A hierarchy of avalanche models on arbitrary topography

I. Luca, K. Hutter, Y. C. Tai, C. Y. Kuo

Research output: Contribution to journalArticlepeer-review

50 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)121-149
Number of pages29
JournalActa Mechanica
Issue number1-4
Publication statusPublished - 2009 Jun

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanical Engineering


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