The motion of a point vortex through gaps in walls
The motion of a point vortex through gaps in walls
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DOI：
10.1017/s0022112005008244
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发表时间：
2006-03
影响因子：
3.7
通讯作者：
D. Crowdy;Jonathan S. Marshall
中科院分区：
文献类型：
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作者：
D. Crowdy;Jonathan S. Marshall
本文提出了一种新的分析方法，用于研究由具有任意数量间隙的直壁所限定的流体区域中点涡的运动。利用多连通圆形区域中Kirchhoff-Routh路径函数的显式公式，结合从多连通圆形区域到多连通狭缝区域的共形映射的新构造，导出了多个物理上有趣的流体区域中点涡运动的控制哈密顿量.计算了几种典型情况下的涡轨迹。这些例子包括找到位于无限海岸线上的一系列岛屿周围的漩涡路径，在无限海洋中的岛屿周围以及位于两个海岬之间的一系列岛屿周围。
New analytical techniques for studying the motion of a point vortex in fluid domains bounded by straight walls having an arbitrary number of gaps are presented. By exploiting explicit formulae for the Kirchhoff–Routh path function in multiply connected circular domains, combined with a novel construction of conformal mappings from such circular domains to multiply connected slit domains, the governing Hamiltonians for the motion of a point vortex in a number of physically interesting fluid regions involving walls with gaps are derived. The vortex trajectories in several illustrative cases are computed. These examples include finding the vortex paths around a chain of islands sitting off an infinite coastline, around islands in an unbounded ocean and around a sequence of islands situated between two headlands.