论文标题
理想2D流体中的尖涡环
Pointed vortex loops in ideal 2D fluids
论文作者
论文摘要
我们在理想的2D流体中研究了一种特殊的奇异涡度，该涡度结合了点涡流和涡流片的特征，即尖锐的涡旋环。我们专注于$ {\ mathbb r}^2 $确定的$ {\ mathbb r}^2 $的区域保护差异轨道。我们表明，极化子组由将环作为集合保存的差异形态组成，因此配置空间是围绕固定区域的环空间，而没有有关涡度分布和附加点的信息。
We study a special kind of singular vorticities in ideal 2D fluids that combine features of point vortices and vortex sheets, namely pointed vortex loops. We focus on the coadjoint orbits of the area-preserving diffeomorphism group of ${\mathbb R}^2$ determined by them. We show that a polarization subgroup consists of diffeomorphisms that preserve the loop as a set, thus the configuration space is the space of loops that enclose a fixed area, without information on vorticity distribution and attached points.
