RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PERSONAL OFFICE
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Regul. Chaotic Dyn.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Regul. Chaotic Dyn., 2017, Volume 22, Issue 8, Pages 893–908 (Mi rcd298)  

This article is cited in 4 scientific papers (total in 4 papers)

Dynamics of Two Point Vortices in an External Compressible Shear Flow

Evgeny V. Vetchanina, Ivan S. Mamaevab

a Udmurt State University, ul. Universitetskaya 1, Izhevsk, 426034 Russia
b Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, 426069 Russia

Abstract: This paper is concerned with a system of equations that describes the motion of two point vortices in a flow possessing constant uniform vorticity and perturbed by an acoustic wave. The system is shown to have both regular and chaotic regimes of motion. In addition, simple and chaotic attractors are found in the system. Attention is given to bifurcations of fixed points of a Poincaré map which lead to the appearance of these regimes. It is shown that, in the case where the total vortex strength changes, the reversible pitch-fork bifurcation is a typical scenario of emergence of asymptotically stable fixed and periodic points. As a result of this bifurcation, a saddle point, a stable and an unstable point of the same period emerge from an elliptic point of some period. By constructing and analyzing charts of dynamical regimes and bifurcation diagrams we show that a cascade of period-doubling bifurcations is a typical scenario of transition to chaos in the system under consideration.

Keywords: point vortices, shear flow, perturbation by an acoustic wave, bifurcations, reversible pitch-fork, period doubling

Funding Agency Grant Number
Russian Science Foundation 15-12-20035
Ministry of Education and Science of the Russian Federation 1.2405.2017/4.6
Russian Foundation for Basic Research 15-38-20879 mol_a_ved
The work of E.V.Vetchanin (Sections 4, 5 and 6) was supported by RSF grant 15-12-20035. The work of I.S.Mamaev (Introduction and Sections 1, 2 and 3) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2405.2017/4.6) and supported by RFBR grant 15-38-20879 mol_a_ved.


DOI: https://doi.org/10.1134/S1560354717080019

References: PDF file   HTML file

Bibliographic databases:

Document Type: Article
MSC: 76B47
Received: 12.12.2016
Language: English

Citation: Evgeny V. Vetchanin, Ivan S. Mamaev, “Dynamics of Two Point Vortices in an External Compressible Shear Flow”, Regul. Chaotic Dyn., 22:8 (2017), 893–908

Citation in format AMSBIB
\Bibitem{VetMam17}
\by Evgeny V. Vetchanin, Ivan S. Mamaev
\paper Dynamics of Two Point Vortices in an External Compressible Shear Flow
\jour Regul. Chaotic Dyn.
\yr 2017
\vol 22
\issue 8
\pages 893--908
\mathnet{http://mi.mathnet.ru/rcd298}
\crossref{https://doi.org/10.1134/S1560354717080019}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000425981500001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85042480563}


Linking options:
  • http://mi.mathnet.ru/eng/rcd298
  • http://mi.mathnet.ru/eng/rcd/v22/i8/p893

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Alexey V. Borisov, Ivan S. Mamaev, Eugeny V. Vetchanin, “Dynamics of a Smooth Profile in a Medium with Friction in the Presence of Parametric Excitation”, Regul. Chaotic Dyn., 23:4 (2018), 480–502  mathnet  crossref  mathscinet
    2. Alexey V. Borisov, Ivan S. Mamaev, Ivan A. Bizyaev, “Three Vortices in Spaces of Constant Curvature: Reduction, Poisson Geometry, and Stability”, Regul. Chaotic Dyn., 23:5 (2018), 613–636  mathnet  crossref
    3. Alexey V. Borisov, Ivan S. Mamaev, Evgeny V. Vetchanin, “Self-propulsion of a Smooth Body in a Viscous Fluid Under Periodic Oscillations of a Rotor and Circulation”, Regul. Chaotic Dyn., 23:7-8 (2018), 850–874  mathnet  crossref
    4. Ivan S. Mamaev, Evgeny V. Vetchanin, “The Self-propulsion of a Foil with a Sharp Edge in a Viscous Fluid Under the Action of a Periodically Oscillating Rotor”, Regul. Chaotic Dyn., 23:7-8 (2018), 875–886  mathnet  crossref
  • Number of views:
    This page:45
    References:16

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019