Hollow vortices, capillary water waves and double quadrature domains
Hollow vortices, capillary water waves and double quadrature domains
复制标题
空心涡流、毛细管水波和双正交域
DOI：
--
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
J. Roenby
中科院分区：
文献类型：
--
作者：
D. Crowdy;J. Roenby
提出了空心涡旋平衡的两类新的解析解。一类涉及一个中心空心漩涡，包括一个具有非零循环的恒压区域，被n个大于等于2的点漩涡的n多边形阵列包围>。这些解推广了Morikawa和Swenson（1971）的非旋转多边形点涡构型。流体（14 1058-73）到多边形中心的点涡被空心涡取代的情况。Morikawa和Swenson的结果表明，n≠3 ？>将线性不稳定到点涡模式不稳定。然而，即使在n = 3的情况下，对于最近发现的由孤立圆形空心涡旋的自然模态之间的共振引起的位移不稳定也是不稳定的。本文还讨论了与沉点涡列共行周期水波的第二类解析解。该分析对具有表面张力的自由表面欧拉流动，特别是对毛细水波的克拉珀经典解，提出了新的理论联系。文中指出，这里发现的平衡流体区域可以用数学解释为一类抽象的平面域，即双正交域。
Two new classes of analytical solutions for hollow vortex equilibria are presented. One class involves a central hollow vortex, comprising a constant pressure region having non-zero circulation, surrounded by an n-polygonal array of point vortices with n ⩾ 2 ?> . The solutions generalize the non-rotating polygonal point vortex configurations of Morikawa and Swenson (1971 Phys. Fluids 14 1058–73) to the case where the point vortex at the centre of the polygon is replaced by a hollow vortex. The results of Morikawa and Swenson would suggest that all equilibria for n ≠ 3 ?> will be linearly unstable to point vortex mode instabilities. However even the n = 3 case turns out to be unstable to a recently discovered displacement instability deriving from a resonance between the natural modes of an isolated circular hollow vortex. A second class of analytical solutions for periodic water waves co-travelling with a submerged point vortex row is also described. The analysis gives rise to new theoretical connections with free surface Euler flows with surface tension and, in particular, with Crapperʼs classical solutions for capillary water waves. It is pointed out that the equilibrium fluid regions found here have a mathematical interpretation as an abstract class of planar domains known as double quadrature domains.
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影响因子：
3.4
作者：
Crowdy D
通讯作者：
Crowdy D
DOI：
10.1016/j.euromechflu.2012.09.007
发表时间：
2013
期刊：
European Journal of Mechanics - B/Fluids
影响因子：
--
作者：
Crowdy D
通讯作者：
Crowdy D
影响因子：
4.6
作者：
D. Crowdy
通讯作者：
D. Crowdy
空心涡平衡结构及其稳定性
影响因子：
3.7
作者：
Llewellyn Smith S
通讯作者：
Llewellyn Smith S