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Formation of levees, troughs and elevated channels by avalanches on erodible slopes

  • A. N. Edwards (a1), S. Viroulet (a1), B. P. Kokelaar (a2) and J. M. N. T. Gray (a1)
Abstract

Snow avalanches are typically initiated on marginally stable slopes with a surface layer of fresh snow that may easily be incorporated into them. The erosion of snow at the front is fundamental to the dynamics and growth of snow avalanches and they may rapidly bulk up, making them much more destructive than the initial release. Snow may also deposit at the rear, base and sides of the flow and the net balance of erosion and deposition determines whether an avalanche grows or decays. In this paper, small-scale analogue experiments are performed on a rough inclined plane with a static erodible layer of carborundum grains. The static layer is prepared by slowly closing down a flow from a hopper at the top of the slope. This leaves behind a uniform-depth layer of thickness $h_{stop}$ at a given slope inclination. Due to the hysteresis of the rough bed friction law, this layer can then be inclined to higher angles provided that the thickness does not exceed $h_{start}$ , which is the maximum depth that can be held static on a rough bed. An avalanche is then initiated on top of the static layer by releasing a fixed volume of carborundum grains. Dependent on the slope inclination and the depth of the static layer three different behaviours are observed. For initial deposit depths above $h_{stop}$ , the avalanche rapidly grows in size by progressively entraining more and more grains at the front and sides, and depositing relatively few particles at the base and tail. This leaves behind a trough eroded to a depth below the initial deposit surface and whose maximal areal extent has a triangular shape. Conversely, a release on a shallower slope, with a deposit of thickness $h_{stop}$ , leads to net deposition. This time the avalanche leaves behind a levee-flanked channel, the floor of which lies above the level of the initial deposit and narrows downstream. It is also possible to generate avalanches that have a perfect balance between net erosion and deposition. These avalanches propagate perfectly steadily downslope, leaving a constant-width trail with levees flanking a shallow trough cut slightly lower than the initial deposit surface. The cross-section of the trail therefore represents an exact redistribution of the mass reworked from the initial static layer. Granular flow problems involving erosion and deposition are notoriously difficult, because there is no accepted method of modelling the phase transition between static and moving particles. Remarkably, it is shown in this paper that by combining Pouliquen & Forterre’s (J. Fluid Mech., vol. 453, 2002, pp. 133–151) extended friction law with the depth-averaged $\unicode[STIX]{x1D707}(I)$ -rheology of Gray & Edwards (J. Fluid Mech., vol. 755, 2014, pp. 503–544) it is possible to develop a two-dimensional shallow-water-like avalanche model that qualitatively captures all of the experimentally observed behaviour. Furthermore, the computed wavespeed, wave peak height and stationary layer thickness, as well as the distance travelled by decaying avalanches, are all in good quantitative agreement with the experiments. This model is therefore likely to have important practical implications for modelling the initiation, growth and decay of snow avalanches for hazard assessment and risk mitigation.

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Copyright
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Corresponding author
Email address for correspondence: aedwards@maths.man.ac.uk
Linked references
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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

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Edwards et al. supplementary movie
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Edwards et al. supplementary movie
A movie showing the travelling wave solution of figure 19 translated back to a 40 by 20 cm section of the $(x,y)$ domain, which the three-dimensional erosion-deposition wave passes through.

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Edwards et al. supplementary movie
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