exceeds it. The difference is used to accelerate the released snow particles―the erosion rate is proportional to the difference between avalanche shear stress and snow-cover shear strength, and inversely proportional to the mean avalanche velocity. A numerical model demonstrates how the flow depth, the velocity profile and the entrainment rate evolve in time for two cases, a visco-plastic (Bingham) fluid and a simple granular (Bagnold) fluid. The simulations converge to asymptotic solutions where the entrainment rate tends to a constant value and the flow depth and both the flow depth and the velocity increase linearly in time.

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Why is it important?

Avalanches are known to erode the snow cover as they flow over it. This process has a strong influence on the dynamics of the avalanche: On the one hand, the eroded snow must be accelerated to the avalanche speed, thereby slowing down the flow. On the other hand, continued entrainment of snow is a condition for avalanches to attain long run-out. Very few dynamical avalanche models include entrainment, and if they do, they use empirical formulae with free parameters that cannot directly be related to measurable snow-cover and avalanche properties. This increases the uncertainty of avalanche run-out calculations significantly beyond the uncertainty in our knowledge of the initial conditions. This paper presents a simplified model in which the entrainment rate is computed self-consistently from the flow rheology and the snow-cover properties.