Instability of Some Ideal Plane Flows
Instability of Some Ideal Plane Flows
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DOI：
10.1137/s0036141002406266
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
Zhiwu Lin
中科院分区：
文献类型：
--
作者：
Zhiwu Lin
我们证明了大类的二维欧拉方程的稳定状态的不稳定性。对于奇剪切流，从Rayleigh方程出发，定义了一类依赖于正参数的算子族。然后我们使用无穷行列式来跟踪这些算子的特征值的符号。纯增长模态的存在是由一个延续论证得出的。采用一种新的中性模式的分析与严格的理由Tollmien的经典方法，我们得到了尖锐的条件，线性，因此非线性不稳定的一般类有界剪切流。对于有界旋转流和无界剪切流，我们得到了类似的结果。
We prove the instability of large classes of steady states of the two-dimensional Euler equation. For an odd shear flow, beginning with the Rayleigh equation, we define a family of operators depending on some positive parameter. Then we use infinite determinants to keep track of the signs of the eigenvalues of these operators. The existence of purely growing modes follows from a continuation argument. Employing a new analysis of neutral modes together with a rigorous justification of Tollmien's classical method, we obtain a sharp condition for linear and hence nonlinear instability of a general class of bounded shear flows. We obtain similar results for bounded rotating flows and unbounded shear flows.