Ideal vortex motion in two dimensions: Symmetries and conservation laws
Ideal vortex motion in two dimensions: Symmetries and conservation laws
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二维理想涡运动：对称性和守恒定律
DOI：
10.1063/1.523897
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发表时间：
1978
影响因子：
1.3
通讯作者：
D. Chapman
中科院分区：
文献类型：
--
作者：
D. Chapman
二维理想流体中涡旋系统运动的每一个守恒定律都与系统的一个对称变换唯一相关，其中一个对称变换可以是尺度变换。在没有边界的无限流体的情况下，五种对称变换是：（a）两个独立的空间平移，（B）空间旋转，（c）时间平移，（d）尺度变换t′ = e 2 ηt，z′k=eηzk，其中η是真实的，zk是涡旋在z平面上的位置。研究了两种约化对称性的情况：上半平面和单位圆的内部。
Each of the conservation laws of the motion of a system of vortices in a two‐dimensional ideal fluid are shown to be uniquely associated with one of the symmetry transformations of the system, one of which can be a scale transformation. In the case of an infinite fluid with no boundaries the five symmetry transformations are: (a) two independent translations in space, (b) spatial rotations, (c) translation in time, and (d) the scale transformation t′ =e2ηt, z′k=eηzk, where η is real and zk are the positions of the vortices in the z plane. Two cases of reduced symmetry are examined: the upper half‐plane and the interior of the unit circle.