Deflecting dams and the formation of oblique shocks in snow avalanches at Flateyri, Iceland

摘要

Snow avalanches are a threat in many populated mountainous regions, and deflecting dams are often built to divert them away from people, and infrastructure, into less harmful areas. When an avalanche is deflected by a dam or wedge, it often generates rapid changes in the flow thickness and velocity, which can be modeled as an oblique shock wave. This paper reviews classical oblique shock theory, which was originally developed for shallow water flows, and uses it to make predictions of the maximum runup height on a deflecting dam, the downstream flow velocity, and the width of the channelized stream. The theory is used to investigate field observations of snow avalanches at Flateyri in Iceland, where a dam has deflected two avalanches away from the town and produced a channelized stream that flowed parallel to the dam. The results indicate that there is no one single set of upstream flow conditions that parameterizes the flow behavior, but the solution evolves as the avalanche propagates along the dam in response to the deceleration imposed by the slope. Fully time-dependent shock capturing numerical simulations of the Skollahvilft avalanche, which hit the dam on 21 February 1999, are used to show how the channelized stream widens as the avalanche slows down and thickens toward the end of the runout zone. The oblique shock relations nevertheless provide useful local order of magnitude estimates for the flow conditions immediately upstream of the shock.