Mathematical modeling of snow entrainment in avalanche motion

The entrainment of snow plays an important role in snow avalanche dynamics. Various ways of incorporating the entrainment effect into avalanche mathematical models are discussed in this paper. The results of calculations using a variety of formulae for the entrainment rate that have been proposed for bed erosion by flows of various physical natures are presented. For various studied entrainment laws it is found that in motion at a steep slope the entrainment takes place in a frontal part of an avalanche. The motion of an avalanche depends mainly on the total depth of the entrainable snow layer and on the length of the entrainment zone, but only weakly on the form of the entrainment law. However the length of an entrainment zone depends on the values of the coefficients entering the entrainment law.