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Similarity solutions for a Voellmy model of snow avalanches with finite mass

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This paper, though independently written, continues an analysis of similarity solutions for the two-dimensional flow of a mass of cohesionless granular material down rough, flat and curved beds, see Savage and Nohguchi [12], Nohguchi, Hutter and Savage [7]. The basal friction force is assumed to be composed of a Mohr-Coulomb type component with a bed friction angle that is position dependent plus a viscous Voellmy-type resistive stress, that is proportional to the velocity squared. This granular flow model is conjectured to adequately model the motion and dispersion of flow avalanches of snow whose air borne powder component can be ignored.

The depth and velocities relative to those of the centre of mass of the moving pile are determined analytically, and it is shown that the pile has a parabolic cap shape and the difference velocity varies linearly with distance from the centre of mass. The length and the position and velocity of the centre mass are calculated numerically. We explicitly show:

  1. (i)

    Existence of a rigid body motion of the moving pile requires either a variable bed friction angle or a bed with gradually varying bed inclination angle or both.

  2. (ii)

    A model avalanche with no Voellmy-type resistive drag on a plane bed will accelerate for ever.

  3. (iii)

    Along a plane bed the centre of mass can reach a final equilibrium speed only when the Voellmy type drag is accounted for and the basal friction angle varies with position.

  4. (iv)

    Along curved beds rigid body motions of the moving pile are possible with accelerating, decelerating and steady centre of mass motions.

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References

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Author notes

  1. K. Hutter

    Present address: Institut für Mechanik, Technische Hochschule Darmstadt, Hochschulstrasse 1, D-6100, Darmstadt, Federal Republic of Germany

  2. Y. Nohguchi

    Present address: National Research Center for Disaster Prevention, Nagaoka Institute of Snow and Ice Studies, Suyoshi, 940, Nagaoka-shi, Japan

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    1. K. Hutter
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    2. Y. Nohguchi
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    Hutter, K., Nohguchi, Y. Similarity solutions for a Voellmy model of snow avalanches with finite mass. Acta Mechanica 82, 99–127 (1990). https://doi.org/10.1007/BF01173741

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