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 -