Widnall instabilities in vortex pairs
Widnall instabilities in vortex pairs
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涡对中的 Widnall 不稳定性
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
L. Jacquin
中科院分区：
文献类型：
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作者：
D. Sipp;L. Jacquin
本文分析了用二维直接数值模拟方法得到的集中涡偶极子上的协同三维短波不稳定性。这些偶极子的特征是它们的纵横比a/b，其中a是基于涡度极矩的涡旋半径，b是涡心之间的距离。在无粘性情况下，我们证明了反对称本征模的选择随着a/b的增加而平稳地增加：当a/b=0.208时，反对称本征模的放大率仅比对称本征模的放大率大1.4%。当a/b=0.288时，这一差异增加到7%.简正波分析的结果可以与Moore和Saffman[Proc.R.Soc.伦敦，爵士。A 346,413(1975)]。这一理论表明，当两个开尔文波相互作用时，就可能发生不稳定现象。
In this article we analyze the cooperative three-dimensional short-wave instabilities developing on concentrated vortex dipoles that have been obtained by means of two-dimensional direct numerical simulations. These dipoles are characterized by their aspect ratio a/b where a is the radius of the vortices based on the polar moments of vorticity and b is the separation between the vortex centroids. In the inviscid case, we show that the selection of the antisymmetric eigenmode smoothly increases with a/b: for a/b=0.208, the amplification rate of the antisymmetric eigenmode is only 1.4% larger than the amplification rate of the symmetric eigenmode. When a/b=0.288, this difference increases up to 7%. The results of the normal mode analysis may be compared to those of an asymptotic stability analysis of a Lamb–Oseen vortex subjected to a weak straining field, following Moore and Saffman [Proc. R. Soc. London, Ser. A 346, 413 (1975)]. This theory shows that the instability may occur whenever two Kelvin waves ex...