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Comment published on 2 March 2020, see Geosciences 2020, 10(3), 96.
Open AccessArticle

On a Continuum Model for Avalanche Flow and Its Simplified Variants

Institute of Mechanics, Lomonossov State University, 119192 Moscow, Russia
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Author to whom correspondence should be addressed.
Deceased.
Geosciences 2020, 10(1), 35; https://doi.org/10.3390/geosciences10010035
Received: 15 November 2019 / Revised: 5 December 2019 / Accepted: 9 December 2019 / Published: 19 January 2020
(This article belongs to the Special Issue Snow Avalanche Dynamics)
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. View Full-Text
Keywords: snow avalanches; mathematical models; snow entrainment; Voellmy and Grigorian friction laws; hydraulic models; runout distance; analytic solutions snow avalanches; mathematical models; snow entrainment; Voellmy and Grigorian friction laws; hydraulic models; runout distance; analytic solutions
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Grigorian, S.S.; Ostroumov, A.V. On a Continuum Model for Avalanche Flow and Its Simplified Variants. Geosciences 2020, 10, 35.

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