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数学与物理
理论数学
Vol. 14 No. 5 (May 2024)
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圆环中2-点涡的可积运动
Integrable Motion of Two-Vortexin Annulus
DOI:
10.12677/pm.2024.145184
,
PDF
,
,
,
被引量
下载: 40
浏览: 67
作者:
焦星月
,
郭 童
,
倪尔东
:中国石油大学(北京)理学院,北京
关键词:
点涡
;
哈密顿系统
;
可积性
;
作用-角变量
;
相对均衡解
;
Point Vortex
;
Hamiltonian System
;
Integrability
;
Action-Angle
;
Quasi-Equilibrium Solutions
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.
文章引用:
焦星月, 郭童, 倪尔东. 圆环中2-点涡的可积运动[J]. 理论数学, 2024, 14(5): 269-280.
https://doi.org/10.12677/pm.2024.145184
参考文献
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[2]
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https://doi.org/10.1073/pnas.27.12.575
[3]
Thomson, J.J.S. (1968) A Treatise on the Motion of Vortex Rings: An Essay to Which the Adams Prize Was Adjudged in 1882, in the University of Cambridge. Dawsons of Pall Mall, London.
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[7]
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Bolsinov, A.V., et al. (2010) Topology and Stability of Integrable Systems. Russian Mathematical Surveys, 65, 259-318.
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戴芋慧, 晋榕榕, 毛玉兰. 圆盘中2-点涡的可积运动[J]. 北京师范大学学报(自然科学 版), 2019, 55(2): 179-184.
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