Short-wavelength stability analysis of thin vortex rings
Short-wavelength stability analysis of thin vortex rings
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DOI：
10.1063/1.1606446
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发表时间：
2003-09
影响因子：
4.6
通讯作者：
Y. Hattori;Y. Fukumoto
中科院分区：
文献类型：
--
作者：
Y. Hattori;Y. Fukumoto
用短波稳定性分析方法研究了薄涡环的线性稳定性。推导了考虑曲率效应的涡环修正Hill-Schrodinger方程。它用于分析评估增长率。数值计算结果表明，当芯环半径之比e较小时，生长速率与解析值吻合较好。两种类型的涡环被认为是：开尔文涡环和高斯涡环。对于Kelvin涡环，最大一级增长率为165256 e。对于高斯涡环，一阶增长率在涡核边缘较大。一阶不稳定性是显着的两个涡环。
The linear stability of thin vortex rings are studied by short-wavelength stability analysis. The modified Hill–Schrodinger equation for vortex rings, which incorporates curvature effect, is derived. It is used to evaluate growth rates analytically. The growth rates are also evaluated by numerical calculation and they agree well with analytical values for small e which is the ratio of core radius to ring radius. Two types of vortex rings are considered: Kelvin’s vortex ring and a Gaussian vortex ring. For Kelvin’s vortex ring the maximum first-order growth rate is found to be 165256e. For the Gaussian vortex ring the first-order growth rate is large in the skirts of the vortex core. The first-order instability is significant for both vortex rings.