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Eigenvalue problems modelling the stability of a plane-parallel shear in a two-layer viscous composite

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Abstract

We present the derivation of a precise statement of a linearized eigenvalue problem that models the stability of a plane-parallel shear flow in a composite consisting of two different layers of heavy Newtonian media. The peculiarities of the influence on the stability of five dimensionless criteria participating in the equations and boundary conditions are discussed. The specific feature of the power conditions of contact is that a spectral parameter α enters these conditions nonlinearly.

As applied to the composite structure, we develop the apparatus of integral relations, which makes it possible to derive the lower integral bounds for the stability parameter (the real part of α), and hence also upper bounds of combinations of critical numbers.

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Authors and Affiliations

  1. Department of Mechanics and Mathematics, Moscow State University, Moscow, 119991, Russia

    D. V. Georgievskii & A. S. Semenov

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  1. D. V. Georgievskii
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  2. A. S. Semenov
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Georgievskii, D.V., Semenov, A.S. Eigenvalue problems modelling the stability of a plane-parallel shear in a two-layer viscous composite. Russ. J. Math. Phys. 19, 461–468 (2012). https://doi.org/10.1134/S1061920812040061

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  • DOI: https://doi.org/10.1134/S1061920812040061

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