Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow
Instability of the Hocking-Stewartson pulse and its implications for three-dimensional Poiseuille flow
复制标题
霍金-斯图尔森脉冲的不稳定性及其对三维泊肃叶流的影响
DOI：
10.1098/rspa.2000.0665
复制
发表时间：
2001
期刊：
影响因子：
--
通讯作者：
T. Bridges
中科院分区：
文献类型：
--
作者：
A. Afendikov;T. Bridges
通过线性化复Ginzburg-朗道（cGL）方程得到的Hocking-Stewartson脉冲的线性稳定性问题用Evans函数表示，Evans函数是一个复解析函数，其零点对应于稳定性指数。本文提出了一种基于复合矩阵法的Evans函数的数值计算方法。利用cGL方程中与平面Poiffille流的展向调制相关的值，我们证明了与中性曲线沿着点相关的Hocking-Stewartson脉冲由于真实的正特征值而总是线性不稳定的。本文还讨论了平行板间非线性Poisonille问题展向结构的意义。
The linear stability problem for the Hocking‐Stewartson pulse, obtained by linearizing the complex Ginzburg‐Landau (cGL) equation, is formulated in terms of the Evans function, a complex analytic function whose zeros correspond to stability exponents. A numerical algorithm based on the compound matrix method is developed for computing the Evans function. Using values in the cGL equation associated with spanwise modulation of plane Poiseuille flow, we show that the Hocking‐Stewartson pulse associated with points along the neutral curve is always linearly unstable due to a real positive eigenvalue. Implications for the spanwise structure of nonlinear Poiseuille problem between parallel plates are also discussed.