Linear stability of a vortex ring revisited
Linear stability of a vortex ring revisited
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重新审视涡环的线性稳定性
DOI：
10.1007/0-306-48420-x_6
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发表时间：
2002
期刊：
影响因子：
--
通讯作者：
Y. Hattori
中科院分区：
文献类型：
--
作者：
Y. Fukumoto;Y. Hattori
我们重新审视了椭圆应变旋涡和嵌在无粘不可压缩流体中的轴对称薄旋涡环对无限小振幅三维扰动的稳定性。Tsai & Widnall（1976）对椭圆应变涡的结果进行了简化，给出了扰动流场的显式表达式。与椭圆不稳定性建立了直接关系。对于开尔文涡旋环，朗肯涡旋的主要扰动是偶极子场。偶极子场在色散曲线交点处引起轴对称波和弯曲波之间的参数共振不稳定性。偶极子效应在极薄磁芯中占主导地位。其机理可归因于扰动涡旋线在环面方向上的拉伸。
We revisit the stability of an elliptically strained vortex and a thin axisymmetric vortex ring, embedded in an inviscid incompressible fluid, to three-dimensional disturbances of infinitesimal amplitude. The results of Tsai & Widnall (1976) for an elliptically strained vortex are simplified by providing an explicit expression for the disturbance flow field. A direct relation is established with the elliptical instability. For Kelvin’s vortex ring, the primary perturbation to the Rankine vortex is a dipole field. We show that the dipole field causes a parametric resonance instability between axisymmetric and bending waves at intersection points of the dispersion curves. It is found that the dipole effect predominates over the straining effect for a very thin core. The mechanism is attributable to stretching of the disturbance vortex lines in the toroidal direction.