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

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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 
@article{VNGU_2015_15_2_a2,
     author = {P. V. Kovtunenko},
     title = {Propagation of perturbations in a thin layer of a fluid with viscosity stratification},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {38--50},
     publisher = {mathdoc},
     volume = {15},
     number = {2},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2015_15_2_a2/}
}
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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/