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Comments on “On a Continuum Model for Avalanche Flow and Its Simplified Variants” by S. S. Grigorian and A. V. Ostroumov

by Dieter Issler

Geosciences 2020, 10(3), 96; https://doi.org/10.3390/geosciences10030096 - 2 Mar 2020

Cited by 5 | Viewed by 3273

Abstract

This note first summarizes the history of the manuscript “On a Continuum Model for Avalanche Flow and Its Simplified Variants” by Grigorian and Ostroumov—published in this Special Issue—since the early 1990s and explains the guiding principles in editing it for publication. The changes are then detailed and some explanatory notes given for the benefit of readers who are not familiar with the early Russian work on snow avalanche dynamics. Finally, the editor’s personal views as to why he still considers this paper of relevance for avalanche dynamics research today are presented in brief essays on key aspects of the paper, namely the role of simple and complex models in avalanche research and mitigation work, the status and possible applications of Grigorian’s stress-limited friction law, and non-monotonicity of the dynamics of the Grigorian–Ostroumov model in the friction coefficient. A comparison of the erosion model proposed by those authors with two other models suggests to enhance it with an additional equation for the balance of tangential momentum across the shock front. A preliminary analysis indicates that continuous scouring entrainment is possible only in a restricted parameter range and that there is a second erosion regime with delayed entrainment. Full article

(This article belongs to the Special Issue Snow Avalanche Dynamics)

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20 pages, 1312 KiB

Open AccessArticle

On a Continuum Model for Avalanche Flow and Its Simplified Variants

by Samvel S. Grigorian and Alexander V. Ostroumov

Geosciences 2020, 10(1), 35; https://doi.org/10.3390/geosciences10010035 - 19 Jan 2020

Cited by 7 | Viewed by 3467

Abstract

Mathematical models of different degrees of complexity, describing the motion of a snow avalanche along a path with given center line and spatially varying width, are formulated and compared. The most complete model integrates the balance equations for mass and momentum over the cross-section and achieves closure through an entrainment function based on shock theory and a modified Voellmy bed friction law where the Coulombic contribution to the bed shear stress is limited by the shear strength of the snow cover. A simplified model results from integrating these balance equations over the (time-dependent) length of the flow and postulating weak similarity of the evolving avalanche shape. On path segments of constant inclination, it can be solved for the flow depth and speed of the front in closed form in terms of the imaginary error function. Finally, the very simplest model assumes constant flow height and length. On an inclined plane, the evolution of flow depth and velocity predicted by the simplified model are close to those from the full model without entrainment and with corresponding parameters, but the simplest model with constant flow depth predicts much higher velocity values. If the friction coefficient is varied in the full model with entrainment, there can be non-monotonous behavior due to the non-linear interplay between entrainment and the limitation on the Coulomb friction. Full article

(This article belongs to the Special Issue Snow Avalanche Dynamics)

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