Mathematical Simulation of the Process of Motion of a Snow Avalanche

Abstract

Abstract A “hydraulic" model of the motion of bed-type snow avalanches is developed, its qualitative particularities are discussed, and results of comparison of prediction and observations are presented. The proposed model allows calculation of the parameters of motion of snow avalanches possible for a given bed depending on the snow situation and other conditions. The characteristics concerned are the distribution of velocities averaged over the cross-section of the flow and the thickness of snow in an avalanche at every instant of its motion. The class of avalanches considered is that in which a compact snow flow moves along a distinct avalanche bed consisting of an accumulation region, a bed, and an avalanche cone. It is proposed to model the avalanche bed with a certain inclined and curved channel of given width and shape of cross-section. The characteristics of the model channel are defined on the basis of a topographic map of the corresponding avalanche bed. The motion of avalanche snow is modelled by the flow of an incompressible “liquid" subjected to the action of gravity, internal resistance, and external friction. Destruction and capture of undisturbed snow by an avalanche from the slope is accounted for by introducing into the equations of motion distributed sources of mass the intensity of which depends on the sought characteristics of the problem and which is defined while solving the problem. On the basis of simple physical considerations connected with the finite shear stress in the snow, it is shown that for sufficiently large avalanches the specific friction force becomes inversely proportional to the thickness of the flow. The proposed mechanism of friction explains the abnormally high mobility of catastrophically large avalanches. The adopted model possesses a number of properties agreeing qualitatively with the observational data for avalanches. Computer solutions have the form of rather prolonged flows with the shape of the front part typical for avalanches and with characteristic wave formations in the flow which sometimes result in pulsating regimes of motion. The report concludes with results of comparison of predicted and observed characteristics of motions of avalanches for some real avalanche beds demonstrating possibilities of the proposed model.