Geodesic
Propagation of perturbations in a thin layer of a fluid with viscosity stratification
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 38-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a non-linear system of equations describing motion of a viscosity-layered fluid with a free surface in a long-wave approximation. In a semi-Lagrangian coordinate system we rewrite the governing equations in a integro-differencial form for which the necessary and sufficient hyperbolicity conditions are stated. An approximation for the integro-differential model in a form of finite-dimensional system of differential conservation laws with a right part is suggested. A modeling of propagation of nonlinear perturbations in a fluid with viscosity stratification was performed. In particular a problem about the evolution of a more viscous fluid column in a less viscous fluid during the passage of wave disturbances is considered.
Keywords: long waves, layered flows, integro-differential equations.
Mots-clés : viscous fluid 
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P. V. Kovtunenko. Propagation of perturbations in a thin layer of a fluid with viscosity stratification. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 15 (2015) no. 2, pp. 38-50. http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a2/

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