How do singularities move in potential flow?
How do singularities move in potential flow?
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DOI：
10.1016/j.physd.2011.06.010
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发表时间：
2011-10-01
影响因子：
4
通讯作者：
Smith, Stefan G. Llewellyn
中科院分区：
文献类型：
--
作者：
Smith, Stefan G. Llewellyn
不可压缩流中点涡的运动方程可以追溯到基尔霍夫。它们是将无限维动力系统即不可压缩欧拉方程简化为有限维系统的范例，被称为“经典应用数学游乐场”。点涡的运动方程可以看作是在计算点涡的速度时，去掉由点涡引起的序次奇点而得到点涡的平移速度的表述。本文回顾了用于获得这一结果的方法，以及它们的历史和局限性。然后提出了一个可以推广到研究高奇点（如偶极子）运动的公式。还讨论了对更复杂的物理情况的扩展。(C) 2011 Elsevier B.V.版权所有
The equations of motion of point vortices embedded in incompressible flow go back to Kirchhoff. They are a paradigm of reduction of an infinite-dimensional dynamical system, namely the incompressible Euler equation, to a finite-dimensional system, and have been called a "classical applied mathematical playground". The equation of motion for a point vortex can be viewed as the statement that the translational velocity of the point vortex is obtained by removing the leading-order singularity due to the point vortex when computing its velocity. The approaches used to obtain this result are reviewed, along with their history and limitations. A formulation that can be extended to study the motion of higher singularities (e.g. dipoles) is then presented. Extensions to more complex physical situations are also discussed. (C) 2011 Elsevier B.V. All rights reserved.