Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction
Nonlinear evolution of two vortex sheets moving separately in uniform shear flows with opposite direction
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DOI：
10.3934/era.2022093
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发表时间：
2022
影响因子：
0.8
通讯作者：
C. Matsuoka
中科院分区：
文献类型：
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作者：
C. Matsuoka
有人认为，当存在足够强的均匀切变时，两个紧密的涡片变得不稳定并同时演化。然而，Moore(Mahematika，1976)在他的线性分析中提出，在某些条件下，一个涡片的演化就好像另一个涡片不存在一样。在本研究中，我们研究了当两个涡片满足摩尔条件时，它们是如何在非线性区域演化的。我们还考虑了密度分层，这并不包括在摩尔的分析中。摩尔的估计只在线性理论中有效，然而，当摩尔条件满足时，即使在非线性区域，摩尔提出的运动也会出现。我们发现，存在一种情况，即一个涡旋片几乎不变形，即使另一个涡旋片变得不稳定并发生很大的变形。我们还指出，当系统中存在密度不稳定性时，即使满足条件，Moore的分析也是无效的。
It has been considered that two close vortex sheets become unstable and evolve simultaneously when sufficiently strong uniform shears exist. However, Moore (Mathematika, 1976) suggested in his linear analysis that a vortex sheet evolves just as if the other vortex sheet were absent under certain conditions. In the current study, we investigate how the two vortex sheets evolve in the nonlinear region when they satisfy Moore's condition. We also consider density stratification, which is not included in Moore's analysis. Moore's estimate is only valid within linear theory; however, a motion suggested by Moore appears even in the nonlinear regime when Moore's condition is satisfied. We found that there is a case that a vortex sheet hardly deforms, even though the other sheet becomes unstable and largely deforms. We also show that there is a case that Moore's analysis is not effective even the condition is satisfied when a density instability exists in the system.