Granular surface flow via successive destabilization: a continuum approach. (English) Zbl 1207.76137

Hoffmann, Andreas; Linz, Stefan J.

Physica D 239, No. 23-24, 2025-2038 (2010).

In this paper a global and localized granular surface flow is analyzed in a model that takes into account the basic forces between a flowing granular layer and an underlying granular bed. Starting from a quantitatively correct description of global stick-slip avalanches on the surfaces of heaps allows to describe localized flows of various types as seen in experiments of A. Daerr and S. Douady [Nature (London) 399, 241 (1999)]. The descriptive level takes into account the free surface and the velocity of the flow solely. The presented model is limited to cases where this surface is effectively one-dimensional so that the model equations are consequently one-dimensional in space. This kind of description makes available to account for the tight coupling between local grain velocity and local height of the so-called lonely waves. The model shows the nature of a wave of mobilization and deposition. Granular material is set into motion in a domino-like manner. In addition destabilization of material behind an avalanche is taken into account. The front velocities are found to be constant and in general head and rear front travel with the same velocity in the model. The front velocities depend on the tilt angle of the heap that those localized structures run down on. A critical angle is observed above which the rear front velocity abruptly switches sign from positive (downslope) to negative (upslope) values. Furthermore, global influences of the surface shape of a flowing granular layer on Bagnold friction are found. This characteristic collisional friction between flowing layers and beds is shown to cause S-shaping of the free surface for rapid flow velocities. Finally, the model also explains the power spectrum of avalanches as experimentally detected by H. Jaeger, C. Liu and S. Nagel [Phys. Rev. Lett. 62, 40 (1989)].

Reviewer: Felix Kaplanski (Tallinn)

MSC:

76T25	Granular flows
74C99	Plastic materials, materials of stress-rate and internal-variable type
37B15	Dynamical aspects of cellular automata

Keywords:

granular matter; avalanches; front propogation; continuum modeling

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