Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
in January 1936
(Translated from 1958)
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IssuesArchive of Issues2016-3pp.257-263

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A.G. Petrov, "The stability of a fluid cylinder in a plane-parallel flow of an ideal fluid," J. Appl. Math. Mech. 80 (3), 257-263 (2016)
Year 2016 Volume 80 Issue 3 Pages 257-263
DOI 10.1016/j.jappmathmech.2016.08.002
Title The stability of a fluid cylinder in a plane-parallel flow of an ideal fluid
Author(s) A.G. Petrov (The Institute of Problems in Mechanics of the Russian Academy of Sciences, Moscow,
Abstract The plane problem of a steady-state potential flow of an ideal fluid around an infinite fluid cylinder with surface tension is considered. A family of solutions is constructed. An approximate relation is found between the Weber number and the ratio of the sizes of the cross-sections of the cylinder along the normal and along the free stream velocity. (A ratio of 11/2 corresponds to the exact McLeod special solution.) The problem of the stability of this flow is solved in the sense of a relaxed Lyapunov definition. For a ratio of the density of the cylinder to the density of the fluid flowing around it of less than 26.35, the flow is stable, and, for a greater value, it is unstable. The conventional Lyapunov stability is proved when the ratio of the densities is less than 11.07.
Received 21 July 2015
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