The construction of exact multipolar equilibria of the two-dimensional Euler equations
The construction of exact multipolar equilibria of the two-dimensional Euler equations
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二维欧拉方程精确多极平衡的构造
DOI：
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发表时间：
2002
期刊：
影响因子：
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通讯作者：
D. Crowdy
中科院分区：
文献类型：
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作者：
D. Crowdy
利用解析曲线的Schwarz函数的思想，构造了一类新的二维欧拉方程的精确多极平衡，其特征是一个环形涡量区包围着一个非旋转流体区。结果推广了最近导出的一类多极涡旋平衡的精确解[Crowdy， Phys]。流体11,2556(1999)]。这些解与等涡度不稳定环空的多涡非线性饱和状态有许多质的相似之处。更一般地说，结果表明了构建稳定欧拉方程的多极平衡的可能性，这些平衡具有或多或少任意几何复杂性的分布旋涡区域。
Using ideas involving the Schwarz function of analytic curves, a new class of exact multipolar equilibria of the two-dimensional Euler equations characterized by an annular region of vorticity enclosing a region of irrotational fluid is constructed. The results generalize a recently derived class of exact solutions for multipolar vortex equilibria [Crowdy, Phys. Fluids 11, 2556 (1999)]. The solutions have many qualitative similarities to the multiple-vortex nonlinear saturation states of an unstable annulus of uniform vorticity. More generally, the results suggest the possibility of constructing multipolar equilibria of the steady Euler equations having distributed vortical regions of more or less arbitrary geometrical complexity.