Considerations on scaling behavior in avalanche flow along cycloidal and parabolic tracks

Peter Gauer

doi:10.1016/j.coldregions.2018.02.012

Abstract

A simple scaling analysis using a simple mass block model supports observations and measurements on snow avalanches, that the maximum front-velocity of “major” avalanches scales with the total drop height of the track. That is Umax∼g Hsc/2 and the average velocity U¯≈2πUmax. The approximation of avalanche tracks as either cycloid or parabola reveal furthermore the connection between the path geometry and the well-known α-β model (Lied and Bakkehøi, 1980). This connection implies a strong dependency of the apparent retardation on the mean steepness of the track. The velocity scaling and the dependency of the retardation on the mean slope angle needs to be reflected in avalanche models.

Highlights

Snow avalanches constitute in many alpine areas a serious threat to settlements and infrastructure
The velocity scaling and the dependency of the retardation on the mean slope angle needs to be reflected in avalanche models
Avalanche practitioners use a series of more or less sophisticated dynamical avalanche models to identify areas endangered by avalanches; models like the Voellmymodel (Voellmy, 1955), the PCM-model (Perla et al, 1980), and more recently RAMMS (Christen et al, 2010), SAMOS-AT (Sampl and Granig, 2009) or similar ones

Summary

Introduction

Snow avalanches constitute in many alpine areas a serious threat to settlements and infrastructure. To this end, avalanche measurements of runout and velocity are qualitatively compared with results from the scaling analysis

Scaling behavior of a simple mass block model

Cycloidal path profile

Compilation of observed trends

Comparison to measurements and observations

Conclusions