Acta Mechanica

, Volume 205, Issue 1–4, pp 121–149 | Cite as

A hierarchy of avalanche models on arbitrary topography



We use the non-Cartesian, topography-based equations of mass and momentum balance for gravity driven frictional flows of Luca et al. (Math. Mod. Meth. Appl. Sci. 19, 127–171 (2009)) to motivate a study on various approximations of avalanche models for single-phase granular materials. By introducing scaling approximations we develop a hierarchy of model equations which differ by degrees in shallowness, basal curvature, peculiarity of constitutive formulation (non-Newtonian viscous fluids, Savage–Hutter model) and velocity profile parametrization. An interesting result is that differences due to the constitutive behaviour are largely eliminated by scaling approximations. Emphasis is on avalanche flows; however, most equations presented here can be used in the dynamics of other thin films on arbitrary surfaces.


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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Division of MechanicsResearch Center for Applied Sciences, Academia SinicaNangang, TaipeiTaiwan
  2. 2.Department of Civil EngineeringNational Chi Nan UniversityPuli, NantouTaiwan
  3. 3.ZürichSwitzerland

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