Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles
Linear and nonlinear decay of cat's eyes in two-dimensional vortices, and the link to Landau poles
复制标题
DOI：
10.1017/s0022112007008944
复制
发表时间：
2007-11
影响因子：
3.7
通讯作者：
M. Turner;A. Gilbert
中科院分区：
文献类型：
--
作者：
M. Turner;A. Gilbert
本文考虑了旋转外部应变场作用下光滑二维涡的演化，该应变场在涡内产生循环、猫眼流线拓扑结构。当外部应变场顺利关闭时，猫眼可能会持续存在，或者随着涡旋松弛回到轴对称而消失。数值研究获得的标准的持久性的猫的眼睛作为一个功能的强度和时间尺度的施加的应变场，高斯涡旋轮廓。在一个弱的外部应变场和高雷诺数的限制，干扰指数衰减，与一个链接到一个朗道极点的线性无粘问题的速率。对于较强的应变场，但不足以强到持久的猫眼，扰动的指数衰减变化：随着时间的增加，衰减减慢，因为非线性反馈的平均轮廓的漩涡。这是通过确定这些修改后的配置文件的朗道极给出的衰减率确认。对于应变场足够强，以产生持久的猫眼，其位置和旋转速率的外部应变场的角速度的范围内确定，并再次链接到朗道极点的平均配置文件，通过非线性效应修改。
This paper considers the evolution of smooth, two-dimensional vortices subject to a rotating external strain field, which generates regions of recirculating, cat's eye stream line topology within a vortex. When the external strain field is smoothly switched off, the cat's eyes may persist, or they may disappear as the vortex relaxes back to axisymmetry. A numerical study obtains criteria for the persistence of cat's eyes as a function of the strength and time scale of the imposed strain field, for a Gaussian vortex profile. In the limit of a weak external strain field and high Reynolds number, the disturbance decays exponentially, with a rate that is linked to a Landau pole of the linear inviscid problem. For stronger strain fields, but not strong enough to give persistent cat's eyes, the exponential decay of the disturbance varies: as time increases the decay slows down, because of the nonlinear feedback on the mean profile of the vortex. This is confirmed by determining the decay rate given by the Landau pole for these modified profiles. For strain fields strong enough to generate persistent cat's eyes, their location and rotation rate are determined for a range of angular velocities of the external strain field, and are again linked to Landau poles of the mean profiles, modified through nonlinear effects.