Abstract
We have investigated the two-dimensional periodic flow of a viscous incompressible fluid in the Stokes approximation inside a rectangular cavity, which is driven by motion of the top and bottom boundaries. We have obtained the analytical solution of this problem by the improved reduction method for a given distribution of the velocities of motion of the boundaries. We have detected the existence of three periodic points in the flow that generate the chaotic motion of a selected passive fluid. The origin of topological chaos in the Stokes flow without stirrers placed inside the cavity has been shown.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 54, No. 3, pp. 87–98, July–September, 2011.
The article has been retracted by the author A. A. Gourjii. It has been found to contain substantial material that was already published in M.A. Stremler and J. Chen (2007) Generating topological chaos in lid-driven cavity flow, Physics of Fluids 19, 103602 (http://dx.doi.org/10.1063/1.2772881) as well as from a Virginia Tech doctoral dissertation: J. Chen (2008) Topological chaos and mixing in lid-driven cavities and rectangular channels, Ph.D. Thesis, Virginia Tech, 203 pp. (available at http://scholar.lib.vt.edu/theses/available/etd-12012008-120110/unrestricted/dissertation.pdf).
An erratum to this article is available at http://dx.doi.org/10.1007/s10958-014-1898-8.
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Meleshko, V.V., Kurylko, O.B. & Gourjii, A.A. RETRACTED ARTICLE: Generation of topological chaos in the stokes flow in a rectangular cavity. J Math Sci 185, 858–871 (2012). https://doi.org/10.1007/s10958-012-0968-z
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DOI: https://doi.org/10.1007/s10958-012-0968-z