Equation of motion for point vortices in multiply connected circular domains
Equation of motion for point vortices in multiply connected circular domains
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DOI：
10.1098/rspa.2009.0070
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发表时间：
2009-08
期刊：
影响因子：
--
通讯作者：
T. Sakajo
中科院分区：
文献类型：
--
作者：
T. Sakajo
论文给出了单位圆内包含许多圆形障碍物（称为圆形域）的有界平面多重连通域中 N 点涡流的运动方程。点涡引起的速度场用与圆形域相关的肖特基-克莱因素数函数来描述。方程的显式表示使我们不仅能够通过点涡近似数值求解欧拉方程，而且能够研究圆形域中局域涡结构之间的相互作用。作为该方程的应用，我们考虑具有单位强度且符号相反的两个点涡的运动。当多重连通域相对于实轴对称时，两点涡旋的运动被简化为多重连通半圆中的单点涡旋的运动，我们对此进行了详细研究。
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 unit strength and of 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 semicircle, which we investigate in detail.