Asymptotic Study of Instability in a Three-Layer Stokes Flow with an Inhomogeneous Layer Thickness. Modeling of the Folding Process
- Authors: Pak V.V.1
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Affiliations:
- Il’ichev Pacific Oceanological Institute, Far Eastern Branch
- Issue: Vol 60, No 6 (2019)
- Pages: 1020-1030
- Section: Article
- URL: https://journals.rcsi.science/0021-8944/article/view/161669
- DOI: https://doi.org/10.1134/S0021894419060063
- ID: 161669
Cite item
Abstract
Zero-Reynolds-number instability in a three-layer Stokes flow of viscous fluid with an inhomogeneous layer thickness in a two-dimensional region with a free boundary is investigated. The method of multiple scales is applied for constructing an asymptotic expansion of the solution of the boundary-value problem for the Stokes equations. The stability of the system of first-approximation equations is analyzed using the Fourier method, and it is concluded that the most significant increase in the zero-Reynolds-number instability occurs in a region of waves whose lengths are comparable with the thickness of the middle layer. In contrast to the case of a constant layer thickness, the instability parameters are variables. The mechanism of formation of geological folds is studied.
About the authors
V. V. Pak
Il’ichev Pacific Oceanological Institute, Far Eastern Branch
Author for correspondence.
Email: pakvv@poi.dvo.ru
Russian Federation, Vladivostok, 690041