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The motion of vortices in a two-dimensional bounded region. / Geshev, P. I.; Chernykh, A. I.

In: Thermophysics and Aeromechanics, Vol. 25, No. 6, 01.11.2018, p. 809-822.

Research output: Contribution to journal › Article › peer-review

Harvard

Geshev, PI & Chernykh, AI 2018, 'The motion of vortices in a two-dimensional bounded region', Thermophysics and Aeromechanics, vol. 25, no. 6, pp. 809-822. https://doi.org/10.1134/S0869864318060033

APA

Geshev, P. I., & Chernykh, A. I. (2018). The motion of vortices in a two-dimensional bounded region. Thermophysics and Aeromechanics, 25(6), 809-822. https://doi.org/10.1134/S0869864318060033

Vancouver

Geshev PI, Chernykh AI. The motion of vortices in a two-dimensional bounded region. Thermophysics and Aeromechanics. 2018 Nov 1;25(6):809-822. doi: 10.1134/S0869864318060033

Author

Geshev, P. I. ; Chernykh, A. I. / The motion of vortices in a two-dimensional bounded region. In: Thermophysics and Aeromechanics. 2018 ; Vol. 25, No. 6. pp. 809-822.

BibTeX

@article{20ad23327b0f4d6b8ee7d799ef22c84f,
title = "The motion of vortices in a two-dimensional bounded region",
abstract = "The Hamiltonian equations of the motion of a system of N ideal point vortices in a simply connected two-dimensional region have been obtained by the methods of the theory of functions of a complex variable. It is shown that the motion of two vortices in a circle is integrated exactly; the periods of this motion have been determined. The motion of two vortices in a region bounded by a lemniscate has been investigated by the method of secant planes in the phase space. The stochastic trajectories have been revealed here, which have continuous power spectra. The sup-posed reason for stochasticity is the walk of the phase point over a homoclinic structure.",
keywords = "ideal fluid, point vortex, Hamiltonian, exact integration, stochastic trajectories",
author = "Geshev, {P. I.} and Chernykh, {A. I.}",
year = "2018",
month = nov,
day = "1",
doi = "10.1134/S0869864318060033",
language = "English",
volume = "25",
pages = "809--822",
journal = "Thermophysics and Aeromechanics",
issn = "0869-8643",
publisher = "PLEIADES PUBLISHING INC",
number = "6",

}

RIS

TY - JOUR

T1 - The motion of vortices in a two-dimensional bounded region

AU - Geshev, P. I.

AU - Chernykh, A. I.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - The Hamiltonian equations of the motion of a system of N ideal point vortices in a simply connected two-dimensional region have been obtained by the methods of the theory of functions of a complex variable. It is shown that the motion of two vortices in a circle is integrated exactly; the periods of this motion have been determined. The motion of two vortices in a region bounded by a lemniscate has been investigated by the method of secant planes in the phase space. The stochastic trajectories have been revealed here, which have continuous power spectra. The sup-posed reason for stochasticity is the walk of the phase point over a homoclinic structure.

AB - The Hamiltonian equations of the motion of a system of N ideal point vortices in a simply connected two-dimensional region have been obtained by the methods of the theory of functions of a complex variable. It is shown that the motion of two vortices in a circle is integrated exactly; the periods of this motion have been determined. The motion of two vortices in a region bounded by a lemniscate has been investigated by the method of secant planes in the phase space. The stochastic trajectories have been revealed here, which have continuous power spectra. The sup-posed reason for stochasticity is the walk of the phase point over a homoclinic structure.

KW - ideal fluid

KW - point vortex

KW - Hamiltonian

KW - exact integration

KW - stochastic trajectories

UR - http://www.scopus.com/inward/record.url?scp=85062440866&partnerID=8YFLogxK

U2 - 10.1134/S0869864318060033

DO - 10.1134/S0869864318060033

M3 - Article

VL - 25

SP - 809

EP - 822

JO - Thermophysics and Aeromechanics

JF - Thermophysics and Aeromechanics

SN - 0869-8643

IS - 6

ER -

ID: 18646444