open access

https://hdl.handle.net/2115/43389

Equation of motion for point vortices in multiply connected circular domains

英語

Hamiltonian

2009-08-08

Royal Society

Proceedings of the Royal Society A : Mathematical, Physical & Engineering Sciences

465(2108)

2589-2611

The paper gives the equation of motion for N point vortices in a bounded planar multiply connected domain inside the unit circle that contains many circular obstacles, called the circular domain. The velocity field induced by the point vortices is described in terms of the Schottky-Klein prime function associated with the circular domain. The explicit representation of the equation enables us not only to solve the Euler equations through the point-vortex approximation numerically, but also to investigate the interactions between localized vortex structures in the circular domain. As an application of the equation, we consider the motion of two point vortices with the unit strength and of the opposite signs. When the multiply connected domain is symmetric with respect to the real axis, the motion of the two point vortices is reduced to that of a single point vortex in a multiply connected semi-circle, which we investigate in detail.

学術雑誌論文

Accepted Manuscript

1364-5021