圆环中2-点涡的可积运动

Integrable Motion of Two-Vortexin Annulus

摘要: 本文运用镜像法得到了圆环区域上 Dirichlet 边值拉普拉斯算子的格林函数和两点涡系统的哈密顿函数，并用作用-角变量方法对系统进行约化。 以两点涡强度相等为例，对圆环分别在内外半径比q = 0.02, q = 0.08, q = 0.2 时得到了以涡度矩 I 为参数的系统相对均衡解的完整分类，最后针对 各种情况刻画出两个点涡的相对运动轨迹。

Abstract: In this paper, the Green's function of the Dirichlet marginal Laplace operator and the Hamiltonian function of the two-point vortex system in annular domain are obtained by the method of image, we make reduction to the system by action-angle variables method, and take the example of the equal strength case to describe their relative motion trajectories and classify the system's quasi-equilibrium solutions were obtained by considering the circular ring at different inner-to-outer radius ratios:q = 0:02, q = 0:08 and q = 0:2, with the vorticity moment I as a parameter.