TY - JOUR

T1 - Non-cartesian, topography-based avalanche equations and approximations of gravity driven flows of ideal and viscous fluids

AU - Luca, I.

AU - Tai, Y. C.

AU - Kuo, C. Y.

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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.

AB - 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.

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U2 - 10.1142/S0218202509003371

DO - 10.1142/S0218202509003371

M3 - Article

AN - SCOPUS:64549099728

VL - 19

SP - 127

EP - 171

JO - Mathematical Models and Methods in Applied Sciences

JF - Mathematical Models and Methods in Applied Sciences

SN - 0218-2025

IS - 1

ER -