 | | Journal of Applied
Mathematics and Mechanics
Russian Academy of Sciences | | Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
(print version) |
Archive of Issues
| Total articles in the database: | | 10512 |
| In Russian (ΟΜΜ): | | 9713
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| In English (J. Appl. Math. Mech.): | | 799 |
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| << Previous article | Volume 80, Issue 3 / 2016 | Next article >> |
| 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, petrovipmech@gmail.com) |
| 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 |
| Link to Fulltext |
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