Modeling shallow gravity-driven solid-fluid mixtures over arbitrary topography

Ioana Luca, Yih-Chin Tai, Chih Yu Kuo

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The purpose of this paper is to derive modeling equations for debris flows on real terrain. Thus, we use curvilinear coordinates adapted to the topography as introduced, e.g., by Bouchut and Westdickenberg [F. Bouchut and M. Westdickenberg, Commun. Math. Sci., 2(3), 359-389, 2004], and develop depth-averaged models of gravity-driven saturated mixtures of solid grains and pore fluid on an arbitrary rigid basal surface. First, by only specifying the interaction force and ordering approximations in terms of an aspect ratio between a typical length perpendicular to the topography, and a typical length parallel to the topography, we derive the governing equations for the shallow flow of a binary mixture, driven by gravitational force. In doing so, the non-uniformity through the avalanche depth of the constituent velocities and of the solid volume fraction is accounted for by coefficients of Boussinesq type. Then, the material behaviour peculiarities of both constituents properly enter the theory. One constituent is a granular solid. For its stresses we propose three models, one of them of Mohr-Coulomb type. The other constituent is a Newtonian/non-Newtonian fluid with small viscosity, obeying a viscous bottom friction condition. The final governing equations for the shallow flow of the mixture, incorporating the constitutive assumptions, are deduced, and the limiting equilibrium is then investigated.

Original languageEnglish
Pages (from-to)1-36
Number of pages36
JournalCommunications in Mathematical Sciences
Volume7
Issue number1
Publication statusPublished - 2009 Jan 1

Fingerprint

Topography
Gravity
Gravitation
Fluid
Fluids
Governing equation
Arbitrary
Modeling
Debris Flow
Curvilinear Coordinates
Non-Newtonian Fluid
Non-uniformity
Binary Mixtures
Newtonian Fluid
Avalanche
Binary mixtures
Debris
Volume Fraction
Aspect Ratio
Perpendicular

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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Modeling shallow gravity-driven solid-fluid mixtures over arbitrary topography. / Luca, Ioana; Tai, Yih-Chin; Kuo, Chih Yu.

In: Communications in Mathematical Sciences, Vol. 7, No. 1, 01.01.2009, p. 1-36.

Research output: Contribution to journalArticle

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