Non-cartesian, topography-based avalanche equations and approximations of gravity driven flows of ideal and viscous fluids

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

Research output: Contribution to journalArticle

14 Citations (Scopus)

Abstract

When dealing with geophysical flows across three-dimensional topography or other thin layer flows, for the physical modelling and for computational reasons, it is more convenient to use curvilinear coordinates adapted to the basal solid surface, instead of the Cartesian coordinates. Using such curvilinear coordinates, e.g. introduced by Bouchut and Westdickenberg, 3 and the corresponding contravariant components of vector and tensor fields, we derive in full generality the governing equations for the avalanche mass. These are next used to deduce (i) the thin layer equations for arbitrary topography, when the flowing mass is an ideal fluid, and (ii) the thin layer equations corresponding to arbitrary topography and to a viscous fluid that experiences bottom friction, modelled by a viscous sliding law.

Original languageEnglish
Pages (from-to)127-171
Number of pages45
JournalMathematical Models and Methods in Applied Sciences
Volume19
Issue number1
DOIs
Publication statusPublished - 2009 Jan 1

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Applied Mathematics

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