Stability of periodic arrays of vortices
Stability of periodic arrays of vortices
复制标题
周期性涡阵列的稳定性
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
L. Tuckerman
中科院分区：
文献类型：
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作者：
T. Dauxois;S. Fauve;L. Tuckerman
本文讨论了Mallier-Maslowe或Kelvin-Stuart涡旋周期阵列的稳定性。我们使用能量-卡西米尔稳定性方法推导出无粘情况下该解的非线性稳定性，该稳定性是解参数和域大小的函数。我们表现出的最大尺寸的域的涡街是稳定的。通过采用数值时间步进代码，我们计算了存在粘性和补偿强迫时Mallier-Maslowe解的线性稳定性。最后，讨论了结果，并与Tabeling等人最近在流体中进行的实验进行了比较。Lett. 3，459（1987）]。电磁驱动的反向旋转涡旋在临界电流以上是不稳定的，并且让位于同向旋转涡旋。文中还讨论了实验装置底部摩擦力的重要性。
The stability of periodic arrays of Mallier–Maslowe or Kelvin–Stuart vortices is discussed. We derive with the energy‐Casimir stability method the nonlinear stability of this solution in the inviscid case as a function of the solution parameters and of the domain size. We exhibit the maximum size of the domain for which the vortex street is stable. By adapting a numerical time‐stepping code, we calculate the linear stability of the Mallier–Maslowe solution in the presence of viscosity and compensating forcing. Finally, the results are discussed and compared to a recent experiment in fluids performed by Tabeling et al. [Europhy. Lett. 3, 459 (1987)]. Electromagnetically driven counter‐rotating vortices are unstable above a critical electric current, and give way to co‐rotating vortices. The importance of the friction at the bottom of the experimental apparatus is also discussed.