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Russian Academy of Sciences
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IssuesArchive of Issues2016-3pp.264-270

Archive of Issues

Total articles in the database: 1813
In Russian (): 1014
In English (J. Appl. Math. Mech.): 799

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Sh. A. Mukhamediev, E.I. Ryzhak and S.V. Sinyukhina, "Stability of a two-layer system of inhomogeneous heavy barotropic fluids," J. Appl. Math. Mech. 80 (3), 264-270 (2016)
Year 2016 Volume 80 Issue 3 Pages 264-270
DOI 10.1016/j.jappmathmech.2016.07.005
Title Stability of a two-layer system of inhomogeneous heavy barotropic fluids
Author(s) Sh. A. Mukhamediev (O. Schmidt Institute of Physics of the Earth of the Russian Academy of Science, Moscow, Russia)
E.I. Ryzhak (O. Schmidt Institute of Physics of the Earth of the Russian Academy of Science, Moscow, Russia, e_i_ryzhak@mail.ru)
S.V. Sinyukhina (O. Schmidt Institute of Physics of the Earth of the Russian Academy of Science, Moscow, Russia)
Abstract Basing on the static energy criterion for a bounded domain of an arbitrary shape and with regard for the boundary conditions at all parts of the boundary, the stability of a two-layer system of inhomogeneous barotropic fluids in the uniform gravity field is studied for arbitrary distributions of their densities and elastic properties over depth. Almost coinciding with each other (up to the strictness of one of the two inequalities), equally valid for an arbitrary number of layers, the necessary and sufficient conditions for stability are obtained, that represents a new exhaustive result for the problem considered. Additionally (with compressibility admitted) possible influence of viscosity (which may be anisotropic), and also the case when the layers consist of solid elastic materials, are considered. In the case of instability, the lower estimates for the greatest rate of disturbances growth are obtained.
Received 2 December 2015
Link to Fulltext http://www.sciencedirect.com/science/article/pii/S0021892816300922
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