The motion of vortices in a two-dimensional bounded region
P.I. Geshev1,2, A.I. Chernykh1,3
1Novosibirsk State University, Novosibirsk, Russia
2Kutateladze Institute of Thermophysics SB RAS, Novosibirsk, Russia
3Institute of Automation and Electrometry SB RAS, Novosibirsk, Russia
E-mail: geshev@itp.nsc.ru
Keywords: ideal fluid, point vortex, Hamiltonian, exact integration, stochastic trajectories
Pages: 809–822
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 supposed reason for stochasticity is the walk of the phase point over a homoclinic structure.
|
