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This article is cited in 2 scientific papers (total in 2 papers)
On the Stability of a System of Two Identical Point Vortices and a Cylinder
A. V. Borisova, L. G. Kurakinbcd a Udmurt State University, Universitetskaya ul. 1, Izhevsk, 426034 Russia
b Water Problems Institute of the Russian Academy of Sciences, ul. Gubkina 3, Moscow, 119333 Russia
c Southern Mathematical Institute, Vladikavkaz Scientific Center of Russian Academy of Sciences, ul. Vatutina 53, Vladikavkaz, 362027 Russia
d Southern Federal University, Bol'shaya Sadovaya ul. 105/42, Rostov-on-Don, 344006 Russia
Abstract:
We consider the stability problem for a system of two identical point vortices and a circular cylinder located between them. The circulation around the cylinder is zero. There are two parameters in the problem: the added mass $a$ of the cylinder and $q=R^2/R_0^2$, where $R$ is the radius of the cylinder and $2R_0$ is the distance between vortices. We study the linearization matrix and the quadratic part of the Hamiltonian of the problem, find conditions of orbital stability and instability in nonlinear statement, and point out parameter domains in which linear stability holds and nonlinear analysis is required. The results for $a\to \infty $ are in agreement with the classical results for a fixed cylinder. We show that the mobility of the cylinder leads to the expansion of the stability region.
Received: March 2, 2020 Revised: March 2, 2020 Accepted: April 27, 2020
Citation:
A. V. Borisov, L. G. Kurakin, “On the Stability of a System of Two Identical Point Vortices and a Cylinder”, Selected issues of mathematics and mechanics, Collected papers. On the occasion of the 70th birthday of Academician Valery Vasil'evich Kozlov, Trudy Mat. Inst. Steklova, 310, Steklov Math. Inst., Moscow, 2020, 33–39; Proc. Steklov Inst. Math., 310 (2020), 25–31
Linking options:
https://www.mathnet.ru/eng/tm4106https://doi.org/10.4213/tm4106 https://www.mathnet.ru/eng/tm/v310/p33
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